On the near-optimality of one-shot classical communication over quantum channels

Anshu, Anurag; Jain, Rahul; Warsi, Naqueeb Ahmad

doi:10.1063/1.5039796

Cited by 24 publications

(14 citation statements)

References 48 publications

(68 reference statements)

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“…We extend this result to the bosonic channel with infinite-dimension Hilbert spaces based on the discretization limiting argument by Guha et al [20]. Related settings were also considered in [21,22,23].…”

mentioning

confidence: 73%

Bosonic Dirty Paper Coding

Pereg

2021

2021 IEEE International Symposium on Information Theory (ISIT)

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mentioning

confidence: 73%

Bosonic Dirty Paper Coding

Pereg

2021

2021 IEEE International Symposium on Information Theory (ISIT)

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“…In this section, we provide a proof for an upper bound on the one-shot entanglement-assisted classical capacity, which is arguably simpler than the approach taken in [MW14]. A proof along these lines was found recently and independently in [AJW18]. Before doing so, we recall the definition of generalized divergence D(ρ σ) [SW12] of two states ρ and σ as any function from two density operators to the reals that is monotone under the action of a quantum channel N , in the sense that…”

Section: Alternative Proof Of An Upper Bound On One-shot Entanglementmentioning

confidence: 89%

“…This concludes the proof. We now apply Lemma 9 in the context of entanglement-assisted communication, to establish an alternate proof of the following upper bound (again emphasizing that a proof along these lines was found recently and independently in [AJW18]):…”

Section: Alternative Proof Of An Upper Bound On One-shot Entanglementmentioning

confidence: 96%

Applications of position-based coding to classical communication over quantum channels

Qi¹,

Wang²,

Wilde³

2018

J. Phys. A: Math. Theor.

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Recently, a coding technique called position-based coding has been used to establish achievability statements for various kinds of classical communication protocols that use quantum channels. In the present paper, we apply this technique in the entanglement-assisted setting in order to establish lower bounds for error exponents, lower bounds on the second-order coding rate, and one-shot lower bounds. We also demonstrate that position-based coding can be a powerful tool for analyzing other communication settings. In particular, we reduce the quantum simultaneous decoding conjecture for entanglement-assisted or unassisted communication over a quantum multiple access channel to open questions in multiple quantum hypothesis testing. We then determine achievable rate regions for entanglement-assisted or unassisted classical communication over a quantum multiple-access channel, when using a particular quantum simultaneous decoder. The achievable rate regions given in this latter case are generally suboptimal, involving differences of Rényi-2 entropies and conditional quantum entropies. IntroductionUnderstanding optimal rates for classical communication over both point-to-point quantum channels and quantum network channels are fundamental tasks in quantum Shannon theory (see, e.g., [Hol12, Wat16, Wil16, Wil17b]). Early developments of quantum Shannon theory are based on the assumption that the information is transmitted over an arbitrarily large number of independent and identically distributed (i.i.d.) uses of a given quantum channel. By taking advantage of this assumption, general formulas have been established for capacities of various communication protocols, with or without preshared entanglement. When a sender and receiver do not share entanglement before communication begins, it is known that the Holevo information of a quantum channel is an achievable rate for classical communication [Hol98, SW97]. Regularizing the Holevo information leads to a multi-letter formula that characterizes the capacity for this task. Regarding communication over quantum network channels, an achievable rate region for classical communication over quantum multiple-access channels was given in [Win01] and regularizing it leads to a characterization of the tions from [AM14, BHOS15] in multiple quantum hypothesis testing. At the same time, we give new achievable rate regions for entanglement-assisted classical communication over multiple-access channels, where the bounds on achievable rates are expressed as a difference of a Rényi entropy of order two and a conditional quantum entropy.This paper is organized as follows. We first summarize relevant definitions and lemmas in Section 2. In this section, we also prove Proposition 3, which relates the hypothesis testing relative entropy to the quantum Rényi relative entropy and is an interesting counterpart to [CMW16, Lemma 5]. In Section 3, we consider entanglement-assisted point-to-point classical communication. By using position-based coding, we establish a lower bound on the entanglement-as...

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“…The entanglement-assisted capacity of a quantum channel with non-causal CSI was determined by Dupuis [19,20], and with causal CSI by the author [52,51]. One-shot communication with CSI is considered in [1] as well. Luo and Devetak [47] considered channel simulation with source side information (SSI) at the decoder, and also solved the quantum generalization of the Wyner-Ziv problem [67].…”

Section: Introductionmentioning

confidence: 99%

Communication over Quantum Channels with Parameter Estimation

Pereg¹

2020

Preprint

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Communication over a random-parameter quantum channel when the decoder is required to reconstruct the parameter sequence is considered. We study scenarios that include either strictly-causal, causal, or non-causal channel side information (CSI) available at the encoder, and also when CSI is not available. This model is the quantum counterpart of the classical rate-and-state channel with state estimation at the decoder. Regularized formulas for the capacity-distortion regions are derived. In the special case of measurement channels, single-letter characterizations are derived for the strictly-causal and causal settings. Furthermore, in the more general case of entanglement-breaking channels, a single-letter characterization is derived when CSI is not available. As a consequence, we obtain regularized formulas for the capacity of random-parameter quantum channels with CSI, generalizing previous results by Boche et al.[5] on classical-quantum channels.

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On the near-optimality of one-shot classical communication over quantum channels

Cited by 24 publications

References 48 publications

Bosonic Dirty Paper Coding

Bosonic Dirty Paper Coding

Applications of position-based coding to classical communication over quantum channels

Communication over Quantum Channels with Parameter Estimation

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