### Abstract

Language | English |
---|---|

Pages | 1-4 |

Number of pages | 3 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 42 |

Issue number | 6 |

DOIs | |

Publication status | Published - 13 Feb 2009 |

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### Keywords

- quantum communications
- physics
- quantum theory

### Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*42*(6), 1-4. https://doi.org/10.1088/1751-8113/42/6/062001

}

*Journal of Physics A: Mathematical and Theoretical*, vol. 42, no. 6, pp. 1-4. https://doi.org/10.1088/1751-8113/42/6/062001

**On the conditions for discrimination between quantum states with minimum error.** / Barnett, S.M.; Croke, S.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the conditions for discrimination between quantum states with minimum error

AU - Barnett, S.M.

AU - Croke, S.

PY - 2009/2/13

Y1 - 2009/2/13

N2 - In quantum communications a transmitting party, Alice, selects from among a set of agreed quantum states to prepare a quantum system for transmission to the receiving party, Bob. Both the set of possible states, {ρˆi}, and the associated probabilities for selection, {pi}, are known to Bob but not, of course, the selected state. His task is to determine as well as he can which state was prepared and he does this by choosing a measurement to perform. If the states are not mutually orthogonal then there is no measurement that will reveal the selected state with certainty. The strategy he chooses will depend on the use for which the information is intended and there exist many figures of merit for Bob's measurement [1, 2]. Among these the simplest is the minimum probability of error or, equivalently, the maximum probability for correctly identifying the state. Necessary and sufficient conditions for realizing a minimum error measurement are known [3-6], but it has proven to be easier to prove sufficiency than necessity. This letter presents an appealingly simple proof that the conditions are necessary.

AB - In quantum communications a transmitting party, Alice, selects from among a set of agreed quantum states to prepare a quantum system for transmission to the receiving party, Bob. Both the set of possible states, {ρˆi}, and the associated probabilities for selection, {pi}, are known to Bob but not, of course, the selected state. His task is to determine as well as he can which state was prepared and he does this by choosing a measurement to perform. If the states are not mutually orthogonal then there is no measurement that will reveal the selected state with certainty. The strategy he chooses will depend on the use for which the information is intended and there exist many figures of merit for Bob's measurement [1, 2]. Among these the simplest is the minimum probability of error or, equivalently, the maximum probability for correctly identifying the state. Necessary and sufficient conditions for realizing a minimum error measurement are known [3-6], but it has proven to be easier to prove sufficiency than necessity. This letter presents an appealingly simple proof that the conditions are necessary.

KW - quantum communications

KW - physics

KW - quantum theory

UR - http://dx.doi.org/10.1088/1751-8113/42/6/062001

U2 - 10.1088/1751-8113/42/6/062001

DO - 10.1088/1751-8113/42/6/062001

M3 - Article

VL - 42

SP - 1

EP - 4

JO - Journal of Physics A: Mathematical and Theoretical

T2 - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 0305-4470

IS - 6

ER -