Quickest detection of a sudden change in the transmittance of an optical channel is paramount for secure and reliable communications. We show that two-mode squeezed vacuum state, pre-shared between the communicating parties, affords a significant reduction in the quickest-change detection latency compared to when no entanglement is pre-shared: either using a classical coherent-state probe or a quantum-augmented coherent-state that was recently shown to outperform a coherentstate probe. In the absence of thermal noise, the quantum relative entropy (QRE)-whose inverse quantifies the quantum-minimum change-detection latency-is infinite. Even though zero noise and hence instantaneous change detection is unphysical, we show the QRE diverges to infinity as the logarithm of the inverse of the thermal-noise mean photon number. We propose a receiver that achieves the aforesaid QRE scaling, quantify performance improvements over known schemes, and discuss the problem of quantum limits of joint communications and change detection.

We provide a complete characterization of the class of multimode quantum Gaussian states that can be reduced to a tensor product of thermal states using only a passive unitary operator. We call these states passive unitary normalizable (PUN) Gaussian states. The characterization of PUN Gaussian states is given in three different ways: ($i$) in terms of their covariance matrices, (ii) using gauge-invariance (a special class of Glauber-Sudarshan p-functions), and (iii) with respect to the recently obtained$(A,\ \Lambda)$parametrization of Gaussian states in [J. Math. Phys. 62, 022102 (2021)]. In terms of the covariance matrix, our characterization states that an n-mode quantum Gaussian state is PUN if and only if its$2n\times 2n$quantum covariance matrix$S_{\mathrm{T}\mathfrak{i}}$is skew-Hamiltonian, i.e., it commutes with the standard symplectic matrix,$\left[\begin{array}{cc} 0 & I_n \\ -I_n & 0 \end{array}\right]$, with$I_{n}$being the$nxn$identity matrix. It is well-known that the so-called gauge-invariant Gaussian states are PUN, but whether the converse is true is not known in the literature to the best of our knowledge. We establish the converse in affirmation. Lastly, in terms of the$(A,\ \Lambda)$-parameterization, we show that a Gaussian state with parameters$(A,\ \Lambda)$is PUN if and only if$A=0$

We study a linear computation problem over a quantum multiple access channel (LC-QMAC), where S servers share an entangled state and separately store classical data streams W1,⋯,WSover a finite field ${\mathbb{F}_d}$. A user aims to compute K linear combinations of these data streams, represented as $Y = {{\mathbf{V}}_1}{W_1} + {{\mathbf{V}}_2}{W_2} + \cdot s + {{\mathbf{V}}_S}{W_S} \in \mathbb{F}_d^{K \times 1}$. To this end, each server encodes its classical information into its local quantum subsystem and transmits it to the user, who retrieves the desired computations via quantum measurements. In this work, we propose an achievable scheme for LC-QMAC based on the stabilizer formalism and the ideas from entanglement-assisted quantum error–correcting codes (EAQECC). Specifically, given any linear computation matrix, we construct a self-orthogonal matrix that can be implemented using the stabilizer formalism. Also, we apply precoding matrices to minimize the number of auxiliary qudits required. Our scheme achieves more computations per qudit, i.e., a higher computation rate, compared to the best-known methods in the literature, and attains the capacity in certain cases.

We investigate covert communication over general memoryless classical-quantum channels with fixed finite-size input alphabets. We show that the square root law (SRL) governs covert communication in this setting when product a ofninput states is used:$L_{\mathrm { SRL}}\sqrt {n}+o(\sqrt {n})$covert bits (but no more) can be reliably transmitted innuses of classical-quantum channel, where$L_{\mathrm { SRL}}\gt 0$is a channel-dependent constant that we callcovert capacity. We also show that ensuring covertness requires$J_{\mathrm { SRL}}\sqrt {n}+o(\sqrt {n})$bits secret key shared by the communicating parties prior to transmission, where$J_{\mathrm { SRL}}\geq 0$is a channel-dependent constant. We assume a quantum-powerful adversary that can perform an arbitrary joint (entangling) measurement on allnchannel uses. We determine the single-letter expressions for$L_{\mathrm { SRL}}$and$J_{\mathrm { SRL}}$, and establish conditions when$J_{\mathrm { SRL}}=0$(i.e., no pre-shared secret key is needed). Finally, we evaluate scenarios where covert communication is not governed by the SRL.

Optical pulse position modulation (PPM) places a laser pulse, a.k.a. a coherent state of amplitude$\alpha$of mean photon number$N=\vert \alpha\vert ^{2}$, in one of$M$consecutive time slots, Ideal photon detection on each slot achieves a mean probability of error$((M-1)/1M)e^{-N}$of distinguishing the$iM$PPM codewords, since$e^{-N}$is the probability the pulse-containing slot does not produce a click, per Poisson-shot-noise photo-detection theory. The quantum (Helstrom) limit of the minimum probability of error is lower than above, has a closed-form expression, and scales as$\sim e^{-2N}$when$Me^{-N}\ll 1$. The optimal receiver must make a quantum joint measurement on all$M$slots. Even though receiver algorithms exist that achieve the$\sim e^{-2N}$scaling in the high$N$regime, none are known that bridge the classical-quantum gap for small$N$, the primary regime of interest for optical PPM. It is also not known how close to the Helstrom limit can one get using LOCC. (local operations and classical communications), i.e., a receiver that slices each of the$M$slots into$n$tiny slices, makes a measurement on the first slice, and based on the measurement result picks a measurement to apply to the next slice, etc., until all the$Mn$slices have been measured. In this paper, we propose an LOCC receiver for demodulating PPM that uses semiclassical coherent feedback control and photon detection, which outperforms all known PPM receivers, including one that employed squeezing, a non-classical operation. To bridge the remaining gap to the Helstrom limit, one might need truly quantum operations within a joint (non-LOCC) receiver.

