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arXiv:quant-ph/0609018 · Quantum Information and Computation

Quantum Gaussian channels with additive correlated classical noise

G. Ruggeri, S. Mancin

Published Mar 1, 2007• 4 citations
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Abstract

We provide a model to study memory effects in quantum Gaussian channels with additive classical noise over an arbitrary number of uses. The correlation among different uses is introduced by contiguous two-mode interactions. Numerical results for few modes are presented. They confirm the possibility to enhance the classical information rate with the aid of entangled inputs, and show a likely asymptotic behavior that should lead to the full capacity of the channel.

DOI
10.26421/qic7.3-6

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We provide a model to study memory effects in quantum Gaussian channels with additive classical noise over an arbitrary number of uses. The correlation among different uses is introduced by contiguous two-mode interactions. Numerical results for few modes are presented. They confirm the possibility to enhance the classical information rate with the aid of entangled inputs, and show a likely asymptotic behavior that should lead to the full capacity of the channel.
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We study the capacity of ddd-dimensional quantum channels with memory modeled by correlated noise. We show that, in agreement with previous results on Pauli qubit channels, there are situations where maximally entangled input states achieve higher values of mutual information than product states. Moreover, a strong dependence of this effect on the nature of the noise correlations as well as on the parity of the space dimension is found. We conjecture that when entanglement gives an advantage in terms of mutual information, maximally entangled states saturate the channel capacity.
We address the classical capacity of a quantum bosonic memory channel with additive noise, subject to an input energy constraint. The memory is modeled by correlated noise emerging from a Gauss-Markov process. Under reasonable assumptions, we show that the optimal modulation results from a ``quantum water-filling'' solution above a certain input energy threshold, similar to the optimal modulation for parallel classical Gaussian channels. We also derive analytically the optimal multimode input state above this threshold, which enables us to compute the capacity of this memory channel in the limit of an infinite number of modes. The method can also be applied to a more general noise environment which is constructed by a stationary Gauss process. The extension of our results to the case of broadband bosonic channels with colored Gaussian noise should also be straightforward.
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.