The fundamental information-theoretic limits of covert, or low probability of detection/intercept (LPD/LPI), communication have been extensively studied for over a decade, resulting in thesquare root law(SRL): onlyL√ncovert bits can be reliably transmitted over time-bandwidth productn, for constantL> 0. Transmitting more either results in detection or decoding errors. The SRL imposes significant constraints on the hardware realization of mathematically guaranteed covert communication. These preclude the use of standard link maintenance operations that are taken for granted in non-covert communication. Thus, experimental validation of covert communication is under-explored: to date, only two experimental studies of SRL-based covert communication are available, both focusing on optical channels. Here, we demonstrate provably secure covert radio-frequency (RF) communication using software-defined radios (SDRs). We combine system design, theory, and experiments by 1) developing a sparse-signaling pulse shape to enable covert transmission of data in an environment with potential mobility, 2) proving the covertness of the resulting system, and 3) validating the theoretical predictions by implementing it on SDRs. We uncover and address unique challenges specific to using SDR architecture for covert communications. This opens practical avenues for implementing covert communication systems and raises further research questions.

We determine the covert capacity for entanglement generation over a noisy quantum channel. While secrecy guarantees that the transmitted information remains inaccessible to an adversary, covert communication ensures that the transmission itself remains undetectable. The entanglement dimension follows a square root law (SRL) in the covert setting, i.e., $O(\sqrt{n})$ Einstein-Podolsky-Rosen (EPR) pairs can be distributed covertly and reliably over $n$ channel uses. We begin with covert communication of classical information under a secrecy constraint. We then leverage this result to construct a coding scheme for covert entanglement generation. Single-letter expressions are derived for the covert key-assisted and unassisted secrecy capacities, as well as for the covert entanglement-generation capacity.

We consider quantum networks, where entangled-photon pairs are distributed using fibre optic links from a centralized source to entangling nodes. The entanglement is then stored (via an entanglement swap) in entangling nodes' quantum memories until used in, e.g., distributed quantum computing, quantum key distribution, quantum sensing, and other applications. Due to the fibre loss, some photons are lost in transmission. Noise in the transmission link and the quantum memory also reduces fidelity. Thus, entangling nodes must keep updated records of photon-pair arrivals to each destination, and their use by the applications. This coordination requires classical information exchange between each entangled node pair. However, the same fibre link may not admit both classical and quantum transmissions, as the classical channels can generate enough noise (i.e., via spontaneous Raman scattering) to make the quantum link unusable. Here, we consider coordinating entanglement distribution using a standard Internet protocol (IP) network instead, and propose a control protocol to enable such. We analyse the increase in latency from transmission over an IP network, together with the effect of photon loss, quantum memory noise and buffer size, to determine the fidelity and rate of entangled pairs. We characterize the relationship between the latency of the non-ideal IP network and the decoherence time of the quantum memories, providing a comparison of promising quantum memory technologies.

We explore covert communication of qubits over an arbitrary quantum channel. Covert communication conceals the transmissions in the channel noise, ensuring that an adversary is unable to detect their presence. We show the achievability of a square root law (SRL) for quantum covert communication similar to that for classical:$M(n) \sqrt{n}$qubits can be transmitted covertly and reliably over$n$uses of a general quantum channel. We lower bound$M (n)$with and without assistance from a two-way covert classical channel. In the former case, we quantify the number of classical covert bits sufficient for our protocol.

We generalize the quantum CUSUM (QUSUM) algorithm for quickest change-point detection, analyzed in finite dimensions by Fanizza, Hirche, and Calsamiglia (Phys. Rev. Lett. 131, 020602, 2023), to infinite-dimensional quantum systems. We employ a novel generalization of Hayashi’s theorem (Hayashi, J. Phys. A: Math. Gen. 34, 3413, 2001) concerning the asymptotics of quantum relative entropy, which we adapt to the infinite-dimensional setting. This enables us to prove that the QUSUM strategy retains its asymptotic optimality, characterized by the relationship between the expected detection delay and the average false alarm time for any pair of states with finite relative entropy. Thus, our findings apply broadly, including continuous-variable systems (e.g., Gaussian states), facilitating the development of optimal change-point detection schemes in quantum optics and other physical platforms, and rendering experimental verification feasible.

We determine the covert capacity for entanglement generation over a noisy quantum channel. While secrecy guarantees that the transmitted information remains inaccessible to an adversary, covert communication ensures that the transmission itself remains undetectable. The entanglement dimension follows a square root law (SRL) in the covert setting, i.e., $O\left( {\sqrt n } \right)$ EPR pairs can be distributed covertly and reliably over n channel uses. We begin with covert communication of classical information under a secrecy constraint. We then leverage this result to construct a coding scheme for covert entanglement generation. Consequently, the covert entanglement-generation capacity is the same as for classical information without secrecy, albeit our scheme employs a larger key.