Quantum illumination (QI) is the task of querying a scene using a transmitter probe whose quantum state is entangled with a reference beam retained in ideal storage, followed by optimally detecting the target-returned light together with the stored reference, to make decisions on characteristics of targets at stand-off range, at precision that exceeds what is achievable with a classical transmitter of the same brightness and otherwise identical conditions. Using tools from perturbation theory, we show that in the limit of low transmitter brightness, high loss, and high thermal background, there is a factor of four improvement in the Chernoff exponent of the error probability in discriminating any number of apriori-known reflective targets when using a Gaussian-state entangled QI probe, over using classical coherent-state illumination (CI). While this advantage was known for detecting the presence or absence of a target, it had not been proven for the generalized task of discriminating between arbitrary target libraries. In proving our result, we derive simple general analytic expressions for the lowest-order asymptotic expansions of the quantum Chernoff exponents for QI and CI in terms of the signal brightness, loss, thermal noise, and the modal expansion coefficients of the target-reflected light's radiant exitance profiles when separated by a spatial mode sorter after entering the entrance pupil of the receiver's aperture.

Stabilizer states are a prime resource for a number of applications in quantum information science, such as secret-sharing and measurement-based quantum computation. This motivates us to study the entanglement of noisy stabilizer states across a bipartition. We show that the spectra of the corresponding reduced states can be expressed in terms of properties of an associated stabilizer code. In particular, this allows us to show that the coherent information is related to the so-called syndrome entropy of the underlying code. We use this viewpoint to find stabilizer states that are resilient against noise, allowing for more robust entanglement distribution in near-term quantum networks. We specialize our results to the case of graph states, where the found connections with stabilizer codes reduces back to classical linear codes for dephasing noise. On our way we provide an alternative proof of the fact that every qubit stabilizer code is equivalent up to single-qubit Clifford gates to a graph code.

We consider sequential hypothesis testing among multiple samples of one among$M$pure quantum states in an equidistant ensemble, i.e., those with identical pair-wise inner products. Each measurement in the sequence is a binary projective measurement that collapses the sample of the state measured at that instant into a linear span of a collection of states from the ensemble or its orthogonal complement. The algorithm adaptively decides if additional samples are needed or sufficient observation has been gathered. We show that our sequential measurement algorithm outperforms the sequential testing (ST) receiver, whose error-probability exponent is known to achieve the quantum Chernoff bound asymptotically in the limit of large (and fixed) number of samples. Even though our algorithm does not attain the quantum limit of minimum error probability (the Helstrom limit), it paves the way for future research on more advanced sequential quantum hypothesis tests, e.g., those that go beyond binary projective measurements on each sample.

We study the problem of operating a quantum switch with memory constraints. In particular, the switch has to allocate quantum memories to clients to generate link-level entanglements (LLEs), and then use these to serve end-to-end entanglements requests. The paper’s main contributions are (i) to characterize the switch’s capacity region and study how it scales with respect to the number of quantum memories and probability of successful LLEs and (ii) to propose a memory allocation policy that is throughput optimal. In addition, when the requests are bipartite and the LLE attempts are always successful, we show that the proposed policy has polynomial time complexity. We evaluate the proposed policy numerically and illustrate its performance depending on the requests arrivals characteristics and the time available to obtain a memory allocation.

We report a lowest-order Taylor-like series expansion that enables efficient analytical computation of primary matrix functions of perturbed quantum states whose perturbation preserves the vector support of the original state. We apply our theory to find simple expressions for four important quantities in quantum information theory: the von Neumann entropy, the quantum relative entropy, the quantum Chernoff bound, and the quantum fidelity. Our results, which we elegantly represent using Fréchet derivatives, require only knowledge of the eigenspectrum of the unperturbed state and the density matrix elements of the perturbation, bypassing eigenanalysis of the full perturbed state. These results were recently used to derive the fundamental quantum limits of identifying diffraction-limited objects in passive incoherent imaging [1] and in an approach to quantify the covert communications capacity of a bosonic channel [2]. We discuss other avenues where our results could be applied.

We develop the capacity region for the bosonic broadcast channel in the presence of thermal noise and photon loss due to the environment. The bosonic channel is a quantum-mechanical description of many practical communication links such as optical, microwave, and radiofrequency. We employ our results to find the capacity region for quantum-secure covert broadcast over such channels and show that time-division is optimal as in the classical covert broadcast scenario. We rely on a strong minimum entropy output conjecture, a direct result of the entropy photon-number inequality (EPnI) conjecture.

We consider the problem of estimating unknown loss η over$n$uses of single-mode lossy thermal noise bosonic channel under an average photon number constraint per mode. We prove that a product of$n$two-mode squeezed vacuum (TMSV) states achieves minimal quantum Cramér-Rao bound (QCRB) over Gaussian quantum states in this scenario, and characterize the optimal receiver structure. We show that TMSV minimizes QCRB over all quantum states in the limit of low input photon number. Finally, we compare the performance of our optimal receiver for TMSV to other receivers.

