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How to measure the quantum measure. In memory of David Ritz Finkelstein. (English) Zbl 1368.81028

Summary: The histories-based framework of Quantum Measure Theory assigns a generalized probability or measure \(\mu(E)\) to every (suitably regular) set \(E\) of histories. Even though \(\mu(E)\) cannot in general be interpreted as the expectation value of a selfadjoint operator (or POVM), we describe an arrangement which makes it possible to determine \(\mu(E)\) experimentally for any desired \(E\). Taking, for simplicity, the system in question to be a particle passing through a series of Stern-Gerlach devices or beam-splitters, we show how to couple a set of ancillas to it, and then to perform on them a suitable unitary transformation followed by a final measurement, such that the probability of a final outcome of “yes” is related to \(\mu(E)\) by a known factor of proportionality. Finally, we discuss in what sense a positive outcome of the final measurement should count as a minimally disturbing verification that the microscopic event \(E\) actually happened.

MSC:

81P05 General and philosophical questions in quantum theory
46G10 Vector-valued measures and integration
81P15 Quantum measurement theory, state operations, state preparations
01A70 Biographies, obituaries, personalia, bibliographies

Biographic References:

Finkelstein, David Ritz
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