The parity operator in quantum optical metrology

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.Comment: to be published in Contemporary Physic

Adaptive phase estimation with two-mode squeezed vacuum and parity measurement

“…This is not a problem in the case of limitless resources or in the case of samples that can withstand large doses of radiation. However, in order to achieve a finer precision given a finite amount of resources, one has to resort to interferometry with quantum states of light, such as N00N states [2] with parity measurements [3,4], in order to achieve sub-shot-noise or the Heisenberg limit (HL) to sensitivity of phase estimation. Squeezed vacuum, which is the brightest experimentally available nonclassical light, has received much attention.…”

Thermal state truncation by using quantum-scissors device

“…As Gerry pointed out that the Wigner function at the origin is the expectation value of the parity operator Π = (−1)n, that is Π = π 2 W (0) [33]. Thus, we have Π ρ th = 1/ (2n + 1) for the input thermal state and…”

Connecting measurement invasiveness to optimal metrological scenarios

“…Parity has been shown to be useful in quantum optical metrology [32,33] and has also been used in Ref. [9] as part of a model where the LGI violation is controlled through a parameter determining the invasiveness of a POVM.…”