We solve the entanglement-assisted (EA) classical capacity region of quantum multiple-access channels with an arbitrary number of senders, which is conjectured by Hsieh, Devetak and Winter. As an example, we consider the bosonic thermal-loss multiple-access channel and solve the rate region enabled by an entanglement source composed of sender-receiver pairwise two-mode squeezed vacuum states. The EA rate region is strictly larger than the capacity region without entanglement-assistance, therefore also larger than the Yen-Shapiro rate-region of Gaussian encoding or coherent-state encoding. When the senders have equal low brightness, we also numerically find that the two-mode squeezed vacuum source is optimal at a corner rate point. With two-mode squeezed vacuum states as the source and phase modulation as the encoding, we also design practical receiver protocols to realize the entanglement advantages. In the parameter region of a large noise background, the receivers can enable a simultaneous rate advantage of 82.0% for each sender with binary phase-shift keying. Due to teleportation and superdense coding, our results for EA classical communication can be directly extended to EA quantum communication at half of the rates.

Motivated by application to quantum radar and the known benefits of quantum illumination in the high-noise low-reflectance regime, we study the design of signaling schemes for covertly probing a distant target over a lossy and noisy bosonic channel. Specifically, we analyze the performance of diffuse and sparse signaling schemes, which achieve covertness by spreading a constant number of photons in many modes or in a few modes, respectively. We benchmark the performance against a converse bound that holds for arbitrary covert quantum illumination schemes. Numerical results suggest the superior performance of the diffuse signaling scheme, which we conjecture outperforms any other covert quantum illumination scheme.

Pre-shared entanglement can significantly boost communication rates in the regime of high thermal noise, and a low-brightness transmitter. In this regime, the ratio between the entanglement-assisted capacity and the Holevo capacity, the maximum reliable-communication rate permitted by quantum mechanics without any pre-shared entanglement as a resource, is known to scale as log(1/N̅S), where N̅S≪ 1 is the mean transmitted photon number per mode. This is especially promising in enabling a large boost to radio-frequency communications in the weak-transmit-power regime, by exploiting pre-shared optical-frequency entanglement, e.g., distributed by the quantum internet. In this paper, we propose a structured design of a quantum transmitter and receiver that leverages continuous-variable pre-shared entanglement from a downconversion source, which can harness this purported infinite-fold capacity enhancement- a problem that has been open for over a decade. Its implication to the breaking of the well-known square root law for covert communications, with entanglement assistance, is discussed.

Quantum technologies are maturing by the day and their near-term applications are now of great interest. Deep-space optical communication involves transmission over the pure-state classical-quantum channel. For optimal detection, a joint measurement on all output qubits is required in general. Since this is hard to realize, current (sub-optimal) schemes perform symbol-by-symbol detection followed by classical post-processing. In this paper we focus on a recently proposed belief propagation algorithm by Renes that passes qubit messages on the factor graph of a classical error-correcting code. More importantly, it only involves single-qubit Pauli measurements during the process. For an example 5-bit code, we analyze the involved density matrices and calculate the error probabilities on this channel. Then we numerically compute the optimal joint detection limit using the Yuen-Kennedy-Lax conditions and demonstrate that the calculated error probabilities for this algorithm appear to achieve this limit. This represents a first step towards achieveing quantum communication advantage. We verify our analysis using Monte-Carlo simulations in practice.

Quantum cryptography provides absolute security against an all-powerful eavesdropper (Eve). However, in practice Eve's resources may be restricted to a limited aperture size so that she cannot collect all paraxial light without alerting the communicating parties (Alice and Bob). In this paper we study a quantum wiretap channel in which the connection from Alice to Eve is lossy, so that some of the transmitted quantum information is inaccessible to both Bob and Eve. For a pureloss channel under such restricted eavesdropping, we show that the key rates achievable with a two-mode squeezed vacuum state, heterodyne detection, and public classical communication assistance-given by the Hashing inequality-can exceed the secret key distillation capacity of the channel against an omnipotent eavesdropper. We report upper bounds on the key rates under the restricted eavesdropping model based on the relative entropy of entanglement, which closely match the achievable rates. For the pure-loss channel under restricted eavesdropping, we compare the secret-key rates of continuous-variable (CV) quantum key distribution (QKD) based on Gaussian-modulated coherent states and heterodyne detection with the discrete variable (DV) decoystate BB84 QKD protocol based on polarization qubits encoded in weak coherent laser pulses.

Cryptographic protocols often involve the assistance of public side channels to which all parties have perfectly noiseless access. For instance, in the BB84 quantum key distribution protocol, the side channel is used to share the bases in which Alice and Bob encoded or measured their qubits. In this paper, we find that in the case of continuous variable communication, by slightly altering this model such that Eve's copy of the initial round of feedback is corrupted by an iota of noise while keeping Alice's copies noiseless, the capacity can be increased dramatically. Specifically, it is known that the private capacity with noiseless feedback for a pure-loss bosonic channel is at most -log(1-η) bits per mode, where η is the transmissivity, in the limit of infinite input photon number. This is a very pessimistic result as there is a finite rate limit even with an arbitrarily large number of input photons. We refer to this as a loss limited rate. However, in our altered model we find that we can achieve a rate of (1/2) log(1+4ηNS) bits per mode with weak security, where NS is the input photon number. This rate diverges with NS, in sharp contrast to the result for the original model. This suggests that physical considerations behind the eavesdropping model should be taken more seriously, as they can create strong dependencies of the achievable rates on the model. For by a seemingly inconsequential weakening of Eve, we obtain a loss-unlimited rate. Our protocol also works verbatim for arbitrary i.i d, noise (not even necessarily Gaussian) injected by Eve in every round, and even if Eve is given access to copies of the initial transmission and noise. The error probability of the protocol decays super-exponentially with the blocklength.

