Nonclassicality and entanglement criteria for bipartite optical fields characterized by quadratic detectors

Abstract

Numerous inequalities involving moments of integrated intensities and revealing nonclassicality and entanglement in bipartite optical fields are derived using the majorization theory, non-negative polynomials, the matrix approach, as well as the Cauchy-Schwarz inequality. Different approaches for deriving these inequalities are compared. Using the experimental photocount histogram generated by a weak noisy twin beam monitored by a photon-number-resolving iCCD camera the performance of the derived inequalities is compared. A basic set of ten inequalities suitable for monitoring the entanglement of a twin beam is suggested. Inequalities involving moments of photocounts (photon numbers) as well as those containing directly the elements of photocount (photon-number) distributions are also discussed as a tool for revealing nonclassicality.

Complete identification of nonclassicality of Gaussian states via intensity moments

“…It is important to note that the NWs in Eqs. (10) and (11) can be used for the detection of nonclassicality for any kind of state of light, i.e., even for non-Gaussian states since the negativity of these NWs refers to nonclassical properties of the quasidistribution Glauber-Sudarshan P function [4, 21,38]. But they become optimal for complete nonclassicality detection only for Gaussian states.…”

Impact of photon addition and subtraction on nonclassical and phase properties of a displaced Fock state

“…Initially, such studies were restricted to the lower-order nonclassical features. In the recent past, various higher-order nonclassical features have been predicted theoretically [38][39][40][41][42] and confirmed experimentally ( [43,44] and references therein) in quantum states generated in nonlinear optical processes. (ii) Phase properties of the nonclassical states have been studied [45] by computing quantum phase fluctuations, phase dispersion, phase distribution functions, etc., under various formalisms, like Susskind and Glogower [46], Pegg-Barnett [47] and Barnett-Pegg [48] formalisms.…”

Reconstruction of Joint Photon-Number Distributions of Twin Beams Incorporating Spatial Noise Reduction

“…To monitor the performance of the noise reduction in the suggested reconstruction method, we need to quan-tify (quantum) correlations between the signal and idler fields both for the experimental photocounts and reconstructed photon numbers. Here, we show that the non-classicality depths τ [32] determined for the nonclassicality identifiers E k , k = 2, 3, 4, defined in terms of intensity moments W l as [33]…”

“…We note that an l-th intensity moment W l is related to the moments c k of photocounts by the formula W l = l k=1 S −1 lk c k that uses the Stirling numbers S lk of the second kind. We remind that a nonclassicality depth τ is given by the number of thermal photons needed to conceal nonclassical properties of an optical field visible in a given non-classicality identifier [33]. For comparison, we also determine the traditional covariance C ∆c of fluctuations of the numbers c s and c i of the signal and idler photocounts and sub-shot-noise parameter R c ,…”