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arXiv:0802.3397 · Physical Review A

Lossy bosonic quantum channel with non-Markovian memory

Oleg V. Pilyavets, Vadim Zborovskii, Stefano Mancini

Published May 19, 2008• 31 citations
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Abstract

We provide a simple model to study memory effects in a lossy bosonic quantum channel over arbitrary number of uses. The noise correlation among different uses is introduced by contiguous modes interactions which results in an exponential decay of the correlations over channel uses (modes). This model allows us to characterize the asymptotic behavior of the channel for classical information transmission.

DOI
10.1103/physreva.77.052324

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We provide a simple model to study memory effects in a lossy bosonic quantum channel over arbitrary number of uses. The noise correlation among different uses is introduced by contiguous modes interactions which results in an exponential decay of the correlations over channel uses (modes). This model allows us to characterize the asymptotic behavior of the channel for classical information transmission.
We evaluate the information capacities of a lossy bosonic channel with correlated noise. The model generalizes the one recently discussed by Pilyavets et al (2008 Phys. Rev. A 77 052324), where memory effects come from the interaction with correlated environments. Environmental correlations are quantified by a multimode squeezing parameter, which vanishes in the memoryless limit. We show that a global encoding/decoding scheme, which involves input-entangled states among different channel uses, is always preferable with respect to a local one in the presence of memory. Moreover, in a certain range of the parameters, we provide an analytical expression for the classical capacity of the channel showing that a global encoding/decoding scheme allows it to be attained. All the results can be applied to a broad class of bosonic Gaussian channels.
We evaluate the information capacities of a lossy bosonic channel with correlated noise. The model generalizes the one recently discussed by Pilyavets et al (2008 Phys. Rev. A 77 052324), where memory effects come from the interaction with correlated environments. Environmental correlations are quantified by a multimode squeezing parameter, which vanishes in the memoryless limit. We show that a global encoding/decoding scheme, which involves input-entangled states among different channel uses, is always preferable with respect to a local one in the presence of memory. Moreover, in a certain range of the parameters, we provide an analytical expression for the classical capacity of the channel showing that a global encoding/decoding scheme allows it to be attained. All the results can be applied to a broad class of bosonic Gaussian channels.
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.
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.