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arXiv:2010.11361 · Journal of the Optical Society of America B

Asymmetric integration projection operators constructed by entangled state representations and parity measurement

Shuai Wang, Zhiping Wang, Jiandong Zhang

Published Apr 14, 2021• 1 citation
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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.

DOI
10.1364/josab.417605

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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.
Abstract Operators play an important role in the formalism of quantum mechanics. By means of the technique of integration within an ordered product of operators and Dirac notation, we analytically prove that a new kind of asymmetric two-mode projection integral operator and another asymmetric two-mode Fock state projection summation operator are equal to the same Hermitian operator. For such Hermitian operator, we also rigorously demonstrate it corresponds to a parity measurement of a two-mode quantum state after passing through a beam splitter. The method used in this work provides a good exercise in quantum mechanics at the graduate level.
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Via the route of developing Dirac's symbolic method by virtue of the technique of integration within an ordered product (IWOP) of operators we derive various entangled state representations, squeezed states, and operator ordering formulae. We show how the entangled states can be applied to many aspects of quantum optics theory. The applications of the entangled states in the interdisciplinary study of quantum optics and Fourier optics are also introduced. All these discussions exhibit the power of Dirac's symbolic method with the aid of the IWOP technique.