### Abstract

General probabilistic theories provide the most general mathematical framework for the theory of probability in an operationally natural manner and generalize classical and quantum theories. In this article, we study state discrimination problems in general probabilistic theories using a Bayesian strategy. After reformulation of the theories with mathematical rigor, we first prove that an optimal observable to discriminate any (finite) number of states always exists in the most general setting. Next, we revisit our recently proposed geometric approach for the problem and show that for two-state discrimination, this approach is indeed effective in arbitrary dimensional cases. Moreover, our method reveals an operational meaning of Gudder's "intrinsic metric" by means of the optimal success probability, which turns out to be a generalization of the trace distance for quantum systems. As its by-product, an information disturbance theorem in general probabilistic theories is derived, generalizing its well known quantum version.

Original language | English |
---|---|

Article number | 093505 |

Journal | Journal of Mathematical Physics |

Volume | 51 |

Issue number | 9 |

DOIs | |

Publication status | Published - 2010 Sep |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Mathematical Physics*,

*51*(9), [093505]. https://doi.org/10.1063/1.3479008

**Optimal observables for minimum-error state discrimination in general probabilistic theories.** / Nuida, Koji; Kimura, Gen; Miyadera, Takayuki.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 51, no. 9, 093505. https://doi.org/10.1063/1.3479008

}

TY - JOUR

T1 - Optimal observables for minimum-error state discrimination in general probabilistic theories

AU - Nuida, Koji

AU - Kimura, Gen

AU - Miyadera, Takayuki

PY - 2010/9

Y1 - 2010/9

N2 - General probabilistic theories provide the most general mathematical framework for the theory of probability in an operationally natural manner and generalize classical and quantum theories. In this article, we study state discrimination problems in general probabilistic theories using a Bayesian strategy. After reformulation of the theories with mathematical rigor, we first prove that an optimal observable to discriminate any (finite) number of states always exists in the most general setting. Next, we revisit our recently proposed geometric approach for the problem and show that for two-state discrimination, this approach is indeed effective in arbitrary dimensional cases. Moreover, our method reveals an operational meaning of Gudder's "intrinsic metric" by means of the optimal success probability, which turns out to be a generalization of the trace distance for quantum systems. As its by-product, an information disturbance theorem in general probabilistic theories is derived, generalizing its well known quantum version.

AB - General probabilistic theories provide the most general mathematical framework for the theory of probability in an operationally natural manner and generalize classical and quantum theories. In this article, we study state discrimination problems in general probabilistic theories using a Bayesian strategy. After reformulation of the theories with mathematical rigor, we first prove that an optimal observable to discriminate any (finite) number of states always exists in the most general setting. Next, we revisit our recently proposed geometric approach for the problem and show that for two-state discrimination, this approach is indeed effective in arbitrary dimensional cases. Moreover, our method reveals an operational meaning of Gudder's "intrinsic metric" by means of the optimal success probability, which turns out to be a generalization of the trace distance for quantum systems. As its by-product, an information disturbance theorem in general probabilistic theories is derived, generalizing its well known quantum version.

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U2 - 10.1063/1.3479008

DO - 10.1063/1.3479008

M3 - Article

VL - 51

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 9

M1 - 093505

ER -