Universal Coding for Classical-Quantum Channel

Hayashi, Masahito

doi:10.1007/s00220-009-0825-1

Cited by 53 publications

(65 citation statements)

References 28 publications

(60 reference statements)

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“…In particular a detailed proof of Lemma 9 is provided. Over the years several code constructions for message transmission over compound cq channels have been established (see [12,22,19,25]). The arguments we invoke below for proving Lemma 9 rely heavily on the techniques Mosonyi's work [25].…”

Section: B Universal Classical-quantum Superposition Codingmentioning

confidence: 99%

Universal superposition codes: Capacity regions of compound quantum broadcast channel with confidential messages

Boche

Janßen

Saeedinaeeni

2020

Journal of Mathematical Physics

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We derive universal codes for transmission of broadcast and confidential messages over classical-quantumquantum and fully quantum channels. These codes are robust to channel uncertainties considered in the compound model. To construct these codes we generalize random codes for transmission of public messages, to derive a universal superposition coding for the compound quantum broadcast channel. As an application, we give a multi-letter characterization of regions corresponding to capacity of the compound quantum broadcast channel for transmitting broadcast and confidential messages simultaneously. This is done for two types of broadcast messages, one called public and the other common.

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Section: B Universal Classical-quantum Superposition Codingmentioning

confidence: 99%

Universal superposition codes: Capacity regions of compound quantum broadcast channel with confidential messages

Boche

Janßen

Saeedinaeeni

2020

Journal of Mathematical Physics

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“…This kind of task is formally called asymmetric hypothesis testing with composite alternative hypothesis. The problem of a composite null hypothesis is that considered in the context of the quantum Sanov theorem, which was solved in [BDK + 05] (see also [Hay02]), and finds application in communication over compound channels [BB09,Mos15] (see also [DD07,Hay09b]).…”

Section: Asymmetric Hypothesis Testing With Composite Alternative Hypmentioning

confidence: 99%

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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“…To prove a coding theorem for the entanglement-assisted classical capacities of compound channels, we use capacity achieving codes for certain compound classical-quantum channels. Such codes were derived in [24], [15], [20] before. In this paper, we use codes from the more recent work [31] instead, which achieve the message transmission capacities of general (not necessarily finite or countable compound channels) with exponentially decreasing errors.…”

Section: Related Workmentioning

confidence: 99%

Entanglement-assisted classical capacities of compound and arbitrarily varying quantum channels

Boche

Janβen

Kaltenstadler

2017

Quantum Inf Process

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We consider classical message transmission under entanglement assistance for compound memoryless and arbitrarily varying quantum channels. In both cases, we prove general coding theorems together with corresponding weak converse bounds. In this way, we obtain single-letter characterizations of the entanglement-assisted classical capacities for both channel models. Moreover, we show that the entanglement-assisted classical capacity does exhibit no strong converse property for some compound quantum channels for the average as well as the maximal error criterion. A strong converse to the entanglement-assisted classical capacities does hold for each arbitrarily varying quantum channel.

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Universal Coding for Classical-Quantum Channel

Cited by 53 publications

References 28 publications

Universal superposition codes: Capacity regions of compound quantum broadcast channel with confidential messages

Universal superposition codes: Capacity regions of compound quantum broadcast channel with confidential messages

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

Entanglement-assisted classical capacities of compound and arbitrarily varying quantum channels

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