In covert communication, Alice tries to communicate with Bob without being detected by a warden Willie. When the distance between Alice and Bob becomes large compared with the distance between Alice and Willie(s), the performance of covert communication will be degraded. In this case, multi-hop message transmission via intermediate relays can help to improve the performance. Hence, in this paper, multi-hop covert communication over a moderate size network and in the presence of multiple collaborating Willies is considered. The relays can transmit covertly using either a single key for all relays or different independent keys at the relays. For each case, we develop efficient algorithms to find optimal paths with maximum throughput and minimum end-to-end delay between Alice and Bob. As expected, employing multiple hops significantly improves the ability to communicate covertly versus the case of a single-hop transmission. Furthermore, at the expense of more shared key bits, analytical results and numerical simulations demonstrate that the multi-hop covert communication with different independent keys at the relays has better performance than the multi-hop covert communication with a single key.

Covert communication conceals the transmission of the message from an attentive adversary. Recent work on the limits of covert communication in additive white Gaussian noise channels has demonstrated that a covert transmitter (Alice) can reliably transmit a maximum of O(√n) bits to a covert receiver (Bob) without being detected by an adversary (Warden Willie) in n channel uses. This paper focuses on the scenario where other “friendly” nodes distributed according to a two-dimensional Poisson point process with density m are present. We propose a strategy where the friendly node closest to the adversary, without close coordination with Alice, produces artificial noise. We show that this method allows Alice to reliably and covertly send O(min{n, mγ/2√n}) bits to Bob in n channel uses, where γ is the path-loss exponent. We also consider a setting where there are Nw collaborating adversaries uniformly and randomly located in the environment and show that in n channel uses, Alice can reliably and covertly send O(min{n, (mγ/2√n/Nwγ)}) bits to Bob when γ>2, and O(min{n, (m√n/Nw2log2Nw)}) when γ=2. Conversely, we demonstrate that no higher covert throughput is possible for γ>2.

We present a square root law for active sensing of phase θ of a single pixel using optical probes that pass through a single-mode lossy thermal-noise bosonic channel. Specifically, we show that, when the sensor uses an n-mode covert optical probe, the mean squared error (MSE) of the resulting estimator θnscales as 〈(θ-θ̂n)2〉 = O(1/√n) improving the scaling necessarily leads to detection by the adversary with high probability. We fully characterize this limit and show that it is achievable using laser light illumination and a heterodyne receiver, even when the adversary captures every photon that does not return to the sensor and performs arbitrarily complex measurement as permitted by the laws of quantum mechanics.

This paper shows the optimality of Pulse-Position Modulation (PPM) for covert communications over discrete-memoryless channels. Specifically, the concatenation of a random m-ary outer code of length O(m) and an inner code consisting of PPM of order m achieves the information-theoretic limits of covert communications. This suggests alternative code constructions for covert communications, in which the sparsity of the PPM symbols ensures covertness and an appropriate choice of the blocklength results in the square root law.

We discuss properties of the “beamsplitter addition” operation, which provides a non-standard scaled convolution of random variables supported on the non-negative integers. We give a simple expression for the action of beamsplitter addition using generating functions. We use this to give a self-contained and purely classical proof of a heat equation and de Bruijn identity, satisfied when one of the variables is geometric.

Recent work has established that when transmitter Alice wishes to communicate reliably to recipient Bob without detection by warden Willie, with additive white Gaussian noise (AWGN) channels between all parties, communication is limited to O(√n) bits in n channel uses. However, this assumes that Willie has an accurate statistical characterization of the channel. When Willie has uncertainty about such and his receiver is limited to a threshold test on the received power, Alice can transmit covertly with a power that does not decrease with n, thus conveying O(n) bits covertly and reliably in n uses of an AWGN channel. Here, we consider covert communication of O(n) bits in n channel uses while generalizing the environment and removing any restrictions on Willie's receiver. We assume that an uninformed “jammer” is present to help Alice, and we consider AWGN and block fading channels. In some scenarios, Willie's optimal detector is a threshold test on the received power. When the channel between the jammer and Willie has multiple fading blocks per codeword, a threshold test on the received power is not optimal. However, we establish that Alice can remain covert with a transmit power that does not decrease with n even when Willie employs an optimal detector.

Many partially-successful attempts have been made to find the most natural discrete-variable version of Shannon's entropy power inequality (EPI). We develop an axiomatic framework from which we deduce the natural form of a discrete-variable EPI and an associated entropic monotonicity in a discrete-variable central limit theorem. In this discrete EPI, the geometric distribution, which has the maximum entropy among all discrete distributions with a given mean, assumes a role analogous to the Gaussian distribution in Shannon's EPI. The entropy power of X is defined as the mean of a geometric random variable with entropy H(X). The crux of our construction is a discrete-variable version of Lieb's scaled addition X ???ηY of two random variables X and Y with η ∈ (0, 1). We discuss the relationship of our discrete EPI with recent work of Yu and Johnson who developed an EPI for a restricted class of random variables that have ultra-log-concave (ULC) distributions. Even though we leave open the proof of the aforesaid natural form of the discrete EPI, we show that this discrete EPI holds true for variables with arbitrary discrete distributions when the entropy power is redefined as eH(X)in analogy with the continuous version. Finally, we show that our conjectured discrete EPI is a special case of the yet-unproven Entropy Photon-number Inequality (EPnI), which assumes a role analogous to Shannon's EPI in capacity proofs for Gaussian bosonic (quantum) channels.

Recently, the fundamental limits of covert, i.e., reliable-yet-undetectable, communication have been established for general memoryless channels and for lossy-noisy bosonic (quantum) channels with a quantum-limited adversary. The key import of these results was the square-root law (SRL) for covert communication, which states that O(√n) covert bits, but no more, can be reliably transmitted over n channel uses with O(√n) bits of secret pre-shared between communicating parties. Here we prove the achievability of the SRL for a general memoryless classical-quantum channel, showing that SRL covert communication is achievable over any quantum communication channel with a product-state transmission strategy. We leave open the converse, which, if proven, would show that even using entangled transmissions and entangling measurements, the SRL for covert communication cannot be surpassed over an arbitrary quantum channel.

