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arXiv:1501.05256 · Physical Review A

Comparative study of nonclassicality, entanglement, and dimensionality of multimode noisy twin beams

Ievgen I. Arkhipov, Jan Peřina, Jan Peřina, Adam Miranowicz

Published Mar 31, 2015• 32 citations
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Abstract

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.

DOI
10.1103/physreva.91.033837

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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.
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.
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.
Robust and reliable method for reconstructing quasidistributions of integrated intensities of twin beams generated in spontaneous parametric down conversion and entangled in photon numbers is suggested. It utilizes the first and second photocount moments and minimizes the declination from experimental photocount histograms. Qualitatively, different forms of quasidistributions for quantum and classical states are suggested in the method. The transition from quantum to classical states caused by an increased detection noise is discussed. Momentum criterion for nonclassicality of twin beams is suggested.
We present a robust tool to analyze nonclassical properties of multimode twin-beam states in the mesoscopic photon-number domain. The measurements are performed by direct detection. The analysis exploits three different nonclassicality criteria for detected photons exhibiting complementary behavior in the explored intensity regime. Joint signal-idler photon-number distributions and quasidistributions of integrated intensities are determined and compared with the corresponding distributions of detected photons. Experimental conditions optimal for nonclassical properties of twin-beam states are identified.
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.
Quantum properties of light, which are crucial resources for quantum technologies, are quite fragile in nature and can be degraded and even concealed by the environment. We show, both theoretically and experimentally, that mesoscopic twin-beam states of light can preserve their nonclassicality even in the presence of major losses and different types of noise, thus suggesting their potential usefulness to encode information in quantum communication protocols. We develop a comprehensive general analytical model for a measurable nonclassicality criterion and find thresholds on noise and losses for the survival of entanglement in the twin beam.