### Abstract

The problem of specifying the optimum quantum detector in multiple hypotheses testing is considered for application to optical communications. The quantum digital detection problem is formulated as a linear programming problem on an infinite-dimensional space. A necessary and sufficient condition is derived by the application of a general duality theorem specifying the optimum detector in terms of a set of linear operator equations and inequalities. Existence of the optimum quantum detector is also established. The optimality of commuting detection operators is discussed in some examples. The structure and performance of the optimal receiver are derived for the quantum detection of narrow-band coherent orthogonal and simplex signals. It is shown that modal photon counting is asymptotically optimum in the limit of a large signaling alphabet and that the capacity goes to infinity in the absence of a bandwidth limitation.

Original language | English (US) |
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Pages (from-to) | 125-134 |

Number of pages | 10 |

Journal | IEEE Transactions on Information Theory |

Volume | 21 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1975 |

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### ASJC Scopus subject areas

- Information Systems
- Computer Science Applications
- Library and Information Sciences

### Cite this

*IEEE Transactions on Information Theory*,

*21*(2), 125-134. https://doi.org/10.1109/TIT.1975.1055351

}

*IEEE Transactions on Information Theory*, vol. 21, no. 2, pp. 125-134. https://doi.org/10.1109/TIT.1975.1055351

**Optimum Testing of Multiple Hypotheses in Quantum Detection Theory.** / Yuen, Horace P.; Kennedy, Robert S.; Lax, Melvin.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Optimum Testing of Multiple Hypotheses in Quantum Detection Theory

AU - Yuen, Horace P.

AU - Kennedy, Robert S.

AU - Lax, Melvin

PY - 1975/1/1

Y1 - 1975/1/1

N2 - The problem of specifying the optimum quantum detector in multiple hypotheses testing is considered for application to optical communications. The quantum digital detection problem is formulated as a linear programming problem on an infinite-dimensional space. A necessary and sufficient condition is derived by the application of a general duality theorem specifying the optimum detector in terms of a set of linear operator equations and inequalities. Existence of the optimum quantum detector is also established. The optimality of commuting detection operators is discussed in some examples. The structure and performance of the optimal receiver are derived for the quantum detection of narrow-band coherent orthogonal and simplex signals. It is shown that modal photon counting is asymptotically optimum in the limit of a large signaling alphabet and that the capacity goes to infinity in the absence of a bandwidth limitation.

AB - The problem of specifying the optimum quantum detector in multiple hypotheses testing is considered for application to optical communications. The quantum digital detection problem is formulated as a linear programming problem on an infinite-dimensional space. A necessary and sufficient condition is derived by the application of a general duality theorem specifying the optimum detector in terms of a set of linear operator equations and inequalities. Existence of the optimum quantum detector is also established. The optimality of commuting detection operators is discussed in some examples. The structure and performance of the optimal receiver are derived for the quantum detection of narrow-band coherent orthogonal and simplex signals. It is shown that modal photon counting is asymptotically optimum in the limit of a large signaling alphabet and that the capacity goes to infinity in the absence of a bandwidth limitation.

UR - http://www.scopus.com/inward/record.url?scp=0016485946&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0016485946&partnerID=8YFLogxK

U2 - 10.1109/TIT.1975.1055351

DO - 10.1109/TIT.1975.1055351

M3 - Article

AN - SCOPUS:0016485946

VL - 21

SP - 125

EP - 134

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

SN - 0018-9448

IS - 2

ER -