We investigate resource allocation for quantum entanglement distribution over an optical network. We characterize and model a network architecture that employs a single broadband quasi-deterministic time-frequency heralded Einstein-Podolsky-Rosen (EPR) pair source, and develop a routing and spectrum allocation scheme for distributing entangled photon pairs over such a network. As our setting allows separately solving the routing and spectrum allocation problems, we first find an optimal polynomial-time routing algorithm. We then employ max-min fairness criterion for spectrum allocation, which presents an NP-hard problem. Thus, we focus on approximately-optimal schemes. We compare their performance by evaluating the max-min and median number of EPR-pair rates assigned by them, and the associated Jain index. We identify two polynomial-time approximation algorithms that perform well, or better than others under these metrics. We also investigate scalability by analyzing how the network size and connectivity affect performance using Watts-Strogatz random graphs. We find that a spectrum allocation approach that achieves higher minimum EPR-pair rate can perform significantly worse when the median EPR-pair rate, Jain index, and computational resources are considered. Additionally, we evaluate the effect of the source node placement on the performance.

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.

We consider entanglement-assisted communication over the qubit depolarizing channel under the security requirement of covert communication, where the transmission itself must be concealed from detection by an adversary. Previous work showed that$O(\sqrt {n})$information bits can be reliably and covertly transmitted innchannel uses without entanglement assistance. However, Gagatsos et al. (2020) showed that entanglement assistance can increase this scaling to$O(\sqrt {n}\log {n})$for continuous-variable bosonic channels. Here, we present a finite-dimensional parallel, and show that$O(\sqrt {n}\log {n})$covert bits can be transmitted reliably overnuses of a qubit depolarizing channel. The coding scheme employs “weakly” entangled states such that their squared amplitude scales as$O\left ({{{\scriptstyle \text {}^{\scriptstyle 1}}\hspace {-0.224em}/\hspace {-0.112em}{\scriptstyle \sqrt {n}}}}\right)$.

We investigate resource allocation for quantum entanglement distribution over an optical network. We characterize and model a network architecture that employs a single quasi-deterministic time-frequency heralded EPR-pair source, and develop a routing scheme for distributing entangled photon pairs over such a network. We focus on max-min fairness in entanglement distribution and compare the performance of various spectrum allocation schemes by examining both the max-min number of EPR pairs assigned by them and the Jain index associated with this assignment.

Quantum Cramér-Rao bound is the ultimate limit of the mean squared error for unbiased estimation of an unknown parameter embedded in a quantum state. While it can be achieved asymptotically for large number of quantum state copies, the measurement required often depends on the true value of the parameter of interest. This paradox was addressed by Hayashi and Matsumoto using a two-stage approach in 2005. Unfortunately, their analysis imposes conditions that severely restrict the class of classical estimators applied to the quantum measurement outcomes, hindering applications of this method. We relax these conditions to substantially broaden the class of usable estimators at the cost of slightly weakening the asymptotic properties of the two-stage method. We apply our results to obtain the asymptotics of quantum-enhanced transmittance sensing.

An upper bound to the identification capacity of discrete memoryless wiretap channels is derived under the requirement of semantic effective secrecy, combining semantic secrecy and stealth constraints. A previously established lower bound is improved by applying it to a prefix channel, formed by concatenating an auxiliary channel and the actual channel. The bounds are tight if the legitimate channel is more capable than the eavesdropper’s channel. An illustrative example is provided for a wiretap channel that is composed of a point-to-point channel, and a parallel, reversely degraded wiretap channel. A comparison with results for message transmission and for identification with only secrecy constraint is provided.

We consider entanglement-assisted communication over the qubit depolarizing channel under the security requirement of covert communication, where not only the information is kept secret, but the transmission itself must be concealed from detection by an adversary. Previous work showed that $O(\sqrt n )$ information bits can be reliably and covertly transmitted in n channel uses without entanglement assistance. However, Gagatsos et al. (2020) showed that entanglement assistance can increase this scaling to $O(\sqrt n \log n)$ for continuous-variable bosonic channels. Here, we present a finite-dimensional parallel, and show that $O(\sqrt n \log n)$ covert bits can be transmitted reliably over n uses of a qubit depolarizing channel.

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.

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.

We study quantum-secure covert-communication over lossy thermal-noise bosonic channels, the quantum mechanical model for many practical channels. We derive the expressions for the covert capacity of these channels: Lno-EA, when Alice and Bob share only a classical secret, and LEA, when they benefit from entanglement assistance. Entanglement assistance alters the fundamental scaling law for covert communication. Instead of Lno-EA√n-rno-EA(n), rno-EA(n) = o(√n), entanglement assistance allows LEA√n log n - rEA(n), rEA(n) = o(√n log n), covert bits to be transmitted reliably over n channel uses. However, noise in entanglement storage erases the log n gain from our achievability; work on the matching converse is ongoing.

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.

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.

