Precise quantum expectation values are crucial for quantum algorithm development, but noise in real-world systems can degrade these estimations. While quantum error correction is resource-intensive, error mitigation strategies offer a practical alternative. This paper presents a framework that combines Virtual Channel Purification (VCP) technique with Conditional Value-at-Risk (CVaR) optimization to improve expectation value estimations in noisy quantum circuits. Our contributions are twofold: first, we derive conditions to compare CVaR values from different probability distributions, offering insights into the reliability of quantum estimations under noise. Second, we apply this framework to VCP, providing analytical bounds that establish its effectiveness in improving expectation values, both when the overhead VCP circuit is ideal (error-free) and when it adds additional noise. By introducing CVaR into the analysis of VCP, we offer a general noise-characterization method that guarantees improved expectation values for any quantum observable. We demonstrate the practical utility of our approach with numerical examples, highlighting how our bounds guide VCP implementation in noisy quantum systems.

We consider the task of faithfully simulating a quantum measurement, acting on a joint bipartite quantum state, in a distributed manner. In this setup, the constituent sub-systems of the joint quantum state are measured by two agents, Alice and Bob. A third agent, Charlie, receives the measurement outcomes sent by Alice and Bob. Charlie uses local and pairwise shared randomness to compute a bivariate function of the measurement outcomes. The objective of three agents is to faithfully simulate the given distributed quantum measurement acting on the given quantum state while minimizing the communication and shared randomness rates. We demonstrate a new inner bound to the rate region using random structured POVMs based on asymptotically good algebraic codes, and characterize the performance limit using single-letter quantum mutual information quantities. This new bound subsumes the largest known inner bound and improves upon it strictly for identified examples. One of the challenges in analyzing these structured POVMs is that they exhibit only pairwise independence and induce only uniform single-letter distributions. We address these in the non-commutative quantum setting, and provide a two-party distributed faithful simulation and function computation protocol.

We propose quantum soft covering problems for fully quantum channels and classical-quantum (CQ) channels using relative entropy as a criterion of operator closeness. We prove covering lemmas by deriving one-shot bounds on the rates in terms of smooth min-entropies and smooth max-divergences, respectively. In the asymptotic regime, we show that for quantum channels, the rate infimum defined as the logarithm of the minimum rank of the input state is the coherent information between the reference and output state; for CQ channels, the rate infimum defined as the logarithm of the minimum number of input codewords is the Helovo information between the input and output state. Furthermore, we present a one-shot quantum decoupling theorem with relative entropy criterion. Our results based on the relative-entropy criterion are tighter than the corresponding results based on the trace norm considered in the literature due to the Pinsker inequality.

We consider the lossy quantum source coding problem, where the task is to compress a given quantum source below its von Neumann entropy. Inspired by the duality connections between the rate-distortion and channel coding problems in the classical setting, we propose a new formulation for the lossy quantum source coding problem. This formulation differs from the existing quantum rate-distortion theory in two aspects. Firstly, we require that the reconstruction of the compressed quantum source fulfill a global error constraint as opposed to the sample-wise local error criterion used in the standard rate-distortion setting. Secondly, to measure the reconstruction error, instead of a distortion observable, we employ the notion of a backward quantum channel which we refer to as a “posterior reference map”. Using these, we characterize the asymptotic performance limit in terms of single-letter coherent information of the given posterior reference map. We also develop analogous formulations for the quantum-classical and classical variants and characterize their asymptotic performance limits in terms of single-letter mutual information quantities with respect to appropriately defined channels analogous to the posterior reference map. We also provide various examples for the three formulations, and shed light on their connection to the standard rate-distortion formulation wherever possible.

In this work, we address the lossy quantum-classical (QC) source coding problem, where the task is to compress the classical information about a quantum source, obtained after performing a measurement, below the Shannon entropy of the measurement outcomes, while incurring a bounded reconstruction error. We propose a new formulation, namely, "rate-channel theory", for the lossy QC source coding problem based on the notion of a backward (posterior) channel. We employ a single-letter posterior channel to capture the reconstruction error in place of the single-letter distortion observable. The formulation requires the reconstruction of the compressed quantum source to satisfy a block error constraint as opposed to the average single-letter distortion criterion in the rate-distortion setting. We also develop an analogous formulation for the classical variant with respect to a corresponding posterior channel. Furthermore, we characterize the asymptotic performance limit of the lossy QC and classical source coding problems in terms of single-letter quantum mutual information and mutual information quantities of the given posterior channel, respectively. We provide examples for the above formulations.

