What Quantum Measurements Measure

Abstract

A solution to the second measurement problem, determining what prior microscopic properties can be inferred from measurement outcomes ("pointer positions"), is worked out for projective and generalized (POVM) measurements, using consistent histories. The result supports the idea that equipment properly designed and calibrated reveals the properties it was designed to measure. Applications include Einstein's hemisphere and Wheeler's delayed choice paradoxes, and a method for analyzing weak measurements without recourse to weak values. Quantum measurements are noncontextual in the original sense employed by Bell and Mermin: if $[A,B]=[A,C]=0,[B,C]\ne 0$, the outcome of an $A$ measurement does not depend on whether it is measured with $B$ or with $C$. An application to Bohm's model of the Einstein-Podolsky-Rosen situation suggests that a faulty understanding of quantum measurements is at the root of this paradox.

29 pages, 5 figures. Similar to published version. Only significant change from v1 is the added paragraph at the end of Sec. V E, plus added Refs. [30], [42]

References in corpus (6)

• Hidden Variables and the Two Theorems of John Bell
• Is the quantum state real? An extended review of $\psi$-ontology theorems
• The contextual fraction as a measure of contextuality
• Translation of Lueders' "Uber die Zustandsanderung durch den Messprozess"
• Particle Path Through a Nested Mach-Zehnder Interferometer
• Contextuality under weak assumptions

Cited by in corpus (20)

• Kochen-Specker Contextuality
• Nonlocality Claims are Inconsistent with Hilbert Space Quantum Mechanics
• Contextual Wavefunction Collapse: An integrated theory of quantum measurement
• Understanding quantum mechanics: a review and synthesis in precise language
• Contextuality or nonlocality; what would John Bell choose today?
• Quantum Measurements and Contextuality
• On Joint Distributions, Counterfactual Values, and Hidden Variables in Relation to Contextuality
• Quantum postulate vs. quantum nonlocality: Is Devil in h?
• Reply to "Comment on 'Nonlocality claims are inconsistent with Hilbert-space quantum mechanics' '"
• Quantum randomness is chimeric
• Relational Quantum Mechanics and Contextuality
• Quantum Information: What Is It All About?
• Varieties of contextuality based on probability and structural nonembeddability
• Multitime Quantum Communication: Interesting But Not Counterfactual
• Inconsistency of a realistic interpretation of quantum measurements: A simple example
• Weak Particle Presence
• A theory of quantum (statistical) measurement
• Weak continuous measurements require more work than strong ones
• Violation of Bell Inequalities: Mapping the Conceptual Implications
• Logical inconsistencies in quantum mechanics