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

TL;DR

This paper introduces a novel class of asymmetric projection operators in entangled state representations, linking them to parity measurements and beam splitters, with applications in quantum metrology.

Contribution

It constructs new asymmetric integration projection operators using entangled states and parity measurement, establishing a new relation between Hermitian operators and entangled state representations.

Findings

Operators are Hermitian and correspond to parity measurements with beam splitters.

The formalism recovers previous results in quantum metrology.

Provides a new framework for understanding quantum measurement processes.

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.