We consider a scenario wherein two parties Alice and Bob are provided$X_{1}^{n}$and$X_{2}^{n}$– samples that are IID from a PMF$P_{X_{1} X_{2}}$. Alice and Bob can communicate to Charlie over (noiseless) communication links of rates$R_{1}$and$R_{2}$, respectively. Their goal is to enable Charlie generate samples$Y^{n}$such that the triple$(X_{1}^{n},X_{2}^{n},Y^{n})$has a PMF that is close, in total variation, to$\prod P_{X_{1} X_{2} Y}$, enabling the three parties achieve strong coordination. In addition, the three parties may posses pairwise shared common randomness at rates$C_{1}$and$C_{2}$. We address the problem of characterizing the set of rate quadruples$(R_{1},R_{2},C_{1},C_{2})$for which the above goal can be accomplished. We propose a new coding scheme based on random algebraic codes–coset codes in particular–of asymptotically large block-length. We analyze its performance and derive a single-letter information-theoretic inner bound. This bound subsumes the largest known inner bound and improves upon it strictly for identified examples. Our findings build on a variant of soft-covering which generalizes its applicability to the algebraic code ensembles. In addition, we provide an outer bound to the rate region for this three party distributed setup.

We consider the task of distilling local purity from a noisy quantum state ρABC, wherein we provide a protocol for three parties, Alice, Bob and Charlie, to distill local purity (at a rate P) from many independent copies of a given quantum state ρABC. The three parties have access to their respective subsystems of ρABC, and are only allowed to use local unitary operations. In addition, Alice and Bob can communicate with Charlie using a one-way multiple-access dephasing channel of link rates R1and R2, respectively. The objective of the protocol is to minimize the usage of the dephasing channel (in terms of rates R1and R2) while maximizing the asymptotic purity that can be jointly distilled from ρABC. To achieve this, we employ ideas from distributed measurement compression protocols, and in turn, characterize a set of sufficient conditions on (P, R1,R2) in terms of quantum information theoretic quantities such that P amount of purity can be distilled using rates R1and R2.

We consider the task of communicating a generic bivariate function of two classical sources over a Classical-Quantum Multiple Access Channel (CQ-MAC). The two sources are observed at the encoders of the CQ-MAC, and the decoder aims at reconstructing a bivariate function from the received quantum state. Inspired by the techniques developed for the classical setting, and employing the technique of simultaneous (joint) decoding developed for the CQ setup, we propose and analyze a coding scheme based on a classical superposition of algebraic structured codes and unstructured codes, and the idea of embedding functions on a prime field. We derive a new set of sufficient conditions that strictly enlarge the largest known set of sources (capable of communicating the bivariate function) for any given CQ-MAC. We provide these conditions in terms of single-letter quantum information-theoretic quantities.

We consider the task of faithfully simulating a distributed quantum measurement, wherein we provide a protocol for the three parties, Alice, Bob and Charlie, to simulate a repeated action of a distributed quantum measurement using a pair of non-product approximating measurements by Alice and Bob, followed by a stochastic mapping at Charlie. The objective of the protocol is to utilize minimum resources, in terms of classical bits needed by Alice and Bob to communicate their measurement outcomes to Charlie, and the common randomness shared among the three parties, while faithfully simulating independent repeated instances of the original measurement. To achieve this, we develop a mutual covering lemma and a technique for random binning of distributed quantum measurements, and, in turn, characterize a set of sufficient communication and common randomness rates required for asymptotic simulatability in terms of single-letter quantum information quantities. In the special case, where the Charlie’s action is restricted to a deterministic mapping, we develop a one-shot performance characterization of the distributed faithful simulation problem. Furthermore, using these results we address a distributed quantum rate-distortion problem, where we characterize the achievable rate distortion region through a single-letter inner bound. Finally, via a technique of single-letterization of multi-letter quantum information quantities, we provide an outer bound for the rate-distortion region.

We consider the task of communicating a generic bivariate function of two classical correlated sources over a Classical-Quantum Multiple Access Channel (CQ-MAC). The two sources are observed at the encoders of the CQ-MAC, and the decoder aims at reconstructing a bivariate function from the received quantum state. We first propose a coding scheme based on asymptotically good algebraic structured codes, in particular, nested coset codes, and provide a set of sufficient conditions for the reconstruction of the function of the sources over a CQ-MAC. The proposed technique enables the decoder to recover the desired function without recovering the sources themselves. We further improve this by employing a coding scheme based on a classical superposition of algebraic structured codes and unstructured codes. This coding scheme allows exploiting the symmetric structure common amongst the sources and also leverage the asymmetries. We derive a new set of sufficient conditions that strictly enlarges the largest known set of sources whose function can be reconstructed over any given CQ-MAC, and identify examples demonstrating the same. We provide these conditions in terms of single-letter quantum information-theoretic quantities.

