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arXiv · 1610.02087

How to Measure the Quantum Measure

Álvaro Mozota Frauca·Rafael Dolnick Sorkin
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Abstract

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.

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Álvaro Mozota Frauca, Rafael Dolnick Sorkin. 2016-10-06. How to Measure the Quantum Measure. https://doi.org/10.1007/s10773-016-3181-x

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