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

Chinese Physics

Entanglement dynamics of Gaussian continuous states in correlated noisy channels

Huatang Tan, Xia Hong-Xing, Gao‐xiang Li

Published Jun 23, 2005• 11 citations
Publisher

Abstract

The evolution of the entanglement of an initial two-mode squeezed vacuum (TMSV) in correlated noisy channels is investigated. It is shown that the correlated environment is helpful for preserving the entanglement of the initial TMSV. The entanglement period of the initial TMSV depends on the correlation property of the correlated environment.

DOI
10.1088/1009-1963/14/7/020

Related papers

Entanglement and purity of two-mode Gaussian states in noisy channels

Alessio Serafini, Fabrizio Illuminati, Matteo G. A. Paris +1 more

We study the evolution of purity, entanglement, and total correlations of general two-mode continuous variable Gaussian states in arbitrary uncorrelated Gaussian environments. The time evolution of purity, von Neumann entropy, logarithmic negativity, and mutual information is analyzed for a wide range of initial conditions. In general, we find that a local squeezing of the bath leads to a faster degradation of purity and entanglement, while it can help to preserve the mutual information between the modes.

arXiv:quant-ph/0310087•Physical Review A•Feb 25, 2004•136 citations

Environment-induced two-mode entanglement in quantum Brownian motion

Christian Hörhammer, H. Büttner

The time evolution of quantum correlations of entangled two-mode continuous variable states is examined in single-reservoir as well as two-reservoir models, representing noisy correlated or uncorrelated non-Markovian quantum channels. For this purpose the model of quantum Brownian motion is extended. Various separability criteria for Gaussian continuous variable systems are applied. In both types of reservoir models moderate non-Markovian effects prolong the separability time scales. However, in these models the properties of the stationary state may differ. In the two-reservoir model the initial entanglement is completely lost and both modes are finally uncorrelated. In a common reservoir both modes interact indirectly via the coupling to the same bath variables. Below a critical bath temperature entanglement between the two modes is preserved even in the steady state. A separability criterion is derived, which depends on the bath temperature and the response function of the open quantum system. Thus, the extended quantum Brownian motion model of a two-mode continuous variable system in a common reservoir provides an example of environment-induced entanglement.

arXiv:0708.2670•Physical Review A•Apr 4, 2008•57 citations

Continuous-variable entanglement in a correlated spontaneous emission laser

Hua-tang Tan, Shi-Yao Zhu, Muhammad Suhail Zubairy

We discuss the generation and evolution of entangled light in a correlated spontaneous emission laser. The master equation for the two-mode field in a cavity is derived and solved analytically. The time-dependent characteristic function in the Wigner representation for the two-mode field is obtained. It shows that the two-mode field in the cavity evolves in a two-mode Gaussian state. The entanglement degree of the two-mode field in the cavity increases initially, then decreases, and finally vanishes as the field evolves from an initial vacuum. The period of the entanglement is extended as the intensity of the driving field is increased. It is found that the entanglement still exists even when the two-mode squeezing disappears. During the entanglement period, the intensity of the field is amplified. The entanglement for the initial field being a two-mode squeezed vacuum and the entanglement of the output field are also discussed.

Physical Review A•Aug 8, 2005•120 citations

Noisy dynamics of Gaussian entanglement: A transient bound entangled phase before separability

Gurvir Singh, Saptarshi Roy, Arvind

We describe Gaussian bound entangled states---entangled states with a positive partial transpose (PPT)---in four-mode continuous-variable systems. These states appear as a transient phase when certain entangled states with a negative partial transpose (NPT), also known as free entangled Gaussian states, are evolved under a noisy environment. Local thermal baths composed of harmonic oscillators are allowed to interact with one or more modes of the system and a wide variety of initial Gaussian entangled (NPT as well as PPT) states are studied. The robustness of entanglement is defined as the time duration for which the entanglement of the initial state is preserved under the noisy dynamics. We access the separability by utilizing standard semidefinite programming techniques. While most states lose their entanglement after a certain time across all bipartitions, an exception is observed for a three-parameter family of states which we call the generalized four-mode squeezed vacuum states, which transition to bound entangled states and remain so for a finite window of time. This dynamical onset of bound entanglement in continuous-variable systems is the central observation of our work. We carry out the analysis for Haar-random four-mode states (both pure and mixed) to scan the state space for a transient bound entangled phase.

