Sequentially independent effects.

*(English)*Zbl 1016.47020In quantum mechanic, an effect is represented by an operator \(E\) on Hilbert space such that \(0\leq E\leq I\). The effects \(E_1,\dots,E_n\) are called sequentially independent if the results of any sequential measurement of \(E_1, \dots,E_n\) does not depend on the order, in which they are measured. The authors show that two effects are sequentially independent if and only if the operators commute. The authors also characterize the sequentially independent three effects.

Reviewer: Vladimir V.Peller (Manhattan)

##### MSC:

47B15 | Hermitian and normal operators (spectral measures, functional calculus, etc.) |

81P10 | Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) |

81P15 | Quantum measurement theory, state operations, state preparations |

47B65 | Positive linear operators and order-bounded operators |

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\textit{S. Gudder} and \textit{G. Nagy}, Proc. Am. Math. Soc. 130, No. 4, 1125--1130 (2002; Zbl 1016.47020)

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