Quantum Zero-Error Capacity and HSW Capacity

정남호

Максим Евгеньевич Широков

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

Guang-Can Guo

The Holevo-Schumacher-Westermoreland (HSW) channel capacity for the qudit unital channels was considered. A simpler formula for computing HSW channel capacity was given. And the HSW channel capacity can be determined by using only pure states. This result simplifies the computation of HSW channel capacity for the qudit unital channel.

Yu-Chun Wu, Zheng-Wei Zhou, Guang‐Can Guo

The Holevo–Schumacher–Westermoreland (HSW) channel capacity for the diagonal unital qudit channels is considered. In Phys. Rev.A69, 022302, the HSW channel capacity for the diagonal unital qudit channels Φ is given as χ(Φ)=1- min ρH(Φ(ρ)), where minimization is over the input states of the channel. In this paper, using the concavity of von Neumann entropy, we show that using only pure states we can work out its HSW channel capacity. Hence, our result simplifies the computation.

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.