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

Eliot Bolduc (), Genevieve Gariepy and Jonathan Leach
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Eliot Bolduc: Institute of Photonics and Quantum Sciences, School of Engineering & Physical Sciences, Heriot-Watt University
Genevieve Gariepy: Institute of Photonics and Quantum Sciences, School of Engineering & Physical Sciences, Heriot-Watt University
Jonathan Leach: Institute of Photonics and Quantum Sciences, School of Engineering & Physical Sciences, Heriot-Watt University

Nature Communications, 2016, vol. 7, issue 1, 1-6

Abstract: 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.

Date: 2016
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DOI: 10.1038/ncomms10439

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