Journal
NATURE COMMUNICATIONS
Volume 7, Issue -, Pages -Publisher
NATURE PUBLISHING GROUP
DOI: 10.1038/ncomms10439
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Funding
- FQRNT [176729, 173779]
- Engineering and Physical Sciences Research Council (EPSRC, UK) [EP/M006514/1, EP/M01326X/1]
- EPSRC [EP/M006514/1, EP/M01326X/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/M006514/1, EP/M01326X/1] Funding Source: researchfish
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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.
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