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Weak values under uncertain conditions

Research output: Contribution to journalJournal article

Published
<mark>Journal publication date</mark>1/01/2010
<mark>Journal</mark>Physica E: Low-dimensional Systems and Nanostructures
Issue number3
Volume42
Number of pages5
Pages (from-to)343-347
Publication statusPublished
Original languageEnglish

Abstract

We analyze the average of weak values over statistical ensembles of pre- and post-selected states. The protocol of weak values, proposed by Aharonov et al. [Phys. Rev. Lett. 60 (1988) 1351], is the result of a weak measurement conditional on the outcome of a subsequent strong (projective) measurement. Weak values can be beyond the range of eigenvalues of the measured observable and, in general, can be complex numbers. We show that averaging over ensembles of pre- and post-selected states reduces the weak value within the range of eigenvalues of over(A, ^). We further show that the averaged result expressed in terms of pre- and post-selected density matrices, allows us to include the effect of decoherence.