Classical Capacity of Classical-Quantum Arbitrarily Varying Channels

Ahlswede, Rudolf; Blinovsky, Vladimir

doi:10.1109/tit.2006.889004

Cited by 40 publications

(74 citation statements)

References 7 publications

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“…We emphasize that, although an explicit example of the advantage that random codes offer over their deterministic counterparts has been given in Ref. 2, it is conjectured in Ref. 4 that A det (I) = A random (I) holds for every AVQC I.…”

Section: Resultsmentioning

confidence: 94%

“…2. So, for this setting as well, a small amount of shared randomness can boost the message transmission capacity from zero to some value strictly larger than zero.…”

Section: Introduction and Historical Remarksmentioning

confidence: 91%

“…Application of the same trick as in case (1) leads to statement (2). The proof of (3) follows a reasoning along the lines of the proof of (2) and will therefore be omitted.…”

Section: Remark 3 It Follows Directly From This Lemma That No Finitementioning

confidence: 97%

“…2 where C random (W ) > 0 and C det (W ) = 0 holds for arbitrarily varying classical-quantum (cq) channels. In this case, by our Corollary 1 below, it is already clear that mere correlation leads to a huge benefit for message transmission.…”

Section: Introduction and Historical Remarksmentioning

confidence: 99%

“…We felt little urge to prove a coding theorem for message transmission using random codes over an AVQC, but expect a regularized version with an additional optimization over input ensembles in the spirit of the coding result given in Ref. 2. Given such a result, it should in principle be possible to find out whether C random (I) > 0 holds, by brute force computer simulations at the worst.…”

Section: Introduction and Historical Remarksmentioning

confidence: 99%

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Arbitrarily small amounts of correlation for arbitrarily varying quantum channels

Boche

Nötzel

2013

Journal of Mathematical Physics

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As our main result show that in order to achieve the randomness assisted message and entanglement transmission capacities of a finite arbitrarily varying quantum channel it is not necessary that sender and receiver share (asymptotically perfect) common randomness. Rather, it is sufficient that they each have access to an unlimited amount of uses of one part of a correlated bipartite source. This access might be restricted to an arbitrary small (nonzero) fraction per channel use, without changing the main result. We investigate the notion of common randomness. It turns out that this is a very costly resource -generically, it cannot be obtained just by local processing of a bipartite source. This result underlines the importance of our main result. Also, the asymptotic equivalence of the maximal-and average error criterion for classical message transmission over finite arbitrarily varying quantum channels is proven. At last, we prove a simplified symmetrizability condition for finite arbitrarily varying quantum channels. C 2013 AIP Publishing LLC. [http://dx.

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Section: Resultsmentioning

confidence: 94%

“…2. So, for this setting as well, a small amount of shared randomness can boost the message transmission capacity from zero to some value strictly larger than zero.…”

Section: Introduction and Historical Remarksmentioning

confidence: 91%

“…Application of the same trick as in case (1) leads to statement (2). The proof of (3) follows a reasoning along the lines of the proof of (2) and will therefore be omitted.…”

Section: Remark 3 It Follows Directly From This Lemma That No Finitementioning

confidence: 97%

Section: Introduction and Historical Remarksmentioning

confidence: 99%

Section: Introduction and Historical Remarksmentioning

confidence: 99%

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