arXiv subjects
Publications and source records attributed to A. S. Holevo.
A multiplicativity conjecture for quantum communication channels is formulated, validity of which for the values of parameter $p$ close to 1 is related to the solution of the fundamental problem of additivity of the channel capacity in quantum information theory. The proof of the conjecture is given for the case of natural numbers $p$.
A class of problems in quantum information theory, having an elementary formulation but still resisting solution, concerns the additivity properties of various quantities characterizing quantum channels, notably the "classical capacity", and the "maximal output purity". All known results, including extensive numerical work, are consistent with the conjecture that these quantities are indeed additive (resp. multiplicative) with respect to tensor products of channels. A proof of this conjecture would have important consequences in quantum information theory. In particular, according to this conjecture, the classical capacity or the maximal purity of outputs cannot be increased by using entangled inputs of the channel. In this paper we state the additivity/multiplicativity problems, give some relations between them, and prove some new partial results, which also support the conjecture.
In information theory the reliability function and its bounds, describing the exponential behavior of the error probability, are the most important quantitative characteristics of the channel performance. From a general point of view, these bounds provide certain measures of distinguishability of a given set of states. In an earlier paper we introduced quantum analogs of the random coding and the expurgation lower bounds for the case of pure signal states. Here we discuss the general case, in particular, we prove the previously conjectured expurgation bound and find the quantum cutoff rate in the case of arbitrary mixed signal states.
We show how to compute or at least to estimate various capacity-related quantities for Bosonic Gaussian channels. Among these are the coherent information, the entanglement assisted classical capacity, the one-shot classical capacity, and a new quantity involving the transpose operation, shown to be a general upper bound on the quantum capacity, even allowing for finite errors. All bounds are explicitly evaluated for the case of a one-mode channel with attenuation/amplification and classical noise.
The reliability function gives the rate of exponential convergence to zero of the error probability in a communication channel. In this paper bounds for the reliability function of a quantum pure state channel are given, reminiscent of the corresponding classical bounds. This in particular suggests an alternative proof of the coding theorem for quantum noiseless channel, which would make no use of the notion of typical subspace. Example of binary quantum channel is considered in some detail.
The more than thirty years old issue of the information capacity of quantum communication channels was dramatically clarified during the last period, when a number of direct quantum coding theorems was discovered. To considerable extent this progress is due to an interplay between the quantum communication theory and quantum information ideas related to more recent development in quantum computing. It is remarkable, however, that many probabilistic tools underlying the treatment of quantum case have their roots, and in some cases direct prototypes, in classical Shannon's theory. This paper presents an outline of some basic ideas and results in that direction.
The purpose of this work is to extend the result of previous papers quant-ph/9611023, quant-ph/9703013 to quantum channels with additive constraints onto the input signal, by showing that the capacity of such channel is equal to the supremum of the entropy bound with respect to all apriori distributions satisfying the constraint. We also make an extension to channels with continuous alphabet. As an application we prove the formula for the capacity of the quantum Gaussian channel with constrained energy of the signal, establishing the asymptotic equivalence of this channel to the semiclassical photon channel. We also study the lower bounds for the reliability function of the pure-state Gaussian channel.
A survey of the probabilistic approaches to quantum dynamical semigroups with unbounded generators is given. An emphasis is made upon recent advances in the structural theory of covariant Markovian master equations. The relations with the classical Levy-Khinchin formula are elucidated. As an example, a complete characterizations of the Galilean covariant irreversible quantum Markovian evolutions is given in terms of the corresponding quantum master and Langevin equations. Important topics for future investigation are outlined.
It is shown that the capacity of a classical-quantum channel with arbitrary (possibly mixed) states equals to the maximum of the entropy bound with respect to all apriori distributions. This completes the recent result of Hausladen, Jozsa, Schumacher, Westmoreland and Wooters, who proved the equality for the pure state channel.