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Annalen der Physik

Continuous‐Variable Entanglement and Wigner‐Function Negativity via Adding or Subtracting Photons

Xiang‐Guo Meng, Kai‐Cai Li, Ji‐Suo Wang, Xiaoyan Zhang, Zhen‐Tao Zhang, Zhenshan S. Yang, Bao‐Long Liang

Published Apr 8, 2020• 36 citations
Publisher

Abstract

Abstract The performance of adding or subtracting photons on two‐mode squeezed thermal states via examining the Einstein–Podolsky–Rosen (EPR) correlation, the Hillery–Zubairy (HZ) correlation, the fidelity of teleportation, and the negativity of Wigner function is theoretically investigated. The normalization factors and the teleportation fidelity are related to Jacobi polynomials, and the (evolved) Wigner functions are simply associated with two‐variable Hermite polynomials. Compared with the original squeezed thermal states, the EPR correlation and the teleportation fidelity can be enhanced by photon subtraction and basically weakened by photon addition symmetric operations, but they cannot be enhanced for both photon addition and subtraction asymmetric cases. Also, HZ correlation can provide a better option relative to the EPR correlation in detecting the entanglement, and the fidelity for teleporting a squeezed state with a large squeezing can also be enhanced via photon addition symmetric operations, in contrast to teleporting a coherent state. Additionally, the nonclassicality is discussed in terms of the negativity of the (evolved) Wigner functions, which shows that photon addition and subtraction and the squeezing cannot restrain the deteriorate of nonclassicality, and the evolved Wigner functions become Gaussian (corresponding to vacuum) with long decay times as a result of amplitude decay.

DOI
10.1002/andp.201900585

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Abstract The performance of adding or subtracting photons on two‐mode squeezed thermal states via examining the Einstein–Podolsky–Rosen (EPR) correlation, the Hillery–Zubairy (HZ) correlation, the fidelity of teleportation, and the negativity of Wigner function is theoretically investigated. The normalization factors and the teleportation fidelity are related to Jacobi polynomials, and the (evolved) Wigner functions are simply associated with two‐variable Hermite polynomials. Compared with the original squeezed thermal states, the EPR correlation and the teleportation fidelity can be enhanced by photon subtraction and basically weakened by photon addition symmetric operations, but they cannot be enhanced for both photon addition and subtraction asymmetric cases. Also, HZ correlation can provide a better option relative to the EPR correlation in detecting the entanglement, and the fidelity for teleporting a squeezed state with a large squeezing can also be enhanced via photon addition symmetric operations, in contrast to teleporting a coherent state. Additionally, the nonclassicality is discussed in terms of the negativity of the (evolved) Wigner functions, which shows that photon addition and subtraction and the squeezing cannot restrain the deteriorate of nonclassicality, and the evolved Wigner functions become Gaussian (corresponding to vacuum) with long decay times as a result of amplitude decay.
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.
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 consider non-Gaussian states generated by photon subtraction (PS) and photon addition (PA) on two-mode squeezed coherent (TMSC) states as resource states for continuous variable quantum teleportation. To this end, we derive the Wigner characteristic function for the family of photon-subtracted and photon-added TMSC states, which is then utilized to calculate the fidelity of teleporting a single-mode coherent state and a squeezed vacuum state. The analysis shows that, while symmetric PS enhances the fidelity of teleportation in an extensive range of squeezing, asymmetric PS enhances the performance marginally and only in the low squeezing regime. The addition operations, however, are less useful, symmetric three-PA leads to a marginal improvement while the other addition operations are useless. We consider the actual experimental setup for PS and PA operations and compute their success probabilities, which should be kept in mind while advocating the use of these operations. We could compute the fidelity of teleportation for a broad range of states because we analytically derive the Wigner characteristic function for these family of states, which we think will be useful for various other applications of these families of states.
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.
For the first time, to the best of our knowledge, based on a two-mode squeezed vacuum (TMSV), we introduce photon-added orthogonal TMSVs and photon-subtracted orthogonal TMSVs via multiphoton addition a † k b † l and multiphoton subtraction a k b l ( k , l are arbitrary integers). As a comparison, we also consider photon-added TMSVs and photon-subtracted TMSVs. We theoretically analyze Einstein–Podolsky–Rosen (EPR) correlation and teleportation fidelity for all these two-mode states. Our results indicate that orthogonalization cannot enhance EPR correlation and teleportation fidelity, at least so far.
Abstract The significance of photon addition in engineering the single‐ and two‐mode (bipartite correlations) nonclassical properties of a quantum state is investigated. Specifically, the behavior of the Wigner function of two quasi‐Werner states constructed by superposing two normalized bipartite m‐photon added coherent states are analyzed. This allows the authors' to quantify the nonclassicality present in the quantum states using Wigner logarithmic negativity (WLN), while quantum correlations are measured using concurrence, entanglement of formation, and quantum discord. The WLN for a two‐mode state corresponds to the sum of the single‐mode nonclassicality and quantum correlations, and both of these are observed to enhance with photon addition manifesting the efficacy of photon addition in the entanglement distillation. Usefulness of photon addition is further established by showing that the performance of the quasi‐Werner states as quantum channel for the teleportation of single‐mode coherent and squeezed states, as quantified via teleportation fidelity, improves with the photon addition. The non‐Gaussian operation is shown effective in stalling the detrimental effects of transmission through noisy channel and/or inefficient detection under realistic scenario. Further, in contrast to a set of existing results, it is established that the negative values of two‐mode Wigner function is not a witness of quantum correlation.