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International Conference on Quantum Information

Entanglement, Postselection, and Precise Inferences in Joint Measurements of Incompatible Observables

Alonso Botero

Published Jan 1, 2008• 2 citations
Publisher

Abstract

We discuss conditions under which joint outcomes of simultaneous measurements of non-commuting canonical observables can be inferred with arbitrary precision. The feat is possible for certain pre- and postselections involving entanglement with ancillary systems.
DOI
10.1364/icqi.2008.jmb68

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According to Heisenberg's uncertainty relation, there is an ultimate limit to how precisely we may predict the outcome of position and momentum measurements on a quantum system. We show that this limit may be violated by an arbitrarily large factor if one aims, instead, to guess the unknown value of a past measurement. For experiments on a single quantum system, the precise assignment of past position and momentum measurement outcomes is accompanied by large uncertainty about their linear combinations, while we show that entanglement with an ancillary system permits accurate retrodiction of any such linear combination. Finally, we show that the outcomes of experiments that jointly measure multiple linear combinations of position and momentum observables by means of ancillary probe particles can also be guessed with no formal lower limit. We present quantitative results for projective measurements and for generalized measurements where all components are prepared in Gaussian states.
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