The maximum rate at which classical information can be reliably transmitted per use of a quantum channel strictly increases in general with N , the number of channel outputs that are detected jointly by the quantum joint-detection receiver (JDR). This phenomenon is known as superadditivity of the maximum achievable information rate over a quantum channel. We study this phenomenon for a pure-state classical-quantum channel and provide a lower bound on CN/N, the maximum information rate when the JDR is restricted to making joint measurements over no more than N quantum channel outputs, while allowing arbitrary classical error correction. We also show the appearance of a superadditivity phenomenon-of mathematical resemblance to the aforesaid problem-in the channel capacity of a classical discrete memoryless channel when a concatenated coding scheme is employed, and the inner decoder is forced to make hard decisions on N -length inner codewords. Using this correspondence, we develop a unifying framework for the above two notions of superadditivity, and show that for our lower bound to CN/N to be equal to a given fraction of the asymptotic capacity C of the respective channel, N must be proportional to V/C2, where V is the respective channel dispersion quantity.

We study the problem of maximizing the multicast throughput in a dense multi-channel multi-radio (MC-MR) wireless network with multiple multicast sessions. Specifically, we consider a fully connected network topology where all nodes are within transmission range of each other. In spite of its simplicity, this topology is practically important since it is encountered in several real-world settings. Further, a solution to this network can serve as a building block for more general scenarios that are otherwise intractable. For this network, we show that the problem of maximizing the uniform multicast throughput across multiple sessions is NP-hard. However, its special structure allows us to derive useful upper bounds on the achievable uniform multicast throughput. We show that an intuitive class of algorithms that maximally exploit the wireless broadcast feature can result in very poor worst case performance. Using a novel group splitting idea, we then design two polynomial time approximation algorithms that are guaranteed to achieve a constant factor of the throughput bound under arbitrary multicast group memberships. These algorithms are simple to implement and provide interesting tradeoffs between the achievable throughput and the total number of transmissions used.

The conditions for a quantum measurement to discriminate a set of states with the minimum probability of error were specified by Yuen, Kennedy and Lax, and are often termed the YKL conditions [1]. Since light is quantum mechanical, the ultimate limit on minimum-error discrimination of an optical modulation constellation is determined by the YKL bound. Standard optical receivers (i.e., direct, homodyne or heterodyne detection)-even at their respective ideal operation limits-cannot achieve this performance. Recently, it was shown that a `sequential waveform nulling' (SWN) receiver can, not only discriminate an arbitrary M-ary coherent-state (ideal laser-light) constellation asymptotically at the YKL bound in the high-power limit, but that it achieves a factor of 4 better in the asymptotic error-probability exponent compared with heterodyne detection-the only conventional optical receiver that can in principle be employed for detecting an arbitrary phase-and-amplitude modulated constellation [2]. The SWN receiver can be built with standard optical components; i.e., beamsplitters, local-oscillator lasers, delay loops and single-photon detectors. However on the other hand, in the high power regime, heterodyne detection is known to achieve a reliable communication rate that asymptotically approaches the Holevo capacity of a lossy-noisy optical channel (the ultimate limit to the classical capacity of a quantum channel) [3]. In fact, in the high power regime, heterodyne detection was also shown recently to achieve the optimal second-order coding rate, when using the optimal (Gaussian) input distribution [4]. In this paper, we show that when restricted to the M-ary phase-shift keying (PSK) ensemble, that the SWN receiver's superiority over heterodyne detection in its asymptotic error exponent of the demodulation error probability, translates to a slightly higher capacity and a pronouncedly higher finite blocklength reliable-communication rate. We also quantify, via a numerical calculation, the dependence of the SWN receiver's capacity on the order in which the PSK constellation points are nulled. Our results suggest that for short-latency PSK-modulated optical communication in the high spectral efficiency regime-for which heterodyne detection is the conventional receiver choice-that it may be beneficial to employ the SWN receiver, despite the widely-regarded capacity optimality of heterodyne detection in this operating regime.

We investigate superadditivity in the maximum achievable rate of reliable classical communication over a quantum channel. The maximum number of classical information bits extracted per use of the quantum channel strictly increases as the number of channel outputs jointly measured at the receiver increases. This phenomenon is called superadditivity. We provide an explanation of this phenomenon by comparing a quantum channel with a classical discrete memoryless channel (DMC) under concatenated codes. We also give a lower bound on the maximum accessible information per channel use at a finite length of quantum measurements in terms of V, which is the quantum version of channel dispersion, and C, the classical capacity of the quantum channel.

Minimum probability of error (MPE) measurements are quantum mechanical measurements that discriminate between a set of candidate states and achieve the minimum error allowed by quantum mechanics. Conditions for a measurement to be an MPE measurement have been derived by Yuen, Kennedy and Lax. But finding explicit measurements that satisfy these conditions is a hard problem in general and even in cases where an explicit measurement is known, calculating the MPE of the measurement is not easy. In some cases, MPE measurements have been found such as when the states form a single orbit under a group action i.e., there is a transitive group action on the states. For such state sets, termed Geometrically Uniform (GU) in [1], it was shown that the `pretty good measurement' (PGM) is optimal. However, calculating the MPE and other performance metrics for the PGM involves inverting large matrices, and it is therefore not easy in general to evaluate. Our first contribution is a formula for the MPE and conditional probabilities of GU sets using group representation theory. Next, we consider sets of pure states that have multiple orbits under the group action. Such states are termed compound geometrically uniform (CGU). CGU sets appear in many practical problems in quantum communication and imaging. For example, they include all linear codes formed using pure-state modulation constellations, which are known to achieve the ultimate (Holevo) capacity of optical communication. Optimal (MPE) measurement for general CGU sets are not known. In this paper, we show how our representation-theoretic description of optimal measurements for GU sets naturally generalizes to the CGU case. We show how to compute the optimal measurement for CGU sets by reducing the problem to solving a few simultaneous equations. The number of equations depends on the sizes of the multiplicity space of irreducible representations. For many group representations (such as those of several practical good linear codes), this is much more tractable than solving large semi-definite programs-which is what is needed to solve for MPE measurements for an arbitrary set of pure states using the Yuen-Kennedy-Lax conditions [2]. We show examples of the evaluation of optimal measurements for CGU states.

