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Journal of the Optical Society of America B

Improving entanglement of even entangled coherent states by a coherent superposition of photon subtraction and addition

Jia-Ni Wu, Shiyou Liu, Liyun Hu, Jie‐Hui Huang, Zhenglu Duan, Yinghua Ji

Published Oct 16, 2015• 45 citations
Publisher

Abstract

A new entangled quantum state is introduced by applying local coherent superposition (CS) (ra†+ta) of photon subtraction and addition to each mode of an even entangled coherent state (EECS). The properties of entanglement are investigated in terms of the Einstein–Podolsky–Rosen (EPR) correlation, the degree of entanglement, and the average fidelity of quantum teleportation. It is found that single- and two-mode CS operations can improve the EPR correlation of the EECS in a big (>0.88) and small (<0.52) region of amplitude, respectively. The enhanced entanglement and fidelity depend on the even or odd order of CS. All optimal results are not achieved at two extreme cases of t=0, 1.

DOI
10.1364/josab.32.002299

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Journal of the Optical Society of America B•Mar 16, 2021•1 citation
A new entangled quantum state is introduced by applying local coherent superposition (CS) (ra†+ta) of photon subtraction and addition to each mode of an even entangled coherent state (EECS). The properties of entanglement are investigated in terms of the Einstein–Podolsky–Rosen (EPR) correlation, the degree of entanglement, and the average fidelity of quantum teleportation. It is found that single- and two-mode CS operations can improve the EPR correlation of the EECS in a big (>0.88) and small (<0.52) region of amplitude, respectively. The enhanced entanglement and fidelity depend on the even or odd order of CS. All optimal results are not achieved at two extreme cases of t=0, 1.
A new entangled quantum state is introduced by applying local coherent superposition (ra^+ +ta) of photon subtraction and addition to each mode of even entangled coherent state (EECS) and the properties of entanglement are investigated. It is found that the Shchukin-Vogel inseparability, the degree of entanglement and the average fidelity of quantum teleportation of the EECS can be improved due to the coherent superposition operation. The effects of improvement by coherent superposition operation are better than those by single (a^+) and two-photon (a^+ b^+) addition operations under a small region of amplitude.
A scheme for improving entanglement is proposed by repeatedly performing number-conserving generalized superposition of products (GSP) operation, i.e., (saa†+ta†a)m with s²+t²=1, on each modes of even entangled coherent state (EECS). Both Einstein-Podolsky-Rosen (EPR) correlation and concurrence are used as the measures for describing entanglement. It is found that both single-mode and two-mode-symmetric GSP operations can be used for the entanglement improvement. In particular, for the optimal EPR correlation, the GSP-EECS with two-mode-symmetric first-order operations presents a better performance for the entanglement improvement than the cases of high-order GSP operations. Compared to several special non-Gaussian operations, including photon subtraction-then-addition (PSTA) (s=0) and photon-addition-then-subtraction (PATS) (s=1), it is shown that the entanglement of GSP-EECS is always superior to those of both PSTA-EECS and PATS-EECS at a small amplitude level. When the GSP-EECS is used as the entangled resource for teleportation, our optimal teleportation fidelity presents the best performance.
We investigate how the entanglement properties of a two-mode state can be improved by performing a coherent superposition operation $t\mathrm{a\ifmmode \hat{}\else \^{}\fi{}}+r{\mathrm{a\ifmmode \hat{}\else \^{}\fi{}}}^{\ifmmode\dagger\else\textdagger\fi{}}$ of photon subtraction and addition, proposed by Lee and Nha [Phys. Rev. A 82, 053812 (2010)], on each mode. We show that the degree of entanglement, the Einstein-Podolsky-Rosen--type correlation, and the performance of quantum teleportation can be all enhanced for the output state when the coherent operation is applied to a two-mode squeezed state. The effects of the coherent operation are more prominent than those of the mere photon subtraction $\mathrm{a\ifmmode \hat{}\else \^{}\fi{}}$ and the addition ${\mathrm{a\ifmmode \hat{}\else \^{}\fi{}}}^{\ifmmode\dagger\else\textdagger\fi{}}$ particularly in the small-squeezing regime, whereas the optimal operation becomes the photon subtraction (case of r=0r=0r=0) in the large-squeezing regime.
We investigate how the entanglement characteristics of a non-Gaussian entangled state are increased or decreased by a local photon subtraction operation. The non-Gaussian entangled state is generated by injecting a single-mode non-Gaussian state and a vacuum state into a 50:50 beam splitter. We consider a photon-added coherent state ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}^{\ifmmode\dagger\else\textdagger\fi{}}|\ensuremath{\alpha}\ensuremath{\rangle}$ and an odd coherent state $|\ensuremath{\alpha}\ensuremath{\rangle}\ensuremath{-}|\ensuremath{-}\ensuremath{\alpha}\ensuremath{\rangle}$ as a single-mode non-Gaussian state. In the regime of small $|\ensuremath{\alpha}|$, we show that the performance of quantum teleportation and the second-order Einstein-Podolsky-Rosen-type correlation can both be enhanced, whereas the degree of entanglement decreases, for the output state when a local photon subtraction operation is applied to the non-Gaussian entangled state. The counterintuitive effect is more prominent in the limit of $|\ensuremath{\alpha}|\ensuremath{\sim}0$.
A new kind of non-Gaussian quantum state is introduced by applying nonlocal coherent superposition (τa + sb) m of photon subtraction to two single-mode squeezed vacuum states, and the properties of entanglement are investigated according to the degree of entanglement and the average fidelity of quantum teleportation. The state can be seen as a single-variable Hermitian polynomial excited squeezed vacuum state, and its normalization factor is related to the Legendre polynomial. It is shown that, for τ = s, the maximum fidelity can be achieved, even over the classical limit (1/2), only for even-order operation m and equivalent squeezing parameters in a certain region. However, the maximum entanglement can be achieved for squeezing parameters with a π phase difference. These indicate that the optimal realizations of fidelity and entanglement could be different from one another. In addition, the parameter τ/s has an obvious effect on entanglement and fidelity.
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.