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On superactivation of zero-error capacities of a quantum channel and its implications

Максим Евгеньевич Широков, Tatiana Shulman

Sep 10, 20130 citations

On Superactivation of Zero-Error Capacities and Reversibility of a Quantum Channel

Максим Евгеньевич Широков, Tatiana Shulman

arXiv:1309.2610Communications in Mathematical PhysicsMar 4, 201530 citations

Onset of superactivation of quantum capacity

Marco Parentin, Bjarne Bergh, Nilanjana Datta +1 more

Superactivation of quantum capacity is the phenomenon whereby two quantum channels, each with zero quantum capacity, can exhibit a strictly positive capacity when used in tandem. In this work, we explore superactivation in the previously unexplored non-asymptotic regime of finitely many channel uses. We give a definition of finite-blocklength superactivation and propose numerical methods that can certify it. Then, focusing on the 50% erasure and positive-partial-transpose channels considered in the original work on superactivation, we show that as few as 17 uses of the joint channel already enable qubit transmission with a fidelity unattainable by any number of uses of either channel alone, demonstrating a strong finite-blocklength form of superactivation and opening the door to experimental demonstration.Superactivation of quantum capacity is the phenomenon whereby two quantum channels, each with zero quantum capacity, can exhibit a strictly positive capacity when used in tandem. In this work, we explore superactivation in the previously unexplored non-asymptotic regime of finitely many channel uses. We give a definition of finite-blocklength superactivation and propose numerical methods that can certify it. Then, focusing on the 50% erasure and positive-partial-transpose channels considered in the original work on superactivation, we show that as few as 17 uses of the joint channel already enable qubit transmission with a fidelity unattainable by any number of uses of either channel alone, demonstrating a strong finite-blocklength form of superactivation and opening the door to experimental demonstration.

quant-pharXiv:2604.27042Apr 30, 20260 citations

Information Geometric Superactivation of Asymptotic Quantum Capacity and Classical Zero-Error Capacity of Zero-Capacity Quantum Channels

László Gyöngyösi

The superactivation of zero-capacity quantum channels makes it possible to use two zero-capacity quantum channels with a positive joint capacity at the output. Currently, we have no theoretical background for describing all possible combinations of superactive zero-capacity channels; hence, there may be many other possible combinations. In this PhD Thesis I provide an algorithmic solution to the problem of superactivation and prove that superactivation effect is rooted in information geometric issues.The superactivation of zero-capacity quantum channels makes it possible to use two zero-capacity quantum channels with a positive joint capacity at the output. Currently, we have no theoretical background for describing all possible combinations of superactive zero-capacity channels; hence, there may be many other possible combinations. In this PhD Thesis I provide an algorithmic solution to the problem of superactivation and prove that superactivation effect is rooted in information geometric issues.

arXiv:1206.5980Jun 25, 20126 citations

Informational geometric analysis of superactivation of asymptotic quantum capacity of zero-capacity optical quantum channels

László Gyöngyösi, Sándor Imre

The superactivation of zero-capacity optical quantum channels makes it possible to use two zero-capacity optical quantum channels with a positive joint capacity at the output. Currently, we have no theoretical results for describing all possible combinations of superactive zero-capacity channels, hence there should be many other possible combinations. This paper shows a fundamentally new method of finding the conditions for the superactivation of the asymptotic Lloyd-Shor-Devetak (LSD) channel capacity of zero-capacity optical quantum channels. We introduce a new geometrical representation, called the quantum informational superball representation. Our method provides a fundamentally new and efficient algorithmic solution for discovering all possible superactive channels and it can be applied to analyze the capacity of these channels.The superactivation of zero-capacity optical quantum channels makes it possible to use two zero-capacity optical quantum channels with a positive joint capacity at the output. Currently, we have no theoretical results for describing all possible combinations of superactive zero-capacity channels, hence there should be many other possible combinations. This paper shows a fundamentally new method of finding the conditions for the superactivation of the asymptotic Lloyd-Shor-Devetak (LSD) channel capacity of zero-capacity optical quantum channels. We introduce a new geometrical representation, called the quantum informational superball representation. Our method provides a fundamentally new and efficient algorithmic solution for discovering all possible superactive channels and it can be applied to analyze the capacity of these channels.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIEFeb 10, 20116 citations

Zero-Error Capacity of Quantum Channels

Elloá B. Guedes, Francisco de Assis, Rex A. C. Medeiros

Springer eBooksJan 1, 20169 citations

Algorithmic superactivation of asymptotic quantum capacity of zero-capacity quantum channels

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