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 recent square root law (SRL) for covert communication demonstrates that Alice can reliably transmit O(√n) bits to Bob in n uses of an additive white Gaussian noise (AWGN) channel while keeping ineffective any detector employed by the adversary; conversely, exceeding this limit either results in detection by the adversary with high probability or nonzero decoding error probability at Bob. This SRL is under the assumption that the adversary knows when Alice transmits (if she transmits); however, in many operational scenarios, he does not know this. Hence, here, we study the impact of the adversary's ignorance of the time of the communication attempt. We employ a slotted AWGN channel model with T(n) slots each containing n symbol periods, where Alice may use a single slot out of T(n). Provided that Alice's slot selection is secret, the adversary needs to monitor all T(n) slots for possible transmission. We show that this allows Alice to reliably transmit O(min{(n log T(n))1/2, n}) bits to Bob (but no more) while keeping the adversary's detector ineffective. To achieve this gain over SRL, Bob does not have to know the time of transmission provided T(n)cTn, cT= O(1).

Unlike standard security methods (e.g. encryption), low probability of detection (LPD) communication does not merely protect the information contained in a transmission from unauthorized access, but prevents the detection of a transmission in the first place. In this work we study the impact of secretly pre-arranging the time of communication. We prove that if Alice has AWGN channels to Bob and the warden, and if she and Bob can choose a single n symbol period slot out of T(n) such slots, keeping the selection secret from the warden (and, thus, forcing him to monitor all T(n) slots), then Alice can reliably transmit O(min{√n log T(n),n}) bits to Bob while keeping the warden's detector ineffective. The result indicates that only an additional log T(n) secret bits need to be exchanged between Alice and Bpob prior to communication to produce a multiplicative gain of √log T(n) in the amount of transmitted covert information.

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.

We present a square root limit on the amount of information transmitted reliably and with low probability of detection (LPD) over additive white Gaussian noise (AWGN) channels. Specifically, if the transmitter has AWGN channels to an intended receiver and a warden, both with non-zero noise power, we prove that o(√n) bits can be sent from the transmitter to the receiver in n channel uses while lower-bounding α + β ≥ 1-ε for any ε > 0, where α and β respectively denote the warden's probabilities of a false alarm when the sender is not transmitting and a missed detection when the sender is transmitting. Moreover, in most practical scenarios, a lower bound on the noise power on the channel between the transmitter and the warden is known and O(√n) bits can be sent in n LPD channel uses. Conversely, attempting to transmit more than O(√n) bits either results in detection by the warden with probability one or a non-zero probability of decoding error at the receiver as n→∞.

We present a square root limit on low probability of detection (LPD) communication over additive white Gaussian noise (AWGN) channels. Specifically, if a warden has an AWGN channel to the transmitter with non-zero noise power, we prove that o(√n) bits can be sent from the transmitter to the receiver in n AWGN channel uses with probability of detection by the warden less than e for any ϵ >; 0, and, if a lower bound on the noise power on the warden's channel is known, then O(√n) bits can be covertly sent in n channel uses. Conversely, trying to transmit more than O(√n) bits either results in detection by the warden with probability one or a non-zero probability of decoding error as n → ∞. Further, we show that LPD communication on the AWGN channel allows one to send a nonzero symbol on every channel use, in contrast to what might be expected from the square root law found recently in image-based steganography.

Low power ad hoc wireless networks operate in conditions where channels are subject to fading. Cooperative diversity mitigates fading in these networks by establishing virtual antenna arrays through clustering the nodes. A cluster in a cooperative diversity network is a collection of nodes that cooperatively transmits a single packet. There are two types of clustering schemes: static and dynamic. In static clustering all nodes start and stop transmission simultaneously, and nodes do not join or leave the cluster while the packet is being transmitted. Dynamic clustering allows a node to join an ongoing cooperative transmission of a packet as soon as the packet is received. In this paper we take a broad view of the cooperative network by examining packet flows, while still faithfully implementing the physical layer at the bit level. We evaluate both clustering schemes using simulations on large multi-flow networks. We demonstrate that dynamically-clustered cooperative networks substantially outperform both statically-clustered cooperative networks and classical point-to-point networks.

Distributed computation of Voronoi cells in sensor networks, i.e. computing the locus of points in a sensor field closest to a given sensor, is a key building block that supports a number of applications in both the data and control planes. For example, knowledge of Voronoi cells facilitates efficient methods for computing the piece-wise approximation of a field, whereby each sensor acts as a representative for the set of points in its Voronoi cell; awareness of Voronoi boundaries and Voronoi neighbors is also useful in load balancing and energy conservation. The methods currently advocated for distributed Voronoi computation in sensor networks are heuristic approximations that can introduce significant inaccuracies that are difficult to rigorously quantify; we demonstrate that these methods may err by a factor of 5 or more in some circumstances. We present and prove an exact method which eliminates these inaccuracies, at the cost of increased messaging overhead, but without necessitating contact with the entire network. To our knowledge, this is the first distributed algorithm that computes accurate Voronoi cells without requiring all-to-all communication. We implement it as a TinyOS module and quantitatively analyze its performance.