Sequentially independent effects. (English) Zbl 1016.47020

In 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.


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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