Experimental realization of any discrete unitary operator
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Implication
Algorithmic study demonstrates optical construction of arbitrary finite-dimensional unitary operators via beam splitters, indicating higher-dimensional quantum experiments are feasible.
Key Points
- To establish a theoretical and algorithmic method for constructing any finite-dimensional discrete unitary operator and measuring any discrete Hermitian observable using optical setups.
- Designed a recursive algorithm that mathematically factorizes any N×N unitary matrix into a sequence of two-dimensional transformations.
- Mapped the decomposed mathematical operations directly to optical devices, specifically networks of two-port beam splitters.
- Demonstrated that any arbitrary discrete unitary operator can be realized physically in the laboratory through sequential beam splitter configurations.
- Showed that observables corresponding to any discrete Hermitian matrix can be measured, making higher-dimensional quantum experiments feasible for various radiation types, including photons and atoms.
Cite This Study
Reck et al. (1994) studied this question.