Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1107.2771 · Physical Review A

Enhancing quantum entanglement for continuous variables by a coherent superposition of photon subtraction and addition

Su‐Yong Lee, Se-Wan Ji, Ho-Joon Kim, Hyunchul Nha

Published Jul 5, 2011• 159 citations
arXivHTMLPDF

Abstract

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 $r=0$) in the large-squeezing regime.

DOI
10.1103/physreva.84.012302

Related papers

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

Jia-Ni Wu, Shiyou Liu, Liyun Hu +3 more

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.

Journal of the Optical Society of America B•Oct 16, 2015•45 citations

Continuous-variable quantum teleportation with non-Gaussian entangled states generated via multiple-photon subtraction and addition

Shuai Wang, Li-Li Hou, Xianfeng Chen +1 more

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 $r$ 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 $r$.

arXiv:1411.7500•Physical Review A•Jun 25, 2015•101 citations

Increasing and decreasing entanglement characteristics for continuous variables by a local photon subtraction

Su‐Yong Lee, Se-Wan Ji, Chang-Woo Lee

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 $|\ensuremath{\alpha}|\ensuremath{\sim}0$.

arXiv:1305.6279•Physical Review A•May 24, 2013•27 citations

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

Shiyou Liu, Jie‐Hui Huang, Liyun Hu +3 more

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.

arXiv:1411.5499•Nov 20, 2014•0 citations

Entanglement of coherent superposition of photon-subtraction squeezed vacuum

Cunjin Liu, Wei Ye, Weidong Zhou +3 more

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.

Frontiers of Physics•Jul 26, 2017•20 citations

Enhancing quantum entanglement by photon addition and subtraction

Carlos Navarrete–Benlloch, Raúl García−Patrón, Jeffrey H. Shapiro +1 more

The non-Gaussian operations effected by adding or subtracting a photon on entangled optical beams emerging from a parametric down-conversion process have been suggested to enhance entanglement. Heralded photon addition or subtraction is, as a matter of fact, at the heart of continuous-variable entanglement distillation. The use of such processes has recently been experimentally demonstrated in the context of the generation of optical coherent-state superpositions or the verification of canonical commutation relations. Here, we carry out a systematic study of the effect of local photon additions and subtractions on a two-mode squeezed vacuum state, showing that the entanglement generally increases with the number of such operations. This is analytically proven when additions or subtractions are restricted to one mode only, while we observe that the highest entanglement is achieved when these operations are equally shared between the two modes. We also note that adding photons typically provides a stronger entanglement enhancement than subtracting photons, while photon subtraction performs better in terms of energy efficiency. Furthermore, we analyze the interplay between entanglement and non-Gaussianity, showing that it is more subtle than previously expected.

arXiv:1201.4120•Physical Review A•Jul 24, 2012•171 citations
We investigate how the entanglement properties of a two-mode state can be improved by performing a coherent superposition operation ta\ifmmode^\elseˆ\fi+ra\ifmmode^\elseˆ\fi\ifmmode†\else\textdagger\fit\mathrm{a\ifmmode \hat{}\else \^{}\fi{}}+r{\mathrm{a\ifmmode \hat{}\else \^{}\fi{}}}^{\ifmmode\dagger\else\textdagger\fi{}}ta\ifmmode^\elseˆ\fi+ra\ifmmode^\elseˆ\fi\ifmmode†\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 a\ifmmode^\elseˆ\fi\mathrm{a\ifmmode \hat{}\else \^{}\fi{}}a\ifmmode^\elseˆ\fi and the addition a\ifmmode^\elseˆ\fi\ifmmode†\else\textdagger\fi{\mathrm{a\ifmmode \hat{}\else \^{}\fi{}}}^{\ifmmode\dagger\else\textdagger\fi{}}a\ifmmode^\elseˆ\fi\ifmmode†\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.
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.
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 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 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 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.
The non-Gaussian operations effected by adding or subtracting a photon on entangled optical beams emerging from a parametric down-conversion process have been suggested to enhance entanglement. Heralded photon addition or subtraction is, as a matter of fact, at the heart of continuous-variable entanglement distillation. The use of such processes has recently been experimentally demonstrated in the context of the generation of optical coherent-state superpositions or the verification of canonical commutation relations. Here, we carry out a systematic study of the effect of local photon additions and subtractions on a two-mode squeezed vacuum state, showing that the entanglement generally increases with the number of such operations. This is analytically proven when additions or subtractions are restricted to one mode only, while we observe that the highest entanglement is achieved when these operations are equally shared between the two modes. We also note that adding photons typically provides a stronger entanglement enhancement than subtracting photons, while photon subtraction performs better in terms of energy efficiency. Furthermore, we analyze the interplay between entanglement and non-Gaussianity, showing that it is more subtle than previously expected.