Abstract

Using the technique of integration within an ordered product of operators and Dirac notation, we introduce asymmetric integration projection operators in entangled state representations. These asymmetric projection operators are proven to be Hermitian. We demonstrate rigorously that they correspond to a parity measurement combined with a balanced beam splitter that provides an alternative method to analyze the signal of parity measurement. We use our method to revisit several previous schemes using parity measurement and exotic inputs. These results suggest that our work is useful for quantum metrology based on parity measurement.

© 2021 Optical Society of America

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