Abstract

An algorithmic proof that any discrete finite-dimensional unitary operator can be constructed in the laboratory using optical devices is given. Our recursive algorithm factorizes any N\ifmmode\times\else\texttimes\fi{}N unitary matrix into a sequence of two-dimensional beam splitter transformations. The experiment is built from the corresponding devices. This also permits the measurement of the observable corresponding to any discrete Hermitian matrix. Thus optical experiments with any type of radiation (photons, atoms, etc.) exploring higher-dimensional discrete quantum systems become feasible.

Keywords

Realization (probability)Beam splitterHermitian matrixUnitary stateOperator (biology)ObservableUnitarityMatrix (chemical analysis)PhysicsUnitary matrixQuantum opticsQuantum mechanicsPure mathematicsAlgebra over a fieldMathematics

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Publication Info

Year
1994
Type
article
Volume
73
Issue
1
Pages
58-61
Citations
1991
Access
Closed

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1991
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Cite This

Michael Reck, Anton Zeilinger, H. J. Bernstein et al. (1994). Experimental realization of any discrete unitary operator. Physical Review Letters , 73 (1) , 58-61. https://doi.org/10.1103/physrevlett.73.58

Identifiers

DOI
10.1103/physrevlett.73.58