We define the squashed entanglement of a quantum channel as the maximum squashed entanglement that can be registered by a sender and receiver at the input and output of a quantum channel, respectively. A new subadditivity inequality for the original squashed entanglement measure of Christandl and Winter leads to the conclusion that the squashed entanglement of a quantum channel is an additive function of a tensor product of any two quantum channels. More importantly, this new subadditivity inequality, along with prior results of Christandl, Winter, et al., establishes the squashed entanglement of a quantum channel as an upper bound on the quantum communication capacity of any channel assisted by unlimited forward and backward classical communication. A similar proof establishes this quantity as an upper bound on the private capacity of a quantum channel assisted by unlimited forward and backward public classical communication. This latter result is relevant as a limitation on rates achievable in quantum key distribution. As an important application, we determine that these capacities can never exceed log((1 + η)=(1 - η)) for a pure-loss bosonic channel for which a fraction η of the input photons make it to the output on average. The best known lower bound on these capacities is equal to log(1=(1 - η)). Thus, in the high-loss regime for which η ≪ 1, this new upper bound demonstrates that the protocols corresponding to the above lower bound are nearly optimal.

This paper defines the squashed entanglement of a quantum channel as the maximum squashed entanglement that can be registered by a sender and receiver at the input and output of a quantum channel, respectively. A new subadditivity inequality for the original squashed entanglement measure of Christandl and Winter leads to the conclusion that the squashed entanglement of a quantum channel is an additive function of a tensor product of any two quantum channels. More importantly, this new subadditivity inequality, along with prior results of Christandl and Winter, establishes the squashed entanglement of a quantum channel as an upper bound on the quantum communication capacity of any channel assisted by unlimited forward and backward classical communication. A similar proof establishes this quantity as an upper bound on the private capacity of a quantum channel assisted by unlimited forward and backward public classical communication. This latter result is relevant as a limitation on rates achievable in quantum key distribution. As an important application, we determine that these capacities can never exceed (log (1+η)/(1-η)) for a pure-loss bosonic channel for which a fraction (η) of the input photons make it to the output on average. The best known lower bound on these capacities is equal to (log (1/(1-η)). Thus, in the high-loss regime for which η ≪ 1), this new upper bound demonstrates that the protocols corresponding to the above lower bound are nearly optimal.

We demonstrate the achievability of a square root limit on the amount of information transmitted reliably and with low probability of detection (LPD) over the single-mode lossy bosonic channel if either the eavesdropper's measurements or the channel itself is subject to the slightest amount of excess noise. Specifically, Alice can transmit O(√n) bits to Bob over n channel uses such that Bob's average codeword error probability is upper-bounded by an arbitrarily small δ > 0 while a passive eavesdropper, Warden Willie, who is assumed to be able to collect all the transmitted photons that do not reach Bob, has an average probability of detection error that is lower-bounded by 1/2 - ε for an arbitrarily small ε > 0. We analyze the thermal noise and pure loss channels. The square root law holds for the thermal noise channel even if Willie employs a quantum-optimal measurement, while Bob is equipped with a standard coherent detection receiver. We also show that LPD communication is not possible with coherent state transmission on the pure loss channel. However, this result assumes Willie to possess an ideal receiver that is not subject to excess noise. If Willie is restricted to a practical receiver with a non-zero dark current, the square root law is achievable on the pure loss channel.

Holevo, Schumacher, and Westmoreland's coding theorem guarantees the existence of codes that are capacity-achieving for the task of sending classical data over a channel with classical inputs and quantum outputs. Although they demonstrated the existence of such codes, their proof does not provide an explicit construction of codes for this task. The aim of this paper is to fill this gap by constructing near-explicit “polar” codes that are capacity-achieving. The codes exploit the channel polarization phenomenon observed by Arikan for the case of classical channels. Channel polarization is an effect in which one can synthesize a set of channels, by “channel combining” and “channel splitting,” in which a fraction of the synthesized channels are perfect for data transmission, while the other channels are completely useless for data transmission, with the good fraction equal to the capacity of the channel. The channel polarization effect then leads to a simple scheme for data transmission: send the information bits through the perfect channels and “frozen” bits through the useless ones. The main technical contributions of this paper are threefold. First, we leverage several known results from the quantum information literature to demonstrate that the channel polarization effect occurs for channels with classical inputs and quantum outputs. We then construct linear polar codes based on this effect, and the encoding complexity isO(NlogN), whereNis the blocklength of the code. We also demonstrate that a quantum successive cancellation decoder works well, in the sense that the word error rate decays exponentially with the blocklength of the code. For this last result, we exploit Sen's recent “noncommutative union bound” that holds for a sequence of projectors applied to a quantum state.

