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

Physica Scripta

Generation of nonclassical states by superposition of number-conserving operations on squeezed thermal state

Wei Ye, Ying Guo, Huan Zhang, Ying Xia, Yun Jie Mao

Published Apr 14, 2021• 1 citation
Publisher

Abstract

Abstract The nonclassicality is the prerequisite for quantum states to be applied into quantum information, especially for quantum metrology. Here we theoretically investigate the non-classical properties of the non-Gaussian state generated by repeatedly operating a number-conserving generalized superposition of products (GSP), i.e., ( s 1 aa † + t 1 a † a ) m with s 1 2 + t 1 2 = 1 , on the squeezed thermal state (STS), in terms of second-order correlation function, Mandel’s Q parameter, quadrature squeezing and Wigner function (WF). It is shown that, compared to the cases of the STS, the GSP-STS with the high-order GSP operations ( m > 1) at the small-squeezing levels can be beneficial to the existence of the photon-antibunching effect, the sub-Poissonian distribution and the partial negativity of the WF, apart from the quadrature squeezing. In addition, for the case of m = 1, we also compare with the non-classical properties of several different non-Gaussian resources, involving the photon-subtracted-then-added (PSTA) STS, the GSP-STS and the photon-added-then-subtracted (PATS) STS. It is found that the PSTA-STS with respect to the sub-Poissonian distribution and the partial negativity of the WF has a better performance than others. Significantly, the generated GSP-STS has an obvious advantage of showing the photon-antibunching effects, compared to the PSTA-STS and the PATS-STS, which means that our scheme may have an excellent guidance for the practical implementations in quantum information.

DOI
10.1088/1402-4896/abf801

Related papers

Nonclassical properties of photon-added two-mode squeezed thermal states and their decoherence in the thermal channel

Xiang‐Guo Meng, Zhen Wang, Hong-Yi Fan +2 more

We investigate nonclassicality and decoherence of field states generated with the non-Gaussian operation of photon addition to a two-mode squeezed thermal state (TSTS) using the normally ordered density operator of the photon-added TSTS (PTSTS). The normalization factor of the PTSTS is just a Jacobi polynomial of the squeezing parameter γ and the average photon number n¯ of the thermal field. We show that the fields in such states exhibit remarkable quantum features, such as sub-Poissonian photon statistics, the anti-bunching effect, and photon-number distribution. The nonclassicality is discussed in phase space based on the partial negativity of the Wigner function (WF) with two-variable Hermite polynomials. The results show that the non-Gaussian WF always exhibits the quantum interference structure caused by the two-mode squeezing operation and has some negative regions for any value of n¯, γ, and the photon-addition numbers m, n. In addition, the effect of decoherence on the PTSTS in the thermal channel is studied by analytically deriving the time-evolution WF. We find that the WF becomes Gaussian (corresponding to a classical thermal state) at long times, losing its nonclassicality as a result of decoherence, and a larger m (or n) leads to a longer decoherence time κt.

Journal of the Optical Society of America B•Jun 29, 2012•40 citations

Photon-subtracted squeezed thermal state: Nonclassicality and decoherence

Liyun Hu, Xue-xiang Xu, Zisheng Wang +1 more

We investigate nonclassical properties of the field states generated by subtracting any number of photons from the squeezed thermal state (STS). It is found that the normalization factor of photon-subtracted STS (PSSTS) is a Legendre polynomial of squeezing parameter $r$ and average photon number $\mathrm{n\ifmmode \bar{}\else \={}\fi{}}$ of the thermal state. Expressions of several quasiprobability distributions of PSSTS are derived analytically. Furthermore, the nonclassicality is discussed in terms of the negativity of the Wigner function (WF). It is shown that the WF of single PSSTS always has negative values if $\mathrm{n\ifmmode \bar{}\else \={}\fi{}}<\mathrm{sinh}{}^{2}r$ at the phase space center. The decoherence effect on PSSTS is then included by analytically deriving the time evolution of WF. The results show that the WF of single PSSTS has negative value if $2\ensuremath{\kappa}t<\mathrm{ln}{1\ensuremath{-}(2\mathrm{n\ifmmode \bar{}\else \={}\fi{}}+1)(\mathrm{n\ifmmode \bar{}\else \={}\fi{}}\ensuremath{-}\mathrm{sinh}{}^{2}r)/[(2\mathfrak{N}+1)(\mathrm{n\ifmmode \bar{}\else \={}\fi{}}\mathrm{cosh}2r+\mathrm{sinh}{}^{2}r)]}$, which is dependent not only on average number $\mathfrak{N}$ of thermal photons in the environment, but also on $\mathrm{n\ifmmode \bar{}\else \={}\fi{}}$ and $r$.

