Entanglement, weak values, and the precise inference of joint measurement outcomes for non-commuting observable pairs

TL;DR

This paper explores how entanglement and weak values enable precise inference of joint measurement outcomes for non-commuting observables in pre-and post-selected ensembles, revealing foundational insights.

Contribution

It demonstrates that for certain dense-spectrum observable pairs, entanglement and weak values allow accurate inference of joint measurement results, advancing quantum measurement theory.

Findings

Precise inference possible for certain dense-spectrum non-commuting observables

Entanglement with other systems enhances measurement inference

Explicit examples of solvable weak value assignments provided

Abstract

The problem of inferring the outcome of a simultaneous measurement of two non-commuting observables is addressed. We show that for certain pairs with dense spectra, precise inferences of the measurement outcomes are possible in pre-and post-selected ensembles, and if the selections involve entangled states with some other system. We show that the problem is related to the problem of assigning weak values to a continuous family of operators, and give explicit examples where this problem is solvable. Some foundational implications are briefly discussed.