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Direct measurement of large-scale quantum states via expectation values of non-Hermitian matrices.

ABSTRACT: In quantum mechanics, predictions are made by way of calculating expectation values of observables, which take the form of Hermitian operators. Non-Hermitian operators, however, are not necessarily devoid of physical significance, and they can play a crucial role in the characterization of quantum states. Here we show that the expectation values of a particular set of non-Hermitian matrices, which we call column operators, directly yield the complex coefficients of a quantum state vector. We provide a definition of the state vector in terms of measurable quantities by decomposing these column operators into observables. The technique we propose renders very-large-scale quantum states significantly more accessible in the laboratory, as we demonstrate by experimentally characterizing a 100,000-dimensional entangled state. This represents an improvement of two orders of magnitude with respect to previous phase-and-amplitude characterizations of discrete entangled states.

SUBMITTER: Bolduc E

PROVIDER: S-EPMC4735685 | biostudies-literature | 2016 Jan

REPOSITORIES: biostudies-literature

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Direct measurement of large-scale quantum states via expectation values of non-Hermitian matrices.

Bolduc Eliot E Gariepy Genevieve G Leach Jonathan J

Nature communications 20160119

In quantum mechanics, predictions are made by way of calculating expectation values of observables, which take the form of Hermitian operators. Non-Hermitian operators, however, are not necessarily devoid of physical significance, and they can play a crucial role in the characterization of quantum states. Here we show that the expectation values of a particular set of non-Hermitian matrices, which we call column operators, directly yield the complex coefficients of a quantum state vector. We pro ...[more]

PMID: 26780858

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