The parity operator in quantum optical metrology

TL;DR

This paper reviews how the parity operator in quantum optics enhances phase measurement sensitivity in interferometry, enabling detection beyond classical limits using entangled states, with potential applications in gravitational wave detection.

Contribution

It provides a comprehensive review of applying the parity operator to quantum metrology, highlighting its role in surpassing the shot-noise limit with entangled states.

Findings

Parity measurements can breach the standard quantum limit.

Heisenberg limit sensitivities are achievable with entangled states.

Potential applications in gravitational wave detection.

Abstract

Photon number states are assigned a parity of if their photon number is even and a parity of if odd. The parity operator, which is minus one to the power of the photon number operator, is a Hermitian operator and thus a quantum mechanical observable though it has no classical analog, the concept being meaningless in the context of classical light waves. In this paper we review work on the application of the parity operator to the problem of quantum metrology for the detection of small phase shifts with quantum optical interferometry using highly entangled field states such as the so-called N00N states, and states obtained by injecting twin Fock states into a beam splitter. With such states and with the performance of parity measurements on one of the output beams of the interferometer, one can breach the standard quantum limit, or shot-noise limit, of sensitivity down to the Heisenberg limit, the greatest degree of phase sensitivity allowed by quantum mechanics for linear phase shifts. Heisenberg limit sensitivities are expected to eventually play an important role in attempts to detect gravitational waves in interferometric detection systems such as LIGO and VIRGO.