How to Measure the Quantum Measure

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.

References in corpus (14)

• Quantum Mechanics as Quantum Measure Theory
• A Classical Sequential Growth Dynamics for Causal Sets
• Ruling Out Multi-Order Interference in Quantum Mechanics
• The past of a quantum particle
• Solving the measurement problem: de Broglie-Bohm loses out to Everett
• Higher-order interference and single-system postulates characterizing quantum theory
• Non-classical paths in interference experiments
• An exercise in "anhomomorphic logic"
• Three Slit Experiments and the Structure of Quantum Theory
• On the superposition principle in interference experiments
• The Random Walk in Generalized Quantum Theory
• A Bell Inequality Analog in Quantum Measure Theory
• Quantum measures and the coevent interpretation
• Two-Site Quantum Random Walk

Cited by in corpus (7)

• A gentle introduction to Schwinger's formulation of quantum mechanics: The groupoid picture
• Schwinger's Picture of Quantum Mechanics I: Groupoids
• Schwinger's Picture of Quantum Mechanics III: The statistical interpretation
• From Green Function to Quantum Field
• Schwinger's Picture of Quantum Mechanics II: Algebras and Observables
• (2+1) Lorentzian quantum cosmology from spin-foams: opportunities and obstacles for semi-classicality
• Probability, Preclusion and Biological Evolution in Heisenberg-Picture Everett Quantum Mechanics