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Acta Physica Sinica

Entanglement of one- and two-mode combination squeezed thermal states and its application in quantum teleportation

Liu Shi-You, Zheng Kai-Min, Fang Jia, Liyun Hu, Xie Fang-Sen

Published Jan 1, 2014• 2 citations
Publisher

Abstract

In view of the fact that one- and two-mode combination squeezed vacuum states may exhibit stronger squeezing in a certain range, we introduce one- and two-mode combination squeezed thermal states (OTCSTS) and investigate the property of entanglement in detail. Using the remarkable property of Weyl ordering, i.e., the order-invariance of Weyl ordered operator under similar transformations, we conveniently derive the analytical expression of entanglement degree-logarithmic negativity, and then present the condition of keeping entanglement for these squeezed thermal states. It is found that the OTCSTS possesses higher entanglement than the usual two-mode squeezed thermal states for any non-zero squeezing parameter. As an application, the quantum teleportation for coherent state is considered by using the OTCSTS as an entangled channel. It is shown that the teleportation fidelity can only be enhanced within a certain range of parameters, which is just the same as the condition of exhibiting stronger squeezing in one quadrature. In addition, the condition of realizing effective quantum teleportation (>1/2) is obtained analytically.

DOI
10.7498/aps.63.140302

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In view of the fact that one- and two-mode combination squeezed vacuum states may exhibit stronger squeezing in a certain range, we introduce one- and two-mode combination squeezed thermal states (OTCSTS) and investigate the property of entanglement in detail. Using the remarkable property of Weyl ordering, i.e., the order-invariance of Weyl ordered operator under similar transformations, we conveniently derive the analytical expression of entanglement degree-logarithmic negativity, and then present the condition of keeping entanglement for these squeezed thermal states. It is found that the OTCSTS possesses higher entanglement than the usual two-mode squeezed thermal states for any non-zero squeezing parameter. As an application, the quantum teleportation for coherent state is considered by using the OTCSTS as an entangled channel. It is shown that the teleportation fidelity can only be enhanced within a certain range of parameters, which is just the same as the condition of exhibiting stronger squeezing in one quadrature. In addition, the condition of realizing effective quantum teleportation (>1/2) is obtained analytically.
Considering the propagation of a two-mode optical field that is initially in a squeezed vacuum state in a thermal environment, we obtain an intuitive expression for inseparability condition of the two-mode mixed state which is given in the coherent state representation. This condition shows that the two modes have quantum entanglement if and only if the coefficient of the correlation term between the two modes is larger than that of the off-diagonal term of each mode in the density matrix. We find that even if the quantum channel is dynamically coupled to the thermal environment, the fidelity for teleporting coherent states larger than 1/2 is still the criterion for quantum teleportation. We also show that the entanglement, squeezing and quantum teleportation conditions are always consistent with each other.
Abstract The coherent photon-subtracted two-mode squeezed thermal states (CPS-TMSTS) are theoretically introduced by successively performing coherent photon subtraction operation on the two-mode squeezed thermal states (TMSTS). Based upon the normalization factor which is related to bivariate Hermite polynomials, the nonclassicality and non-Gaussianity are analyzed according to the Wigner function. It is shown that the coherent photon subtraction operation is an effective manner in generating nonclassicality and non-Gaussianity. Furthermore, the fidelity in teleporting coherent states using CPS-TMSTS as entangled resources is quantified both analytically and numerically. It is shown that the quantities of fidelity are clearly larger than that in the original TMSTS, and it can be further improved by modulating control parameters effectively. The CPS-TMSTS, as the ideal entangled resources with higher quantum teleportation fidelity, shall have potential applications in quantum optics tasks.
I theoretically investigate how the entanglement properties of a two-mode squeezed vacuum state (TMSVS) can be enhanced by operating quantum-optical catalysis on each mode of the TMSVS. The quantum-optical catalysis is simply mixing one photon at the beam splitter and post-select the beam-splitter (BS) output based on detection of one photon, first proposed by Lvovsky and Mlynek [Phys. Rev. Lett. 88, 250401 (2002)]. I find that there exists some enhancement in the entanglement properties (namely, entanglement entropy, second-order Einstein-Podolsky-Rosen correlation, and the fidelity of quantum teleportation) in certain parameter ranges spanned by the low transmissivities of the BSs and the small squeezing parameter of the input TMSVS.
We introduce a kind of non-Gaussian entangled state, which can be obtained by operating a non-local coherent photon-subtraction operation on a two-mode squeezed vacuum. It is found that its normalization factor is only related to the Legendre polynomials, which is a compact expression. Its statistical properties are discussed by the negative region Wigner function with the analytical expression. As an application, the quantum teleportation for coherent states is considered by using the non-Gaussian state as an entangled channel. It is found that the teleportation fidelity can be enhanced by this non-Gaussian operation.
We introduce a kind of entangled state—a photon-addition two-mode squeezed thermal state (TMSTS)—by adding photons to each mode of the TMSTS. Using the P-representation of thermal state, the compact expression of the normalization factor is derived, a Jacobi polynomial. The nonclassicality is investigated by exploring especially the negativity of Wigner function. The entanglement is discussed by using Shchukin–Vogel criteria. It is shown that the photon addition to the TMSTS may be more effective for the entanglement enhancement than the photon subtraction from the TMSTS. In addition, the quantum teleportation is also examined, which shows that symmetrical photon-added TMSTS may be more useful for quantum teleportation than the nonsymmetric case.
We theoretically analyze the Einstein-Podolsky-Rosen (EPR) correlation, the quadrature squeezing, and the continuous-variable quantum teleportation when considering non-Gaussian entangled states generated by applying multiple-photon subtraction and multiple-photon addition to a two-mode squeezed vacuum state (TMSVs). Our results indicate that in the case of the multiple-photon-subtracted TMSVs with symmetric operations, the corresponding EPR correlation, the two-mode squeezing degree, the sum squeezing, and the fidelity of teleporting a coherent state or a squeezed vacuum state can be enhanced for any squeezing parameter rrr and these enhancements increase with the number of subtracted photons in the low-squeezing regime, while asymmetric multiple-photon subtractions will generally reduce these quantities. For the multiple-photon-added TMSVs, although it holds stronger entanglement, its EPR correlation, two-mode squeezing, sum squeezing, and the fidelity of a coherent state are always smaller than that of the TMSVs. Only when considering the case of teleporting a squeezed vacuum state does the symmetric photon addition make somewhat of an improvement in the fidelity for large-squeezing parameters. In addition, we analytically prove that a one-mode multiple-photon-subtracted TMSVs is equivalent to that of the one-mode multiple-photon-added one. And one-mode multiple-photon operations will diminish the above four quantities for any squeezing parameter rrr.