Capacity of a bosonic memory channel with Gauss-Markov noise

Details Capacity of a bosonic memory channel with Gauss-Markov noise Capacity of a bosonic memory channel with Gauss-Markov noise

2009-07-06

arxiv.org/abs/0907.0982v3

Phys. Rev. A 80, 062313 (2009)

Physics

Quantum Physics

11 pages, 4 figures, final corrections made

Scientific paper

10.1103/PhysRevA.80.062313

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.

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