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arXiv:2007.08310 · Physical Review Applied

Experimental Quantification of the Entanglement of Noisy Twin Beams

Václav Michálek, Jan Peřina, Ondřej Haderka

Published Aug 3, 2020• 13 citations
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Abstract

Gradual loss of the entanglement of a twin beam containing around 25 photon pairs with the increasing external noise is experimentally investigated. The entanglement is quantified by the nonclassicality depths and the nonclassicality counting parameters related to several nonclassicality criteria. The reduction of intensity moments of the analyzed multimode twin beams to single-mode ones allows determination of the negativity as another quantifier of the entanglement. Both the raw photocount histograms and the reconstructed photon-number distributions are analyzed in parallel.

DOI
10.1103/physrevapplied.14.024003

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Gradual loss of the entanglement of a twin beam containing around 25 photon pairs with the increasing external noise is experimentally investigated. The entanglement is quantified by the nonclassicality depths and the nonclassicality counting parameters related to several nonclassicality criteria. The reduction of intensity moments of the analyzed multimode twin beams to single-mode ones allows determination of the negativity as another quantifier of the entanglement. Both the raw photocount histograms and the reconstructed photon-number distributions are analyzed in parallel.
The nonclassicality, entanglement, and dimensionality of a noisy twin beam are determined using a characteristic function of the beam written in the Fock basis. One-to-one correspondence between the negativity quantifying entanglement and the nonclassicality depth is revealed. Twin beams, which are either entangled or nonclassical (independent of their entanglement), are observed only for the limited degrees of noise, which degrades their quantumness. The dimensionality of the twin beam quantified by the participation ratio is compared with the dimensionality of entanglement determined from the negativity. Partitioning of the degrees of freedom of the twin beam into those related to entanglement and to noise is suggested. Both single-mode and multimode twin beams are analyzed. Weak nonclassicality based on integrated-intensity quasidistributions of multimode twin beams is studied. The relation of the model to the experimental twin beams is discussed.
Numerous nonclassicality criteria based on the probabilities of experimental photocount or theoretical photon-number distributions are derived using several approaches. Relations among the derived criteria are revealed and the fundamental criteria are identified. They are grouped into parametric systems that allow the analysis of the nonclassicality from different points of view (``local'' nonclassicality, pairwise character of photon correlations, etc.). Considering their structure, the criteria may be divided into groups that differ in the power to resolve the nonclassicality. Quantification of the nonclassicality using the Lee nonclassicality depth and the nonclassicality counting parameter is discussed. The number of field modes used is identified as an important parameter that may cause unexpected results. An appropriate linear transformation of a photocount (photon-number) distribution into its sss-ordered form, needed for the determination of the nonclassicality depth, is derived. For comparison, the derived criteria are applied both to an experimental photocount histogram of a twin beam and the reconstructed photon-number distributions with different levels of the noise.
States obtained from multimode twin beams by symmetric as well as asymmetric photon subtraction are experimentally investigated. Using the joint photocount distributions measured by an intensified CCD camera, their joint photon-number distributions are reconstructed. Mean photon numbers, Fano factors, and noise-reduction parameters are determined for the group of states reached by subtracting up to four photocounts in each beam. Photon subtraction is monitored using the nonclassicality depths and joint quasidistributions of integrated intensities of the emerging states. The non-Gaussianity of the obtained states is also determined. The states reached by coherent photon subtraction are also analyzed. The investigations represent an important step towards the use of photon-subtracted twin beams in sub-shot-noise metrology and imaging. Published by the American Physical Society 2024
Different non-classicality criteria expressed in the form of inequalities among intensity moments and elements of photon-number distributions are applied to noisy twin beams and other two-mode states obtained from a twin beam by using a beam splitter. Their performance in revealing the non-classicality is judged in comparison with the exact results provided by suitable entanglement and local non-classicality quantifiers. Whereas the non-classicality of noisy twin beams is always revealed by these criteria, not all the nonclassical states obtained at the output of the beam splitter can be identified by these experimentally easily reachable criteria.
Using the characteristic function of a twin beam composed of both paired and noise components we derive the corresponding statistical operator in the Fock-state basis. Applying the Peres-Horodecki criterion for a partially transposed statistical operator, we determine the negativity of the twin beam to quantify entanglement. In parallel, nonclassicality of the twin beam is quantified by nonclassical depth which is the acceptable amount of noise photons that preserves non-classicality manifested by negative values of the Glauber-Sudarshan quasiprobability function. The connection between entanglement and non-classicality is discussed considering the noise present either in one or both fields constituting the twin beam. Also the state of dimensionality via the Schmidt number as well as von Neumann entropy of the twin beam is analyzed.
Photons in twin beams exhibit correlations in both photon number and spatial detection position. Here spatial correlations in detection positions are exploited to develop a method for reconstructing the joint photon-number distribution of a twin beam from the experimental photocount histograms. This considerably reduces experimental noise, making it superior to the usual methods. This practical reconstruction method for spatially resolved photon counting is suitable for any application that requires joint photon-number distributions of twin beams, in e.g.e.g.e.g. metrology, or future quantum communication protocols.