The parity operator: Applications in quantum metrology

Abstract

In this paper, we review the use of parity as a detection observable in quantum metrology as well as introduce some original findings with regards to measurement resolution in Ramsey spectroscopy and quantum non-demolition (QND) measures of atomic parity. Parity was first introduced in the context of Ramsey spectroscopy as an alternative to atomic state detection. It was latter adapted for use in quantum optical interferometry where it has been shown to be the optimal detection observable saturating the quantum Cramér-Rao bound for path symmetric states. We include a brief review of the basics of phase estimation and the connection between parity-based detection and the quantum Fisher information as it applies to quantum optical interferometry. We also discuss the efforts made in experimental methods of measuring photon-number parity and close the paper with a discussion on the use of parity leading to enhanced measurement resolution in multi-atom spectroscopy. We show how this may be of use in the construction of high-precision multiatom atomic clocks.We dedicate this paper to the memory of Jonathan P. Dowling, whose body of work had a tremendous impact on the fields of quantum optical interferometry and quantum metrology.

Quantum Fisher information maximization in an unbalanced interferometer

“…If the input state is separable, we employ the notations from (B2) to the QFI (G4) and the result is formally identical to the above one except that V cov = 0. In order to find the optimum transmission coefficient in the most general case, we apply the replacement (12) to equation (34) arriving at the result…”

“…The condition for having no metrological advantage with an external phase reference translates into F (i) = F (2p) , an equality that must be valid for any value of T . From equations (30) and (34) we immediately have…”

“…Finally, for a number of input states [14,24,25,[29][30][31][32][33][34], we obtain the optimum transmission coefficient, T opt , and thoroughly discuss the QFI performance for each scenario. Whenever possible, we compare our findings with previously reported ones in the literature.…”

Multi-headed symmetrical superpositions of coherent states

“…8 symmetry. Meanwhile, we can get the parity values through the relation Π = π 2 W ρ (0) after knowing the Wigner function [29]. In Fig.…”

Proposal for a quantum random number generator using coherent light an a non-classical observable

“…a field prepared in a coherent state by a phase-stabilized laser [13] (though even this condition will be later relaxed), and does not depend on beam splitting and on the path of the light propagation. Instead, it relies on the measurement of a quantum mechanical observable having no classical analog: photon-number parity [14], which is simply the evenness or oddness of photon numbers. The scheme is based on the fact that for a sufficiently large enough coherent state amplitude the average parity for the coherent state is zero, leading to the probability of producing the outcome "even" or "odd" under photon-number parity measurements being equalized to P even = P odd = 1/2.…”