Channel polarization is a phenomenon in which a particular recursive encoding induces a set of synthesized channels from many instances of a memoryless channel, such that a fraction of the synthesized channels becomes near perfect for data transmission and the other fraction becomes near useless for this task. Mahdavifar and Vardy have recently exploited this phenomenon to construct codes that achieve the symmetric private capacity for private data transmission over a degraded wiretap channel. In this paper, we build on their work and demonstrate how to construct quantum wiretap polar codes that achieve the symmetric private capacity of a degraded quantum wiretap channel with a classical eavesdropper. Due to the Schumacher-Westmoreland correspondence between quantum privacy and quantum coherence, we can construct quantum polar codes by operating these quantum wiretap polar codes in superposition, much like Devetak's technique for demonstrating the achievability of the coherent information rate for quantum data transmission. Our scheme achieves the symmetric coherent information rate for quantum channels that are degradable with a classical environment. This condition on the environment may seem restrictive, but we show that many quantum channels satisfy this criterion, including amplitude damping channels, photon-detected jump channels, dephasing channels, erasure channels, and cloning channels. Our quantum polar coding scheme has the desirable properties of being channel-adapted and symmetric capacity-achieving along with having an efficient encoder, but we have not demonstrated that the decoding is efficient. Also, the scheme may require entanglement assistance, but we show that the rate of entanglement consumption vanishes in the limit of large blocklength if the channel is degradable with classical environment.

In the low-energy high-energy-efficiency regime of classical optical communications - relevant to deep-space optical channels - there is a big gap between reliable communication rates achievable via conventional optical receivers and the ultimate (Holevo) capacity. Achieving the Holevo capacity requires not only optimal codes but also receivers that make collective measurements on long (modulated) codeword waveforms, and it is impossible to implement these collective measurements via symbol-by-symbol detection along with classical postprocessing [1], [2]. Here, we apply our recent results on the classical-quantum polar code [3] - the first near-explicit, linear, symmetric-Holevo-rate achieving code - to the lossy optical channel, and we show that it almost closes the entire gap to the Holevo capacity in the low photon number regime. In contrast, Arikan's original polar codes, applied to the DMC induced by the physical optical channel paired with any conceivable structured optical receiver (including optical homodyne, heterodyne, or direct-detection) fails to achieve the ultimate Holevo limit to channel capacity. However, our polar code construction (which uses the quantum fidelity as a channel parameter rather than the classical Bhattacharyya quantity to choose the “good channels” in the polar-code construction), paired with a quantum successive-cancellation receiver - which involves a sequence of collective non-destructive binary projective measurements on the joint quantum state of the received codeword waveform - can attain the Holevo limit, and can hence in principle achieve higher rates than Arikan's polar code and decoder directly applied to the optical channel. However, even a theoretical recipe for construction of an optical realization of the quantum successive-cancellation receiver remains an open question.

We develop a theory of quantum M-ary phase shift keying in which quantum states of optical modes are modulated at the transmitter by applying one of M uniformly-spaced phase shifts. We allow full freedom in choosing modulation states with any number of signal, i.e., transmitted, and ancilla modes, subject only to an average energy, i.e., photon number, constraint in either the signal modes alone or in the signal and ancilla modes together. For lossless operation and unrestricted POVM measurements at the receiver, we find the explicit form of the modulation state that minimizes the average error probability under an energy constraint of N photons. Multiple signal modes, mixed states, and entanglement with an ancilla are shown to be unnecessary for optimum performance. We show that communication with zero error is possible if and only if N ≥ (M - 1)/2.

An important practical open question has been to design explicit, structured optical receivers that achieve the Holevo limit in the contexts of optical communication and “quantum reading.” The Holevo limit is an achievable rate that is higher than the Shannon limit of any known optical receiver. We demonstrate how a sequential decoding approach can achieve the Holevo limit for both of these settings. A crucial part of our scheme for both settings is a non-destructive “vacuum-or-not” measurement that projects an n-symbol modulated codeword onto the n-fold vacuum state or its orthogonal complement, such that the post-measurement state is either the n-fold vacuum or has the vacuum removed from the support of the n symbols' joint quantum state. The sequential decoder for optical communication requires the additional ability to perform multimode optical phase-space displacements - realizable using a beamsplitter and a laser, while the sequential decoder for quantum reading also requires the ability to perform phase-shifting (realizable using a phase plate) and online squeezing (a phase-sensitive amplifier).

We study the general coherent-state hypothesis testing problem and the capacity of the pure-loss optical channel with a coherent processing receiver (a receiver that uses coherent feedback control and direct detection). We describe the binary hypothesis minimum probability of error receiver as optimizing the communication efficiency at each instant, based on recursively updated knowledge of the receiver. Using this viewpoint, we give a natural generalization of the designs to general M-ary hypothesis testing problems. We analyze the information capacity with coherent receivers, and compare the result with that with direct detection receivers and with arbitrary quantum receivers (the Holevo limit), using the appropriate scalings in the low photon number regime.

When classical information is sent over a channel with quantum-state modulation alphabet, such as the free-space optical (FSO) channel, attaining the ultimate (Holevo) limit to channel capacity requires the receiver to make joint measurements over long codeword blocks. In recent work, we showed a receiver for a pure-state channel that can attain the ultimate capacity by applying a single-shot optical (unitary) transformation on the received codeword state followed by simultaneous (but separable) projective measurements on the single-modulation-symbol state spaces. In this paper, we study the ultimate tradeoff between photon efficiency and spectral efficiency for the FSO channel. Based on our general results for the pure-state quantum channel, we show some of the first concrete examples of codes and laboratory-realizable joint-detection optical receivers that can achieve fundamentally higher (superadditive) channel capacity than receivers that physically detect each modulation symbol one at a time, as is done by all conventional (coherent or direct-detection) optical receivers.

