Duality between source coding with quantum side information and c-q channel coding

Cheng, Hao-Chung; Hanson, Eric P.; Datta, Nilanjana; Hsieh, Min-Hsiu

doi:10.48550/arxiv.1809.11143

Cited by 13 publications

(16 citation statements)

References 22 publications

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“…The following lower bound follows by a standard argument, due to Nagaoka [46], as was also observed, e.g., in [14]. For readers' convenience, we write out the details in Appendix B.…”

Section: Strong Converse Exponent With Constant Compositionmentioning

confidence: 54%

“…4 we need a constant composition version of the classical-quantum channel coding theorem. Such a result was established, for instance, by Hayashi in [27], and very recently by Cheng, Hanson, Datta and Hsieh in [14], with a different exponent, by refining another random coding argument by Hayashi [26]. We give a slightly modified proof in Appendix C. Further appendices contain various technical ingredients of the proofs, and in Appendix A we give a more detailed discussion of the concepts of divergence radius and mutual information for general divergences and α-z Rényi divergences, which may be of independent interest.…”

Section: Introductionmentioning

confidence: 64%

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Divergence radii and the strong converse exponent of classical-quantum channel coding with constant compositions

Mosonyi

Ogawa

2018

Preprint

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There are different inequivalent ways to define the Rényi capacity of a channel for a fixed input distribution P . In a 1995 paper [16] Csiszár has shown that for classical discrete memoryless channels there is a distinguished such quantity that has an operational interpretation as a generalized cutoff rate for constant composition channel coding. We show that the analogous notion of Rényi capacity, defined in terms of the sandwiched quantum Rényi divergences, has the same operational interpretation in the strong converse problem of classical-quantum channel coding. Denoting the constant composition strong converse exponent for a memoryless classical-quantum channel W with composition P and rate R as sc(W, R, P ), our main result is that

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“…The following lower bound follows by a standard argument, due to Nagaoka [46], as was also observed, e.g., in [14]. For readers' convenience, we write out the details in Appendix B.…”

Section: Strong Converse Exponent With Constant Compositionmentioning

confidence: 54%

Section: Introductionmentioning

confidence: 64%

Divergence radii and the strong converse exponent of classical-quantum channel coding with constant compositions

Mosonyi

Ogawa

2018

Preprint

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“…for all x n ∈ A δ1 (p X ), by ( 40), ( 46), (48), and (49), respectively. Thus, by Lemma 6, there exists a POVM D k such that Pr (E 2 | E c 1 ) ≤ 2 −n(I(X;B)ρ− R−ε3(δ)) , which tends to zero as n → ∞, provided that…”

Section: Part 1 a Achievability Proofmentioning

confidence: 99%

“…compression with SSI is also studied in [43][44][45][46][47][48][49]. Compression with SSI given entanglement assistance was recently considered by Khanian and Winter [50][51][52].…”

mentioning

confidence: 99%

Classical State Masking over a Quantum Channel

Pereg,

Deppe,

Boche

2021

Preprint

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Transmission of classical information over a quantum state-dependent channel is considered, when the encoder can measure channel side information (CSI) and is required to mask information on the quantum channel state from the decoder. In this quantum setting, it is essential to conceal the CSI measurement as well. A regularized formula is derived for the masking equivocation region, and a full characterization is established for a class of measurement channels.

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“…For example, the quantum Augustin and Rényi information determine the error exponent of communications over a classical-quantum channel using certain random codebooks and that of composite quantum hypothesis testing [DW17, CHT19, CGH18, MO17, MO21, HT16]. The quantum conditional Rényi entropies have profound applications to quantum cryptographic protocols, such as bounding the convergence rate of privacy amplification [Dup21], analyzing the security of quantum key distributions [Ren05, KRS09,Tom12], and bounding the error exponent of source coding with quantum side information [CHDH18,CHDH21]. The above-mentioned quantities share a common feature-they require optimizing some order-α quantum Rényi divergence over the set of all quantum states.…”

Section: Introductionmentioning

confidence: 99%

Minimizing Quantum Renyi Divergences via Mirror Descent with Polyak Step Size

You¹,

Cheng

Li³

2021

Preprint

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Quantum information quantities play a substantial role in characterizing operational quantities in various quantum information-theoretic problems. We consider numerical computation of four quantum information quantities: Petz-Augustin information, sandwiched Augustin information, conditional sandwiched Rényi entropy and sandwiched Rényi information. To compute these quantities requires minimizing some order-α quantum Rényi divergences over the set of quantum states. Whereas the optimization problems are obviously convex, they violate standard bounded gradient/Hessian conditions in literature, so existing convex optimization methods and their convergence guarantees do not directly apply. In this paper, we propose a new class of convex optimization methods called mirror descent with the Polyak step size. We prove their convergence under a weak condition, showing that they provably converge for minimizing quantum Rényi divergences. Numerical experiment results show that entropic mirror descent with the Polyak step size converges fast in minimizing quantum Rényi divergences.

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Duality between source coding with quantum side information and c-q channel coding

Cited by 13 publications

References 22 publications

Divergence radii and the strong converse exponent of classical-quantum channel coding with constant compositions

Divergence radii and the strong converse exponent of classical-quantum channel coding with constant compositions

Classical State Masking over a Quantum Channel

Minimizing Quantum Renyi Divergences via Mirror Descent with Polyak Step Size

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