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arXiv:quant-ph/0509016 · Journal of Physics A Mathematical and General

A dynamical model for quantum memory channels

Vittorio Giovannetti

Published Nov 30, 2005• 52 citations
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Abstract

A dynamical model for quantum channels is introduced which allows one to pass continuously from the memoryless case to the case in which memory effects are present. The quantum and classical communication rates of the model are defined and explicit expression is provided in some limiting case. In this context, we introduce noise attenuation strategies where part of the signals are sacrificed to modify the channel environment. The case of qubit channel with phase damping noise is analysed in detail.

DOI
10.1088/0305-4470/38/50/008

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A dynamical model for quantum channels is introduced which allows one to pass continuously from the memoryless case to the case in which memory effects are present. The quantum and classical communication rates of the model are defined and explicit expression is provided in some limiting case. In this context, we introduce noise attenuation strategies where part of the signals are sacrificed to modify the channel environment. The case of qubit channel with phase damping noise is analysed in detail.
A dynamical model for quantum channel is introduced which allows one to pass continuously from the memoryless case to the case in which memory effects are present. The quantum and classical communication rates of the model are defined and explicit expression are provided in some limiting case. In this context we introduce noise attenuation strategies where part of the signals are sacrificed to modify the channel environment. The case of qubit channel with phase damping noise is analyzed in details.
With increasing communication rates via quantum channels, memory effects become unavoidable whenever the use rate of the channel is comparable to the typical relaxation time of the channel environment. We introduce a model of a bosonic memory channel, describing correlated noise effects in quantum-optical processes via attenuating or amplifying media. To study such a channel model, we make use of a proper set of collective field variables, which allows us to unravel the memory effects, mapping the nnn-fold concatenation of the memory channel to a unitarily equivalent, direct product of nnn single-mode bosonic channels. We hence estimate the channel capacities by relying on known results for the memoryless setting. Our findings show that the model is characterized by two different regimes, in which the cross correlations induced by the noise among different channel uses are either exponentially enhanced or exponentially reduced.
The notion of forgetfulness, used in discrete quantum memory channels, is slightly weakened in order to be applied to the case of continuous channels. This is done in the context of quantum memory channels with Markovian noise. As a case study, we apply the notion of weak forgetfulness to a bosonic memory channel with additive noise. A suitable encoding and decoding unitary transformation allows us to unravel the effects of the memory, hence the channel capacities can be computed using known results from the memoryless setting.
Quantum memory channels are attracting growing interest, motivated by both realistic possibilities of transferring information by means of quantum hardware and inadequacies of the memoryless approximation. In fact, subsequent uses of the same quantum transmission resource can be significantly correlated. In this paper we review two Hamiltonian models describing memory effects in a purely dephasing spin-boson channel and in a channel with damping visualized by a micromaser system, respectively. In both cases, we show that the quantum information transmission rates are higher than in the memoryless limit.
We introduce a general model describing correlated noise effects in quantum optical communication via attenuating media. The memory effects account for the environment finite relaxation times, which are unavoidable in any realistic model. The use of a proper set of collective field variables allows us to unravel the memory, showing that the n-fold concatenation of the memory channel is unitarily equivalent to the direct product of n single-mode lossy bosonic channels. We then compute the ultimate (classical and quantum) transmission rates, showing their enhancement with respect to the memoryless case and proving that coherent state encoding is optimal.
In this paper we study quantum communication channels with correlated noise effects, i.e., quantum channels with memory. We derive a model for correlated noise channels that includes a channel memory state. We examine the case where the memory is finite, and derive bounds on the classical and quantum capacities. For the entanglement-assisted and unassisted classical capacities it is shown that these bounds are attainable for certain classes of channel. Also, we show that the structure of any finite-memory state is unimportant in the asymptotic limit, and specifically, for a perfect finite-memory channel where no information is lost to the environment, achieving the upper bound implies that the channel is asymptotically noiseless.