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Algorithmic solution to superactivation of zero-capacity optical quantum channels

László Gyöngyösi, Sándor Imre

Published Jan 1, 2010• 1 citation
Publisher

Abstract

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 results for describing all possible combinations of superactive zero-capacity channels, hence there should be many possible - still undiscovered - combinations. Our method gives an algorithmic solution to the superactivation problem, and provides an efficient algorithmic solution for discovering “superactive” zero-capacity optical quantum channels. We analyze the superactivation property of the amplitude damping quantum channel model. This model has great importance in practical communications, since this channel model describes energy dissipation due to the noise of the optical channel. To discover these superactive zero-capacity channels, an extremely large set of possible quantum states has to be analyzed, however an efficient algorithmic framework is still missing for this purpose. We show a fundamentally new method of finding the conditions for “superactive” zero-capacity optical quantum channels.

DOI
10.1109/pgc.2010.5705957

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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 results for describing all possible combinations of superactive zero-capacity channels, hence there should be many possible - still undiscovered - combinations. Our method gives an algorithmic solution to the superactivation problem, and provides an efficient algorithmic solution for discovering “superactive” zero-capacity optical quantum channels. We analyze the superactivation property of the amplitude damping quantum channel model. This model has great importance in practical communications, since this channel model describes energy dissipation due to the noise of the optical channel. To discover these superactive zero-capacity channels, an extremely large set of possible quantum states has to be analyzed, however an efficient algorithmic framework is still missing for this purpose. We show a fundamentally new method of finding the conditions for “superactive” zero-capacity optical quantum 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.
This paper introduces a fundamentally new method of finding the conditions for the superactivation of the zero-error capacity of quantum channels.The zero-error capacity of the quantum channel describes the amount of information which can be transmitted perfectly through a noisy quantum channel.The superactivation of the zero-error capacity of quantum channels makes it possible to use two quantum channels, each with zero zero-error capacity, with a positive joint zero-error capacity.Currently we have no theoretical background for describing all possible combinations of superactive quantum channels, hence there should be many other possible combinations.We give an algorithmic solution to the problem.To analyze the superactivation of the zero-error capacity, we introduce a new geometrical representation, called the quantum superball.Our method can be the first efficient algorithmic solution to discover the still unknown combinations to determine the superactivation of the zero-error capacity of quantum channels, without the extremely high computational costs.
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.
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.
This paper defines a fundamentally new approach of capacity recovery of very noisy, practically completely useless optical quantum channels. The transmission of information through classical channels and quantum channels differs in many ways. The capacity recovery of very noisy communication channels cannot be imagined for classical systems, and this effect has no analogue in classical systems. The capacity recovery of very noisy quantum channels makes it possible to use two very noisy optical-fiber based quantum channels with a positive joint capacity at the output. Our method gives an algorithmic solution to the capacity recovery problem, and provides an efficient algorithmic solution for finding recoverable very noisy optical quantum 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. Here we show, that noisy Gaussian quantum channels with the help of entanglement and coherent optical devices, can be used to transmit quantum information perfectly. It will be demonstrated that using the superactivation effect, it is possible to develop efficient quantum repeaters with the elimination of the very inefficient and expensive purification process.