We consider the task of faithfully simulating a distributed quantum measurement and function computation, and demonstrate a new achievable rate-region. For this, we develop the technique of randomly generating algebraic structured POVMs. To overcome the challenges caused by algebraic construction, we develop (i) a Pruning Trace inequality which is a tighter version of the known operator Markov inequality and (ii) a covering lemma which does not require the operator Chernoff inequality and hence applicable to pairwise-independent codewords. We demonstrate rate gains for this problem over traditional coding schemes and provide a multi-party distributed faithful simulation and function computation protocol.

We consider the problem of communicating a general bivariate function of two classical sources observed at the encoders of a classical-quantum multiple access channel. Building on the techniques developed for the case of a classical channel, we propose and analyze a coding scheme based on coset codes. The proposed technique enables the decoder recover the desired function without recovering the sources themselves. We derive a new set of sufficient conditions that are weaker than the current known for identified examples. This work is based on a new ensemble of coset codes that are proven to achieve the capacity of a classical-quantum point-to-point channel.

We consider the problem of characterizing an inner bound to the capacity region of a 3—user classical-quantum interference channel (3—CQIC). The best known coding scheme for communicating over CQICs is based on unstructured random codes and employs the techniques of message splitting and superposition coding. For classical 3—user interference channels (ICs), it has been proven that coding techniques based on coset codes - codes possessing algebraic closure properties - strictly outperform all coding techniques based on unstructured codes. In this work, we develop analogous techniques based on coset codes for 3to1—CQICs - a subclass of 3—user CQICs. We analyze its performance and derive a new inner bound to the capacity region of 3to1—CQICs that subsume the current known largest and strictly enlarges the same for identified examples.

In this problem, Alice and Bob, are provided$X_{1}^{n}$and$X_{2}^{n}$that are IID$px_{1}x_{2}$. Alice and Bob can communicate to Charles over (noiseless) links of rate$R_{1}$and$R_{2}$, respectively. Their goal is to enable Charles generate samples$Y^{n}$such that the triple$(X_{1}^{n},\ X_{2}^{n},\ Y^{n})$has a PMF that is close, in total variation, to$\prod p_{X_{1}X_{2}\mathrm{Y}}$. In addition, the three parties may posses shared common randomness at rate$C$. We address the problem of characterizing the set of rate triples$(R_{1},\ R_{2},\ C)$for which the above goal can be accomplished. We build on our recent findings and propose a new coding scheme based on coset codes. We analyze its information-theoretic performance and derive a new inner bound. We identify examples for which the derived inner bound is analytically proven to contain rate triples that are not achievable via any known unstructured code based coding techniques. Our findings build on a variant of soft-covering which generalizes its applicability to the algebraic structured code ensembles. This adds to the advancement of the use structured codes in network information theory.

We consider a scenario wherein two parties Alice and Bob are provided X1nand X2n-samples that are IID from a PMF pX1X2. Alice and Bob can communicate to Charles over (noiseless) communication links of rate R1and R2respectively. Their goal is to enable Charles generate samples Ynsuch that the triple (X1n, X2nYn). In addition, the three parties may posses shared common randomness at rate C. We address the problem of characterizing the set of rate triples (R1, R2, C) for which the above goal can be accomplished. We provide a set of sufficient conditions, i.e., an achievable rate region for this three party setup. Our work also provides a complete characterization of a point-to-point setup wherein Bob is absent and Charles is provided with side-information.

We investigate faithful simulation of distributed quantum measurements as an extension of Winter's measurement compression theorem. We characterize a set of communication and common randomness rates needed to provide faithful simulation of distributed measurements. To achieve this, we introduce binning and mutual packing lemma for distributed quantum measurements. These techniques can be viewed as the quantum counterpart of their classical analogues. Finally, using these results, we develop a distributed quantum-to-classical rate distortion theory and characterize a rate region analogous to Berger-Tung's in terms of single-letter quantum mutual information quantities.

Cellular heterogeneous networks (HetNets) are going to be one of the key enablers for 5G. Downlink/Uplink decoupling (DUDe) is a concept in which a mobile device is connected with Macro cell for downlink communication and with small cell for uplink communication in LTE/LTE-A HetNets. It improves uplink data rate, reduces power consumption of devices, balances load between Macro cell and small cells. Due to incorporation of DUDe, a mobile device has to perform separate uplink and downlink handovers unlike traditional handovers in coupled LTE networks. In this paper, we propose various handover schemes for DUDe LTE networks. Apart from this, we have mathematically analysed the received SINR by small cells taken part in decoupling, with respect to a device moving in decoupling regions of these small cells, in multiple cell interference scenario. Simulation results show the signaling impact of DUDe in handovers, increased uplink SINR, decreased power consumption of devices in both single small cell and multiple small cell scenarios.