### Abstract

Buschs theorem deriving the standard quantum probability rule can be regarded as a more general form of Gleasons theorem. Here we show that a further generalization is possible by reducing the number of quantum postulates used by Busch. We do not assume that the positive measurement outcome operators are effects or that they form a probability operator measure. We derive a more general probability rule from which the standard rule can be obtained from the normal laws of probability when there is no measurement outcome information available, without the need for further quantum postulates. Our general probability rule has prediction-retrodiction symmetry and we show how it may be applied in quantum communications and in retrodictive quantum theory.

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

Article number | 043025 |

Number of pages | 13 |

Journal | New Journal of Physics |

Volume | 16 |

DOIs | |

Publication status | Published - 29 Apr 2014 |

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### Keywords

- quantum information
- quantum probability
- quantum theory

### Cite this

*New Journal of Physics*,

*16*, [043025]. https://doi.org/10.1088/1367-2630/16/4/043025

}

*New Journal of Physics*, vol. 16, 043025. https://doi.org/10.1088/1367-2630/16/4/043025

**Quantum probability rule : a generalization of the theorems of Gleason and Busch.** / Barnett, Stephen M.; Cresser, James D.; Jeffers, John; Pegg, David T.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Quantum probability rule

T2 - New Journal of Physics

AU - Barnett, Stephen M.

AU - Cresser, James D.

AU - Jeffers, John

AU - Pegg, David T.

PY - 2014/4/29

Y1 - 2014/4/29

N2 - Buschs theorem deriving the standard quantum probability rule can be regarded as a more general form of Gleasons theorem. Here we show that a further generalization is possible by reducing the number of quantum postulates used by Busch. We do not assume that the positive measurement outcome operators are effects or that they form a probability operator measure. We derive a more general probability rule from which the standard rule can be obtained from the normal laws of probability when there is no measurement outcome information available, without the need for further quantum postulates. Our general probability rule has prediction-retrodiction symmetry and we show how it may be applied in quantum communications and in retrodictive quantum theory.

AB - Buschs theorem deriving the standard quantum probability rule can be regarded as a more general form of Gleasons theorem. Here we show that a further generalization is possible by reducing the number of quantum postulates used by Busch. We do not assume that the positive measurement outcome operators are effects or that they form a probability operator measure. We derive a more general probability rule from which the standard rule can be obtained from the normal laws of probability when there is no measurement outcome information available, without the need for further quantum postulates. Our general probability rule has prediction-retrodiction symmetry and we show how it may be applied in quantum communications and in retrodictive quantum theory.

KW - quantum information

KW - quantum probability

KW - quantum theory

UR - http://www.scopus.com/inward/record.url?scp=84899885677&partnerID=8YFLogxK

U2 - 10.1088/1367-2630/16/4/043025

DO - 10.1088/1367-2630/16/4/043025

M3 - Article

VL - 16

JO - New Journal of Physics

JF - New Journal of Physics

SN - 1367-2630

M1 - 043025

ER -