Semiclassical models for multiple-user optical communication cannot assess the ultimate limits on reliable communication as permitted by the laws of physics. In all optical communications settings that have been analyzed within a quantum framework so far, the gaps between the quantum limit to the capacity and the Shannon limit for structured receivers become most significant in the low photon-number regime. Here, we present a quantum treatment of a multiple-transmitter multiple-receiver multi-spatial-mode free-space interference channel with diffraction-limited loss and a thermal background. We consider the performance of a laser-light (coherent state) encoding in conjunction with various detection strategies such as homodyne, heterodyne, and joint detection. Joint detection outperforms both homodyne and heterodyne detection whenever the channel exhibits “very strong” interference. We determine the capacity region for homodyne or heterodyne detection when the channel has “strong” interference, and we conjecture the existence of a joint detection strategy that outperforms the former two strategies in this case. Finally, we determine the Han-Kobayashi achievable rate regions for both homodyne and heterodyne detection and compare them to a region achievable by a conjectured joint detection strategy. In these latter cases, we determine achievable rate regions if the receivers employ a recently discovered minentropy quantum simultaneous decoder.

Duty cycling or periodic sleep scheduling of RF transceivers of nodes in a wireless ad hoc or sensor network can significantly reduce energy consumption. This paper sheds light on the fundamental limits of the end-to-end data delivery latency and the per-flow throughput in a wireless network with multiple interfering flows, in the presence of "coordinated" duty cycling. We propose green wave sleep scheduling (GWSS) - inspired by synchronized traffic lights - for scheduling sleep-wake slots and routing data in a duty cycling wireless network, whose performance can approach the aforementioned limits. Particularly, we derive a general latency lower bound and show that GWSS is latency optimal on various structured topologies, such as the line, grid and the tree, at low traffic load. For an arbitrary network, finding a solution to the delay-efficient sleep scheduling problem is NP-hard. But for the 2D grid topology, we show that a non-interfering construction of GWSS is optimal in the sense of scaling laws of latency and capacity. Finally, using results from percolation theory, we extend GWSS to random wireless networks, where nodes are placed in a square area according to the Poisson point process. Aided by strong numerical evidence for a new conjecture on percolation on a semi-directed lattice that we propose, we demonstrate the latency optimality of GWSS on a random extended network, i.e., for an area-n random network with unit-density-Poisson distributed nodes, and a node-active (duty-cycling) rate p, GWSS can achieve a per-flow throughput scaling of T(n, p) = Ω(p/√n) bits/sec and latency D(n, p) scaling of O(√n) + O(1/p) hops/packet/flow.

While scheduling the nodes in a wireless network to sleep periodically can save energy, it also incurs higher latency and lower throughput. We consider the problem of designing optimal sleep schedules in wireless networks, and show that finding sleep schedules that can minimize the latency over a given subset of source-destination pairs is NP-hard. We also derive a latency lower bound given by d + O(1/p) for any sleep schedule with a required active rate (i.e., the fraction of active slots of each node) p, and the shortest path length d. We offer a novel solution to optimal sleep scheduling using green-wave sleep scheduling (GWSS), inspired by coordinated traffic lights, which is shown to meet our latency lower bound (hence is latency-optimal) for topologies such as the line, grid, ring, torus and tree networks, under light traffic. For high traffic loads, we propose non-interfering GWSS, which can achieve the maximum throughput scaling law given by T(n,p) = ¿(p/¿n) bits/sec on a grid network of size n, with a latency scaling law D(n,p) = O(¿n) + O(1/p). Finally, we extend GWSS to a random network with n Poisson-distributed nodes, for which we show an achievable throughput scaling law of T(n,p) = ¿(p/¿(n log n)) bits/sec and a corresponding latency scaling law D(n,p) = O(¿(n/log n)) + O(1/p); hence meeting the well-known Gupta-Kumar achievable throughput rate ¿(1/¿(n log n)) when p ¿ 1.

We consider the problem of demodulating M-ary optical PPM (pulse-position modulation) waveforms, and propose a structured receiver whose mean probability of symbol error is smaller than all known receivers, and approaches the quantum limit. The receiver uses photodetection coupled with optimized phase-coherent optical feedback control and a phase-sensitive parametric amplifier. We present a general framework of optical receivers known as the conditional pulse nulling receiver, and present new results on ultimate limits and achievable regions of spectral versus photon efficiency tradeoffs for the single-spatial-mode pure-loss optical communication channel.

Determining the ultimate classical information carrying capacity of electromagnetic waves requires quantum-mechanical analysis to properly account for the bosonic nature of these waves. Recent work has established capacity theorems for bosonic single-user and broadcast channels, under the presumption of two minimum output entropy conjectures. Despite considerable accumulated evidence that supports the validity of these conjectures, they have yet to be proven. In this paper, it is shown that the second conjecture suffices to prove the classical capacity of the bosonic wiretap channel, which in turn would also prove the quantum capacity of the lossy bosonic channel. The preceding minimum output entropy conjectures are then shown to be simple consequences of an entropy photon-number inequality (EPnl), which is a conjectured quantum-mechanical analog of the entropy power inequality (EPI) from classical information theory.

We show that when coherent-state encoding is employed in conjunction with coherent detection, the Bosonic broadcast channel is equivalent to a classical degraded Gaussian broadcast channel whose capacity region is dual to that of the classical Gaussian multiple-access channel. We further show that if a minimum output-entropy conjecture holds true, then the ultimate classical information capacity of the Bosonic broadcast channel can be achieved by a coherent-state encoding. We provide some evidence in support of the conjecture.

The capacity C for transmitting classical information is investigated for noisy bosonic channel models. An exact result is obtained for the pure-loss case. Upper and lower bounds are established for channels with active noise sources