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Journal of Optics B Quantum and Semiclassical Optics

Entanglement in quantum-optical bilinear devices

Matteo G. A. Paris

Published Jan 1, 1999• 4 citations
Publisher

Abstract

We examine the entanglement arising from the bilinear coupling of two nearly single-mode optical beams. We consider both the case of active and passive linear devices. The two modes are initially prepared in a pair of uncorrelated pure Gaussian states, and the degree of entanglement is analytically evaluated in terms of the excess information entropy at the output. A general formula is obtained and relevant cases are analysed in some detail.

DOI
10.1088/1464-4266/1/3/301

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We examine the entanglement arising from the bilinear coupling of two nearly single-mode optical beams. We consider both the case of active and passive linear devices. The two modes are initially prepared in a pair of uncorrelated pure Gaussian states, and the degree of entanglement is analytically evaluated in terms of the excess information entropy at the output. A general formula is obtained and relevant cases are analysed in some detail.
We investigate the entangling capability of passive optical elements, both qualitatively and quantitatively. We present a general necessary and sufficient condition for the possibility of creating distillable entanglement in an arbitrary multimode Gaussian state with the help of passive optical elements, thereby establishing a general connection between squeezing and the entanglement that is attainable by nonsqueezing operations. Special attention is devoted to general two-mode Gaussian states, for which we provide the optimal entangling procedure, present an explicit formula for the attainable degree of entanglement, and discuss several practically important special cases.
The entanglement of general asymmetric pure Gaussian two-mode states is examined in terms of the coefficients of the quadrature components of the wave function. The entanglement criterion and the entanglement of formation are directly evaluated as a function of these coefficients, without the need for local unitary transformations. These reproduce results for the special case of symmetric pure states which employ a relation between squeezed states and Einstein-Podolsky-Rosen correlations. The modification of the quadrature coefficients and the corresponding entanglement due to application of various optical elements is also derived.
It is theoretically proved that the two output light beams can be used as a pair of EPR(Einstin-Podolsky-Rosen) entangled beams when the incident light upon a beam splitter is a single mode quadrature-squeezed coherent state or a squeezed quantum soliton. It is the simplest scheme for preparing entangled states to our knowledge. The formulas explicitly show the correlation between the two nonclassical optical fields: squeezed states and entangled states. The affection of squeezing degree on entanglement is also investigated.
We study the energy exchange between two bosonic systems that interact via bilinear transformations in the mode operators. The first mode is considered as the thermodynamic system, while the second is regarded as the bath. This work finds its roots in a very recent formulation of quantum thermodynamics [Bera et al., Quantum 3, 121 (2019)] which allows one to consider baths that are not described by the usual Boltzmann-Gibbs canonical form. Baths can possess quantum properties, such as squeezing or coherence, and can be initially correlated with the system, even through entanglement. We focus mainly on the case of Gaussian states, by quantifying the relation between their defining parameters, namely the mean values of the quadratures and the covariance matrix, and relevant thermodynamical quantities such as the heat exchanged and the work performed during the interaction process. We fully solve the case of initially uncorrelated Gaussian states and provide the most general form of the first law of thermodynamics in this case. We also discuss the case of initially correlated states by considering a number of relevant examples, studying how correlations can assist some phenomena, e.g., work extraction or anomalous heat flows. Finally, we present an information-theoretic approach based on the Renyi entropy of order two for clarifying more generally the role of correlations on heat exchanges.