Channel Simulation With Quantum Side Information

Luo, Zhiguo; Devetak, Igor

doi:10.1109/tit.2008.2011424

Cited by 43 publications

(70 citation statements)

References 26 publications

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“…Indeed, if we view each message generation in a protocol as a channel, then the information cost can be seen to be equal to the sum of the asymptotic costs of simulating many copies of each such channel with side information at the receiver and feedback to the sender [39], a task related to the reverse Shannon theorem [9,45,25,2,8,10], with application in particular in the setting of rate distortion theory with side-information at the receiver [47]. Using known bounds for this task [39], this yields a strengthening of the classical amortized communication result for bounded round complexity [17,14]. That is, we prove a bounded round variant of the result of Braverman and Rao about amortized communication and information complexity.…”

Section: Quantum Information Complexitymentioning

confidence: 99%

“…In the fully quantum setting, channel simulation, with side information at the receiver and with environment given as feedback to the sender, is equivalent to the state redistribution task [39,22,49,44]. This insight leads to the new, fully quantum definitions of information cost and complexity, and the link between state redistribution and protocol compression is then apparent.…”

Section: Quantum Information Complexitymentioning

confidence: 99%

“…It is rather in the interpretation of every message transmission as the simulation of a channel (the generation of the message from the input, previous messages, and randomness) with feedback to the sender and side information at the receiver, a variant of the setting of the classical reverse Shannon theorem studied in the information theory literature [9,25,8,39]. …”

Section: A Different Perspective On Classical Information Costmentioning

confidence: 99%

“…When there is side information S at the receiver, I(M ; I|S) characterizes the amount of information that needs to be sent over the noiseless channel from sender to receiver, and it is shown in Ref. [39] that asymptotically, this quantity characterizes the optimal (unidirectional) classical communication rate for this task when sufficient shared randomness is available. In Ref.…”

Section: A Different Perspective On Classical Information Costmentioning

confidence: 99%

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Quantum Information Complexity

Touchette

2015

Proceedings of the Forty-Seventh Annual ACM Symposium on Theory of Computing

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We define a new notion of information cost for quantum protocols, and a corresponding notion of quantum information complexity for bipartite quantum tasks. These are the fully quantum generalizations of the analogous quantities for bipartite classical tasks that have found many applications recently, in particular for proving communication complexity lower bounds and direct sum theorems. Finding such a quantum generalization of information complexity was one of the open problems recently raised by Braverman (STOC'12).Previous attempts have been made to define such a quantity for quantum protocols, with particular applications in mind; our notion differs from these in many respects. First, it directly provides a lower bound on the quantum communication cost, independent of the number of rounds of the underlying protocol. Secondly, we provide an operational interpretation for quantum information complexity: we show that it is exactly equal to the amortized quantum communication complexity of a bipartite task on a given input. This generalizes a result of Braverman and Rao (FOCS'11) to quantum protocols. Along the way to prove this result, we even strengthens the classical result in a bounded round scenario, and also prove important structural properties of quantum information cost and complexity.We prove that using this definition leads to the first general direct sum theorem for bounded round quantum communication complexity. Previous direct sum results in quantum communication complexity either held for some particular classes of functions, or were general but only held for single-round protocols. We also discuss potential applications of the new quantities to obtain lower bounds on quantum communication complexity.

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Section: Quantum Information Complexitymentioning

confidence: 99%

Section: Quantum Information Complexitymentioning

confidence: 99%

Section: A Different Perspective On Classical Information Costmentioning

confidence: 99%

Section: A Different Perspective On Classical Information Costmentioning

confidence: 99%

See 2 more Smart Citations

Quantum Information Complexity

Touchette

2015

Proceedings of the Forty-Seventh Annual ACM Symposium on Theory of Computing

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“…To do this, we consider the problem related to channel simulation [15]- [17], [60], [61]. Roughly speaking, the problem is described as follows.…”

Section: Appendix C Simulation Of Test Channelmentioning

confidence: 99%

Nonasymptotic and Second-Order Achievability Bounds for Coding With Side-Information

Watanabe

Kuzuoka

Tan

2015

IEEE Trans. Inform. Theory

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Abstract-We present novel non-asymptotic or finite blocklength achievability bounds for three side-information problems in network information theory. These include (i) the WynerAhlswede-Körner (WAK) problem of almost-lossless source coding with rate-limited side-information, (ii) the Wyner-Ziv (WZ) problem of lossy source coding with side-information at the decoder and (iii) the Gel'fand-Pinsker (GP) problem of channel coding with noncausal state information available at the encoder. The bounds are proved using ideas from channel simulation and channel resolvability. Our bounds for all three problems improve on all previous non-asymptotic bounds on the error probability of the WAK, WZ and GP problems-in particular those derived by Verdú. Using our novel non-asymptotic bounds, we recover the general formulas for the optimal rates of these side-information problems. Finally, we also present achievable second-order coding rates by applying the multidimensional Berry-Esséen theorem to our new non-asymptotic bounds. Numerical results show that the second-order coding rates obtained using our non-asymptotic achievability bounds are superior to those obtained using existing finite blocklength bounds.

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Universal coding for transmission of private information

Datta

Hsieh

2010

Journal of Mathematical Physics

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We consider the scenario in which Alice transmits private classical messages to Bob via a classical-quantum channel, part of whose output is intercepted by an eavesdropper, Eve. We prove the existence of a universal coding scheme under which Alice's messages can be inferred correctly by Bob, and yet Eve learns nothing about them. The code is universal in the sense that it does not depend on specific knowledge of the channel. Prior knowledge of the probability distribution on the input alphabet of the channel, and bounds on the corresponding Holevo quantities of the output ensembles at Bob's and Eve's end suffice.Comment: 31 pages, no figures. Published versio

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Channel Simulation With Quantum Side Information

Cited by 43 publications

References 26 publications

Quantum Information Complexity

Quantum Information Complexity

Nonasymptotic and Second-Order Achievability Bounds for Coding With Side-Information

Universal coding for transmission of private information

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