Hybrid zero-capacity channels

Strelchuk, Sergii; Oppenheim, Jonathan

doi:10.1103/physreva.86.022328

Cited by 3 publications

(4 citation statements)

References 15 publications

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“…Strategies to check if a general channel has zero or nonzero quantum capacity are limited 61 , 62 . To test if a channel has zero quantum capacity, one can check whether the channel is PPT or anti-degradable.…”

Section: Introductionmentioning

confidence: 99%

“…To test if a channel has zero quantum capacity, one can check whether the channel is PPT or anti-degradable. For special channels these two checks can be done algebraically 52 , 62 , 63 , but in general, they require numerically solving a semi-definite program 64 . Even if one performs these checks, their results can be inconclusive because there may exist zero capacity channels that are neither PPT nor anti-degradable.…”

Section: Introductionmentioning

confidence: 99%

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Entropic singularities give rise to quantum transmission

Siddhu

2021

Nat Commun

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When can noiseless quantum information be sent across noisy quantum devices? And at what maximum rate? These questions lie at the heart of quantum technology, but remain unanswered because of non-additivity— a fundamental synergy which allows quantum devices (aka quantum channels) to send more information than expected. Previously, non-additivity was known to occur in very noisy channels with coherent information much smaller than that of a perfect channel; but, our work shows non-additivity in a simple low-noise channel. Our results extend even further. We prove a general theorem concerning positivity of a channel’s coherent information. A corollary of this theorem gives a simple dimensional test for a channel’s capacity. Applying this corollary solves an open problem by characterizing all qubit channels whose complement has non-zero capacity. Another application shows a wide class of zero quantum capacity qubit channels can assist an incomplete erasure channel in sending quantum information. These results arise from introducing and linking logarithmic singularities in the von-Neumann entropy with quantum transmission: changes in entropy caused by this singularity are a mechanism responsible for both positivity and non-additivity of the coherent information. Analysis of such singularities may be useful in other physics problems.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Entropic singularities give rise to quantum transmission

Siddhu

2021

Nat Commun

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“…We have given some evidence that its asymptotic performance is superior to that of the original DPS hierarchy. Indeed, [43] shows that even for constant n, a variant of the r th DPS hierarchy has error lower-bounded by Ω(1/r). But our hierarchy converges in a constant number of steps for any fixed local dimension.…”

Section: Discussion and Open Questionsmentioning

confidence: 99%

An Improved Semidefinite Programming Hierarchy for Testing Entanglement

Harrow

Natarajan

2017

Commun. Math. Phys.

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We present a stronger version of the Doherty-Parrilo-Spedalieri (DPS) hierarchy of approximations for the set of separable states. Unlike DPS, our hierarchy converges exactly at a finite number of rounds for any fixed input dimension. This yields an algorithm for separability testing which is singly exponential in dimension and polylogarithmic in accuracy. Our analysis makes use of tools from algebraic geometry, but our algorithm is elementary and differs from DPS only by one simple additional collection of constraints.

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“…It is of great interest because it may provide clues about novel methods of transmitting the frail quantum data in the presence of the strongly deleterious noise in the channel.One important aspect for the channels whose capacity is currently known to be superactivated is the requirement that they must come from two distinct classes: the first one comes from the set of binding entanglement channels [3], and the second one comes either from * ss870@cam.ac.uk the set of zero-capacity erasure channels with the rational erasure probability or depolarizing channels in the regime when they become antidegradable [2]. The capacity of the channel from each of those classes cannot be superactivated by another channel within same class [5]. Apart from these two families of channels, it is not known if there exist qualitatively different zerocapacity channels that give rise to the superactivation of the quantum capacity.…”

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confidence: 99%

Parrondo's paradox and superactivation of classical and quantum capacity of communication channels with memory

Strelchuk¹

2013

Phys. Rev. A

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There exist memoryless zero-capacity quantum channels that when used jointly result in a channel with positive capacity. This phenomenon is called superactivation. Making use of Parrondo's paradox, we exhibit examples of the superactivation-like effect for the capacity of classical communication channels as well as quantum and private capacity of quantum channels with memory. There are several ingredients necessary for superactivation of quantum capacity to occur in the memoryless case. The first one is the requirement for the quantum channels which are suitable for superactivation to come from two distinct families: binding entanglement channels and erasure channels. The second one is the ability to utilize inputs which are entangled across the uses of the channels. Our construction uses a single family of erasure channels with classical memory to achieve the same superactivation-like effect for quantum capacity without any of the ingredients above.

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Hybrid zero-capacity channels

Cited by 3 publications

References 15 publications

Entropic singularities give rise to quantum transmission

Entropic singularities give rise to quantum transmission

An Improved Semidefinite Programming Hierarchy for Testing Entanglement

Parrondo's paradox and superactivation of classical and quantum capacity of communication channels with memory

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