arXiv:1008.5256•Physical Review A•Oct 29, 2010•115 citations

Nonclassicality and decoherence of photon-added squeezed thermal state in thermal environment

Liyun Hu, Zhi‐Ming Zhang

Theoretical analysis is given of nonclassicality and decoherence of the field states generated by adding any number of photons to the squeezed thermal state (STS). Based on the fact that the squeezed number state can be considered as a single-variable Hermite polynomial excited state, the compact expression of the normalization factor is derived, a Legendre polynomial. The nonclassicality is investigated by exploring the sub-Poissonian and negative Wigner function (WF). The results show that the WF of single-photon–added STS (PASTS) always has negative values at the phase space center. The decoherence effect on PASTS is examined by the analytical expression of WF. It is found that a longer threshold value of decay time than in single-photon–subtraction STS is included in single PASTS.

arXiv:1110.6587•Journal of the Optical Society of America B•Mar 2, 2012•36 citations

Nonclassical properties and decoherence of fields in photon-added squeezing-enhanced thermal states

Zhen Wang, Xiang‐Gao Meng, Heng-Mei Li +1 more

We put forward the photon-added squeezing-enhanced thermal states (PASETS) theoretically by adding photon to the squeezed enhancing thermal states (SETS) repeatedly. Based on the normally ordered density operator of PASETS, we investigate the nonclassical behavior of the PASETS by evaluating, both analytically and numerically, Mandel's Q-parameter, photon-number distribution (PND), and Wigner function (WF). It is found that smaller squeezing parameter r and thermal photon number nc can lead to more chance of the appearance of sub-Poissonian statistics. And it is shown that the PND of PASETS exhibit more remarkable oscillations than that of SETS in stronger squeezing case. The WF exhibit partial negativity in phase space and the squeezing parameter r can result in both squeezing and rotating effect. By investigating the fidelity between PASETS and SETS shows that the fidelity tender to steady values in the high value of squeezing parameter or thermal photon number. In addition, the decoherence effect on the PASETS is examined by the time-evolution of the analytical WF in thermal channel. The results show that the PASETS shall lose nonclassicality and non-Gaussianity and reduce to classical states with Gaussian distribution after sufficient time interaction with the thermal noise. And larger photon-added number or thermal photon number shall render shorter decoherence time.

International Journal of Modern Physics B•Apr 29, 2014•9 citations

Coherent operation of photon subtraction and addition for squeezed thermal states: analysis of nonclassicality and decoherence

Shuai Wang, Xue-xiang Xu, Hong‐Chun Yuan +2 more

We study nonclassical properties of the optical field when photon subtraction/addition coherent operation ta+ra† (|t|2+|r|2=1) acts on a squeezed thermal state (STS) by examining its quadrature squeezing, sub-Poissonian statistics, and negativity of the Wigner function. The degree of squeezing of the coherent operated squeezed thermal state (COSTS) becomes weaker. The Mandel Q parameter decreases with r and quickly becomes negative, which implies sub-Poissonian statistics. Both the negative dip and negative area of the Wigner function increase with r for small squeezing values of κ. Decoherence of the COSTS in an amplitude-damping channel is studied by the time evolution of the Wigner function. The length of time that this nonclassical field preserves its partial negativity of the Wigner function can be modulated by the coherent operation. All these results indicate that the nonclassicality of the STS is sensitive to the coherent operation.

