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2007

The Entropy Photon-Number Inequality and its Consequences

Guha, Saikat, Erkmen, Baris I., Shapiro, Jeffrey H.

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Determining the ultimate classical information carrying capacity of electromagnetic waves requires quantum-mechanical analysis to properly account for the bosonic nature of these waves.

Recent work has established capacity theorems for bosonic single-user, broadcast, and wiretap channels, under the presumption of two minimum output entropy conjectures.
Despite considerable accumulated evidence that supports the validity of these conjectures, they have yet to be proven.
Here we show that the preceding minimum output entropy conjectures are simple consequences of an Entropy Photon-Number Inequality, which is a conjectured quantum-mechanical analog of the Entropy Power Inequality (EPI) from classical information theory.

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Built on

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics
1995
Earlier work this paper cites.
V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, J. H. Shapiro, and H. P. Yuen, Phys. Rev. Lett. 92
2004
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V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, J. H. Shapiro, B. J. Yen, and H. P. Yuen, in Quantum Information, Statistics, Probability
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V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, and J. H. Shapiro, Phys. Rev. A 70
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O. Rioul, “Information theoretic proofs of entropy power inequalities,” arxiv cs.IT/0704.175
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A density operator is Hermitian, with eigenvalues that form a probability distribution. Thus, the von Neumann entropy of a density operator ρ ^ \hat{\rho} is the Shannon entropy of its eigenvalues
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The coherent states, { | α ⟩ } \{|\alpha\rangle\} , are not
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To show that ( 13
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Assume that ( 13
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Then

S. Guha, J. H. Shapiro, and B. I. Erkmen, Phys. Rev. A 76
2007
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S. Guha and J. H. Shapiro, Unpublished notes
2007
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