### Abstract

It is known that 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 positive-operator-valued measures (POVM's); 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.

Original language | English |
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Article number | 032336 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 71 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Mar 2005 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Physics and Astronomy(all)

### Cite this

**Distinguishing two single-mode Gaussian states by homodyne detection : An information-theoretic approach.** / Nha, Hyunchul; Carmichael, H. J.

Research output: Contribution to journal › Article

*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 71, no. 3, 032336. https://doi.org/10.1103/PhysRevA.71.032336

}

TY - JOUR

T1 - Distinguishing two single-mode Gaussian states by homodyne detection

T2 - An information-theoretic approach

AU - Nha, Hyunchul

AU - Carmichael, H. J.

PY - 2005/3/1

Y1 - 2005/3/1

N2 - It is known that 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 positive-operator-valued measures (POVM's); 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.

AB - It is known that 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 positive-operator-valued measures (POVM's); 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.

UR - http://www.scopus.com/inward/record.url?scp=18444364771&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=18444364771&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.71.032336

DO - 10.1103/PhysRevA.71.032336

M3 - Article

VL - 71

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 3

M1 - 032336

ER -