Journal of the Optical Society of America B•Aug 15, 2011•10 citations

Improvement of the entanglement properties for entangled states using a superposition of number-conserving operations

Huan Zhang, Wei Ye, Ying Xia +3 more

Abstract The non-Gaussian operation, which can be easily implemented by current techniques, is an effective way for the improvement of the continuous-variable entanglement. Here, we theoretically propose a scheme for generating a number-conserving two-mode generalized superposition of products (TM-GSP) state by performing the -order GSP operations i.e. on an input two-mode squeezed vacuum (TMSV) state. Then, the entanglement properties of the TM-GSP state are analyzed detailedly by means of logarithmic negative, Einstein–Podolsky–Rosen (EPR) correlation and two-mode squeezing property. It is shown that, in contrast to the TMSV case, for the optimal choices of s 1 and s 2 , the entanglement properties of the TM-GSP state can be improved by using symmetric GSP operations ( ) and single-side GSP operations . Furthermore, the fidelity effect is also considered when the TM-GSP state is used as the entangled resource under the Braunstein and Kimble scheme. In terms of the optimal teleportation fidelity, it is found that the effect of the single GSP operation is equivalent to that of the case . This phenomenon also exists in logarithmic negative, EPR correlation and two-mode squeezing property. These results show that the prepared TM-GSP state may provide a well application in the fields of quantum information processing.

