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

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

2007-09-19

arxiv.org/abs/0709.2910v3

Physics

Quantum Physics

5 pages, no figures. Revised version: corrected typos, particularly in Eq. 8, and expanded references

Scientific paper

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.

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