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New kind of asymmetric projection integral operators and parity measurement

S. Wang, Z. P. Wang, Jiandong Zhang

Published Oct 22, 2020• 0 citations
OpenAlex

Abstract

By means of the technique of integration within an ordered product of operators and Dirac notation, we introduce a kind of Hermitian operator constructed by entangled state representations. For such a Hermitian operator, we rigorously prove that it corresponds to a parity measurement combined with a beam splitter when any two-mode quantum state passes through such device. Therefore we obtain a new relation between a Hermitian operator and the entangled state representations.

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By means of the technique of integration within an ordered product of operators and Dirac notation, we introduce a kind of Hermitian operator constructed by entangled state representations. For such a Hermitian operator, we rigorously prove that it corresponds to a parity measurement combined with a beam splitter when any two-mode quantum state passes through such device. Therefore we obtain a new relation between a Hermitian operator and the entangled state representations.
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.
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 A beam splitter operator is a very important linear device in the field of quantum optics and quantum information. It can not only be used to prepare complete representations of quantum mechanics, entangled state representation, but it can also be used to simulate the dissipative environment of quantum systems. In this paper, by combining the transform relation of the beam splitter operator and the technique of integration within the product of the operator, we present the coherent state representation of the operator and the corresponding normal ordering form. Based on this, we consider the applications of the coherent state representation of the beam splitter operator, such as deriving some operator identities and entangled state representation preparation with continuous-discrete variables. Furthermore, we extend our investigation to two single and two-mode cascaded beam splitter operators, giving the corresponding coherent state representation and its normal ordering form. In addition, the application of a beam splitter to prepare entangled states in quantum teleportation is further investigated, and the fidelity is discussed. The above results provide good theoretical value in the fields of quantum optics and quantum information.