arXiv:1107.4385 · Physical Review Letters

When Does Noise Increase the Quantum Capacity?

Fernando G. S. L. Brandão, Jonathan Oppenheim, Sergii Strelchuk

Published Jan 25, 2012• 33 citations

Abstract

Superactivation is the property that two channels with zero quantum capacity can be used together to yield a positive capacity. Here we demonstrate that this effect exists for a wide class of inequivalent channels, none of which can simulate each other. We also consider the case where one of two zero-capacity channels is applied, but the sender is ignorant of which one is applied. We find examples where the greater the entropy of mixing of the channels, the greater the lower bound for the capacity. Finally, we show that the effect of superactivation is rather generic by providing an example of superactivation using the depolarizing channel.

DOI: 10.1103/physrevlett.108.040501

Related papers

Activation and superactivation of single-mode Gaussian quantum channels

Youngrong Lim, Ryuji Takagi, Gerardo Adesso +1 more

Activation of quantum capacity is a surprising phenomenon according to which the quantum capacity of a certain channel may increase by combining it with another channel with zero quantum capacity. Superactivation describes an even more particular occurrence, in which both channels have zero quantum capacity, but their composition has a nonvanishing one. We investigate these effects for all single-mode phase-insensitive Gaussian channels, which include thermal attenuators and amplifiers, assisted by a two-mode positive-partial-transpose channel. Our result shows that activation phenomena are special but not uncommon. We can reveal superactivation in a broad range of thermal attenuator channels, even when the transmissivity is quite low, or the thermal noise is high. This means that we can transmit quantum information reliably through very noisy Gaussian channels with the help of another Gaussian channel, whose quantum capacity is also zero. We further show that no superactivation is possible for entanglement-breaking Gaussian channels in physically relevant circumstances by proving the nonactivation property of the coherent information of bosonic entanglement-breaking channels with finite input energy.

arXiv:1901.03147Physical Review AMar 25, 201917 citations

An Extreme form of Superactivation for Quantum Zero-Error Capacities

Toby S. Cubitt, Graeme Smith

The zero-error capacity of a channel is the rate at which it can send information perfectly, with zero probability of error, and has long been studied in classical information theory. We show that the zero-error capacity of quantum channels exhibits an extreme form of non-additivity, one which is not possible for classical channels, or even for the usual capacities of quantum channels. By combining probabilistic arguments with algebraic geometry, we prove that there exist channels E1 and E2 with no zero-error classical capacity whatsoever, C_0(E1) = C_0(E2) = 0, but whose joint zero-error quantum capacity is positive, Q_0(E1 x E2) >= 1. This striking effect is an extreme from of the superactivation phenomenon, as it implies that both the classical and quantum zero-error capacities of these channels can be superactivated simultaneously, whilst being a strictly stronger property of capacities. Superactivation of the quantum zero-error capacity was not previously known.

arXiv:0912.2737Dec 14, 20091 citation

An Extreme Form of Superactivation for Quantum Zero-Error Capacities

Toby S. Cubitt, Graeme Smith

The zero-error capacity of a channel is the rate at which it can send information perfectly, with zero probability of error, and has long been studied in classical information theory. We show that the zero-error capacity of quantum channels exhibits an extreme form of nonadditivity, one which is not possible for classical channels, or even for the usual capacities of quantum channels. By combining probabilistic arguments with algebraic geometry, we prove that there exist channels and with no zero-error classical capacity whatsoever, , but whose joint zero-error quantum capacity is positive, . This striking effect is an extreme form of the superactivation phenomenon, as it implies that both the classical and quantum zero-error capacities of these channels can be superactivated simultaneously, while being a strictly stronger property of capacities. Superactivation of the quantum zero-error capacity was not previously known.

IEEE Transactions on Information TheoryFeb 28, 201228 citations

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

Sergii Strelchuk

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.

arXiv:1305.1326Physical Review ASep 11, 20133 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.

arXiv:1206.5980Jun 25, 20126 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.

quant-pharXiv:2604.27042Apr 30, 20260 citations