Arbitrarily Varying and Compound Classical-Quantum Channels and a Note on Quantum Zero-Error Capacities

Bjelaković, Igor; Boche, Holger; Janßen, Gisbert; Nötzel, Janis

doi:10.1007/978-3-642-36899-8_11

Cited by 32 publications

(49 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The rate, according to Proposition 16 is ≥ min K(N )<K I(ρ; N ) − 2δ, where δ = 2 log(|A||B|) + Remark Along the same lines, the use of permutation-symmetrization and the Postselection Lemma allow to give a new proof of the coding theorem for arbitrarily varying cq-channels [9], by reducing it to a compound cq-channel [8], cf. also [36].…”

Section: Proof (Of Theorem 15)mentioning

confidence: 99%

On Zero-Error Communication via Quantum Channels in the Presence of Noiseless Feedback

Duan

Severini

Winter

2016

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

We initiate the study of zero-error communication via quantum channels when the receiver and sender have at their disposal a noiseless feedback channel of unlimited quantum capacity, generalizing Shannon's zero-error communication theory with instantaneous feedback.We first show that this capacity is a function only of the linear span of Choi-Kraus operators of the channel, which generalizes the bipartite equivocation graph of a classical channel, and which we dub "non-commutative bipartite graph". Then we go on to show that the feedback-assisted capacity is non-zero (allowing for a constant amount of activating noiseless communication) if and only if the non-commutative bipartite graph is non-trivial, and give a number of equivalent characterizations. This result involves a far-reaching extension of the "conclusive exclusion" of quantum states [Pusey/Barrett/Rudolph, Nature Phys. 8(6):475-478, 2012].We then present an upper bound on the feedback-assisted zero-error capacity, motivated by a conjecture originally made by Shannon and proved later by Ahlswede. We demonstrate this bound to have many good properties, including being additive and given by a minimax formula. We also prove a coding theorem showing that this quantity is the entanglement-assisted capacity against an adversarially chosen channel from the set of all channels with the same Choi-Kraus span, which can also be interpreted as the feedbackassisted unambiguous capacity. The proof relies on a generalization of the "Postselection Lemma" (de Finetti reduction) [Christandl/König/Renner, Phys. Rev. Lett. 102:020504, 2009] that allows to reflect additional constraints, and which we believe to be of independent interest. This capacity is a relaxation of the feedback-assisted zero-error capacity; however, we have to leave open the question of whether they coincide in general.We illustrate our ideas with a number of examples, including classical-quantum channels and Weyl diagonal channels, and close with an extensive discussion of open questions. a A preliminary version of this paper was presented as a poster at QIP 2012, 12-16 December 2011

show abstract

Section: Proof (Of Theorem 15)mentioning

confidence: 99%

On Zero-Error Communication via Quantum Channels in the Presence of Noiseless Feedback

Duan

Severini

Winter

2016

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

show abstract

“…[13]), we use the results of Section 3 to show the existence of a common randomness assisted quantum code. Additionally, we have to consider the security.…”

Section: Proof I) Achievementmentioning

confidence: 99%

“…By (58), he is able to decode 2 n|Γ | log Jn messages. By [13], for every B q ∈ Conv((B s ) s∈θ ) we have…”

Section: Ii) Conversementioning

confidence: 99%

“…To determine our capacity formula, we follow the idea of [13] and [39] in the classical cases: At first, we consider a mixed channel model that is called the arbitrarily varying classical-quantum wiretap channel. Then, we apply Ahlswede's robustification technique to establish the common randomness assisted secrecy capacity of an arbitrarily varying classical-quantum wiretap channel.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Classical-quantum arbitrarily varying wiretap channel: common randomness assisted code and continuity

Boche

Cai

Deppe

et al. 2016

Quantum Inf Process

Self Cite

View full text Add to dashboard Cite

We determine the secrecy capacities under common randomness assisted coding of arbitrarily varying classical-quantum wiretap channels. Furthermore, we determine the secrecy capacity of a mixed channel model which is compound from the sender to the legitimate receiver and varies arbitrarily from the sender to the eavesdropper. We examine when the secrecy capacity is a continuous function of the system parameters as an application and show that resources, e.g., having access to a perfect copy of the outcome of a random experiment, can guarantee continuity of the capacity function of arbitrarily varying classical-quantum wiretap channels.

show abstract

“…For readers convenience, we give a proof that is a slight modification of our proof of Lemma 10 in Ref. 5, which in turn is just a reformulation of Ahlswede's original proof to the quantum setting. …”

Section: Equivalence Of Maximal-and Average Error Criterionmentioning

confidence: 99%

Arbitrarily small amounts of correlation for arbitrarily varying quantum channels

Boche

Nötzel

2013

Journal of Mathematical Physics

View full text Add to dashboard Cite

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.

show abstract

Arbitrarily Varying and Compound Classical-Quantum Channels and a Note on Quantum Zero-Error Capacities

Cited by 32 publications

References 28 publications

On Zero-Error Communication via Quantum Channels in the Presence of Noiseless Feedback

On Zero-Error Communication via Quantum Channels in the Presence of Noiseless Feedback

Classical-quantum arbitrarily varying wiretap channel: common randomness assisted code and continuity

Arbitrarily small amounts of correlation for arbitrarily varying quantum channels

Contact Info

Product

Resources

About