New kind of asymmetric integration projection operators constructed by entangled state representations and parity measurement

Abstract

By means of the technique of integration within an ordered product of operators and Dirac notation, we introduce a new kind of asymmetric integration projection operators in entangled state representations. These asymmetric projection operators are proved to be the Hermitian operator. Then, we rigorously demonstrate that they correspond 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 representation. As applications, we recover the previous results of the parity measurement in quantum metrology by our formalism.