Distinguishing two single-mode Gaussian states by homodyne detection: An information-theoretic approach

Abstract

It is known that the quantum fidelity, as a measure of the closeness of two quantum states, is operationally equivalent to the minimal overlap of the probability distributions of the two states over all possible POVMs; the POVM realizing the minimum is optimal. We consider the ability of homodyne detection to distinguish two single-mode Gaussian states, and investigate to what extent it is optimal in this information-theoretic sense. We completely identify the conditions under which homodyne detection makes an optimal distinction between two single-mode Gaussian states of the same mean, and show that if the Gaussian states are pure, they are always optimally distinguished.

6 pages, 4 figures, published version with a detailed discussion

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• Renyi relative entropies of quantum Gaussian states
• A limit formula for the quantum fidelity
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• Upper bounds on the relative energy difference of pure and mixed Gaussian states with a fixed fidelity
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• Purification Complexity without Purifications
• Selective cloning of Gaussian states by linear optics
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