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Optical Implementation of 2 × 2 Universal Unitary Matrix Transformations
Author(s) -
MachoOrtiz Andrés,
PérezLópez Daniel,
Capmany José
Publication year - 2021
Publication title -
laser and photonics reviews
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.778
H-Index - 116
eISSN - 1863-8899
pISSN - 1863-8880
DOI - 10.1002/lpor.202000473
Subject(s) - unitary state , unitary transformation , computer science , unitary matrix , realization (probability) , matrix (chemical analysis) , photonics , topology (electrical circuits) , quantum , mathematics , physics , quantum mechanics , statistics , materials science , law , combinatorics , political science , composite material
Abstract Unitary operations are a specific class of linear transformations that have become an essential ingredient for the realization of classical and quantum information processing. The ability of implementing any n ‐dimensional unitary signal transformation by using a reconfigurable optical hardware has recently led to the pioneering concept of programmable linear optical processor, whose basic building block (BB) must be correctly designed to guarantee that the whole system is able to perform n × n universal (i.e., arbitrary) unitary matrix transformations. Here, it is demonstrated that the present architectures of the BB do not fulfil the universal unitary property (at least) in 2 × 2 optical processors, limiting the number of unitary matrix transformations that may be generated. Aiming to solve this fundamental constraint, the theoretical tools required to analyze and design 2 × 2 universal unitary optical circuits and their corresponding BBs are presented. The consequences of this mathematical framework are explored, obtaining a simple route to implement different BB architectures, all of them guaranteeing a true universal unitary functionality in the resulting 2 × 2 optical processors. These findings may pave the way to revisit the design of high‐dimensional unitary optical processors, unleashing the potential of programmable integrated photonics technology.