Laser Physics Letters•Jun 26, 2019•13 citations
Abstract The nonclassicality is the prerequisite for quantum states to be applied into quantum information, especially for quantum metrology. Here we theoretically investigate the non-classical properties of the non-Gaussian state generated by repeatedly operating a number-conserving generalized superposition of products (GSP), i.e., ( s 1 aa † + t 1 a † a ) m with s 1 2 + t 1 2 = 1 , on the squeezed thermal state (STS), in terms of second-order correlation function, Mandel’s Q parameter, quadrature squeezing and Wigner function (WF). It is shown that, compared to the cases of the STS, the GSP-STS with the high-order GSP operations ( m > 1) at the small-squeezing levels can be beneficial to the existence of the photon-antibunching effect, the sub-Poissonian distribution and the partial negativity of the WF, apart from the quadrature squeezing. In addition, for the case of m = 1, we also compare with the non-classical properties of several different non-Gaussian resources, involving the photon-subtracted-then-added (PSTA) STS, the GSP-STS and the photon-added-then-subtracted (PATS) STS. It is found that the PSTA-STS with respect to the sub-Poissonian distribution and the partial negativity of the WF has a better performance than others. Significantly, the generated GSP-STS has an obvious advantage of showing the photon-antibunching effects, compared to the PSTA-STS and the PATS-STS, which means that our scheme may have an excellent guidance for the practical implementations in quantum information.
We investigate nonclassicality and decoherence of field states generated with the non-Gaussian operation of photon addition to a two-mode squeezed thermal state (TSTS) using the normally ordered density operator of the photon-added TSTS (PTSTS). The normalization factor of the PTSTS is just a Jacobi polynomial of the squeezing parameter γ and the average photon number n¯ of the thermal field. We show that the fields in such states exhibit remarkable quantum features, such as sub-Poissonian photon statistics, the anti-bunching effect, and photon-number distribution. The nonclassicality is discussed in phase space based on the partial negativity of the Wigner function (WF) with two-variable Hermite polynomials. The results show that the non-Gaussian WF always exhibits the quantum interference structure caused by the two-mode squeezing operation and has some negative regions for any value of n¯, γ, and the photon-addition numbers m, n. In addition, the effect of decoherence on the PTSTS in the thermal channel is studied by analytically deriving the time-evolution WF. We find that the WF becomes Gaussian (corresponding to a classical thermal state) at long times, losing its nonclassicality as a result of decoherence, and a larger m (or n) leads to a longer decoherence time κt.
We investigate nonclassical properties of the field states generated by subtracting any number of photons from the squeezed thermal state (STS). It is found that the normalization factor of photon-subtracted STS (PSSTS) is a Legendre polynomial of squeezing parameter rrr and average photon number $\mathrm{n\ifmmode \bar{}\else \={}\fi{}}$ of the thermal state. Expressions of several quasiprobability distributions of PSSTS are derived analytically. Furthermore, the nonclassicality is discussed in terms of the negativity of the Wigner function (WF). It is shown that the WF of single PSSTS always has negative values if $\mathrm{n\ifmmode \bar{}\else \={}\fi{}}<\mathrm{sinh}{}^{2}r$ at the phase space center. The decoherence effect on PSSTS is then included by analytically deriving the time evolution of WF. The results show that the WF of single PSSTS has negative value if $2\ensuremath{\kappa}t<\mathrm{ln}{1\ensuremath{-}(2\mathrm{n\ifmmode \bar{}\else \={}\fi{}}+1)(\mathrm{n\ifmmode \bar{}\else \={}\fi{}}\ensuremath{-}\mathrm{sinh}{}^{2}r)/[(2\mathfrak{N}+1)(\mathrm{n\ifmmode \bar{}\else \={}\fi{}}\mathrm{cosh}2r+\mathrm{sinh}{}^{2}r)]}$, which is dependent not only on average number N\mathfrak{N}N of thermal photons in the environment, but also on $\mathrm{n\ifmmode \bar{}\else \={}\fi{}}$ and rrr.
Theoretical analysis is given of nonclassicality and decoherence of the field states generated by adding any number of photons to the squeezed thermal state (STS). Based on the fact that the squeezed number state can be considered as a single-variable Hermite polynomial excited state, the compact expression of the normalization factor is derived, a Legendre polynomial. The nonclassicality is investigated by exploring the sub-Poissonian and negative Wigner function (WF). The results show that the WF of single-photon–added STS (PASTS) always has negative values at the phase space center. The decoherence effect on PASTS is examined by the analytical expression of WF. It is found that a longer threshold value of decay time than in single-photon–subtraction STS is included in single PASTS.
We put forward the photon-added squeezing-enhanced thermal states (PASETS) theoretically by adding photon to the squeezed enhancing thermal states (SETS) repeatedly. Based on the normally ordered density operator of PASETS, we investigate the nonclassical behavior of the PASETS by evaluating, both analytically and numerically, Mandel's Q-parameter, photon-number distribution (PND), and Wigner function (WF). It is found that smaller squeezing parameter r and thermal photon number nc can lead to more chance of the appearance of sub-Poissonian statistics. And it is shown that the PND of PASETS exhibit more remarkable oscillations than that of SETS in stronger squeezing case. The WF exhibit partial negativity in phase space and the squeezing parameter r can result in both squeezing and rotating effect. By investigating the fidelity between PASETS and SETS shows that the fidelity tender to steady values in the high value of squeezing parameter or thermal photon number. In addition, the decoherence effect on the PASETS is examined by the time-evolution of the analytical WF in thermal channel. The results show that the PASETS shall lose nonclassicality and non-Gaussianity and reduce to classical states with Gaussian distribution after sufficient time interaction with the thermal noise. And larger photon-added number or thermal photon number shall render shorter decoherence time.
We study nonclassical properties of the optical field when photon subtraction/addition coherent operation ta+ra† (|t|2+|r|2=1) acts on a squeezed thermal state (STS) by examining its quadrature squeezing, sub-Poissonian statistics, and negativity of the Wigner function. The degree of squeezing of the coherent operated squeezed thermal state (COSTS) becomes weaker. The Mandel Q parameter decreases with r and quickly becomes negative, which implies sub-Poissonian statistics. Both the negative dip and negative area of the Wigner function increase with r for small squeezing values of κ. Decoherence of the COSTS in an amplitude-damping channel is studied by the time evolution of the Wigner function. The length of time that this nonclassical field preserves its partial negativity of the Wigner function can be modulated by the coherent operation. All these results indicate that the nonclassicality of the STS is sensitive to the coherent operation.
Abstract The non-Gaussian operation, which can be easily implemented by current techniques, is an effective way for the improvement of the continuous-variable entanglement. Here, we theoretically propose a scheme for generating a number-conserving two-mode generalized superposition of products (TM-GSP) state by performing the -order GSP operations i.e. on an input two-mode squeezed vacuum (TMSV) state. Then, the entanglement properties of the TM-GSP state are analyzed detailedly by means of logarithmic negative, Einstein–Podolsky–Rosen (EPR) correlation and two-mode squeezing property. It is shown that, in contrast to the TMSV case, for the optimal choices of s 1 and s 2 , the entanglement properties of the TM-GSP state can be improved by using symmetric GSP operations ( ) and single-side GSP operations . Furthermore, the fidelity effect is also considered when the TM-GSP state is used as the entangled resource under the Braunstein and Kimble scheme. In terms of the optimal teleportation fidelity, it is found that the effect of the single GSP operation is equivalent to that of the case . This phenomenon also exists in logarithmic negative, EPR correlation and two-mode squeezing property. These results show that the prepared TM-GSP state may provide a well application in the fields of quantum information processing.