arXiv:2503.12694•Physical Review A•Nov 12, 2025•0 citations

Environment-assisted creation and enhancement of two-mode entanglement in a joint decoherent model

Shao-Hua Xiang, Bin Shao, Kehui Song

We investigate the entanglement dynamics of two modes in a common squeezed thermal environment by means of the characteristic function method and the logarithmic negativity. When the two modes are prepared initially in separable squeezed states, we find that the external environment can not only induce but also enhance the two-mode entanglement if their initial squeezing parameters are suitably chosen. When the two modes are initially in a two-mode squeezed vacuum state, we find that whether the initial entanglement is degraded or increased depends strongly on the difference between the squeezing parameters of the considered bath and of a quantum state. Finally, we give a condition of all two-mode entangled Gaussian states to be the decoherence-free state in a given squeezed bath.

Physical Review A•Nov 10, 2008•23 citations

Evolution of a two-mode squeezed vacuum for amplitude decay via continuous-variable entangled state approach

Xiang‐Gao Meng, Ji‐Suo Wang, Bao‐Long Liang +1 more

Extending the recent work completed by Fan et al. [ Front. Phys. 9(1), 74 (2014)] to a two-mode case, we investigate how a two-mode squeezed vacuum evolves when it undergoes a two-mode amplitude dissipative channel, with the same decay rate κ, using the continuous-variable entangled state approach. Our analytical results show that the initial pure-squeezed vacuum state evolves into a definite mixed state with entanglement and squeezing, decaying over time as a result of amplitude decay. We also investigate the time evolutions of the photon number distribution, the Wigner function, and the optical tomogram in this channel. Our results indicate that the evolved photon number distribution is related to Jacobi polynomials, the Wigner function has a standard Gaussian distribution (corresponding to the vacuum) at long periods, losing its nonclassicality due to amplitude decay, and a larger squeezing leads to a longer decay time.

Frontiers of Physics•Sep 29, 2018•46 citations
The evolution of the entanglement of an initial two-mode squeezed vacuum (TMSV) in correlated noisy channels is investigated. It is shown that the correlated environment is helpful for preserving the entanglement of the initial TMSV. The entanglement period of the initial TMSV depends on the correlation property of the correlated environment.
We study the evolution of purity, entanglement, and total correlations of general two-mode continuous variable Gaussian states in arbitrary uncorrelated Gaussian environments. The time evolution of purity, von Neumann entropy, logarithmic negativity, and mutual information is analyzed for a wide range of initial conditions. In general, we find that a local squeezing of the bath leads to a faster degradation of purity and entanglement, while it can help to preserve the mutual information between the modes.
The time evolution of quantum correlations of entangled two-mode continuous variable states is examined in single-reservoir as well as two-reservoir models, representing noisy correlated or uncorrelated non-Markovian quantum channels. For this purpose the model of quantum Brownian motion is extended. Various separability criteria for Gaussian continuous variable systems are applied. In both types of reservoir models moderate non-Markovian effects prolong the separability time scales. However, in these models the properties of the stationary state may differ. In the two-reservoir model the initial entanglement is completely lost and both modes are finally uncorrelated. In a common reservoir both modes interact indirectly via the coupling to the same bath variables. Below a critical bath temperature entanglement between the two modes is preserved even in the steady state. A separability criterion is derived, which depends on the bath temperature and the response function of the open quantum system. Thus, the extended quantum Brownian motion model of a two-mode continuous variable system in a common reservoir provides an example of environment-induced entanglement.
We discuss the generation and evolution of entangled light in a correlated spontaneous emission laser. The master equation for the two-mode field in a cavity is derived and solved analytically. The time-dependent characteristic function in the Wigner representation for the two-mode field is obtained. It shows that the two-mode field in the cavity evolves in a two-mode Gaussian state. The entanglement degree of the two-mode field in the cavity increases initially, then decreases, and finally vanishes as the field evolves from an initial vacuum. The period of the entanglement is extended as the intensity of the driving field is increased. It is found that the entanglement still exists even when the two-mode squeezing disappears. During the entanglement period, the intensity of the field is amplified. The entanglement for the initial field being a two-mode squeezed vacuum and the entanglement of the output field are also discussed.
We describe Gaussian bound entangled states---entangled states with a positive partial transpose (PPT)---in four-mode continuous-variable systems. These states appear as a transient phase when certain entangled states with a negative partial transpose (NPT), also known as free entangled Gaussian states, are evolved under a noisy environment. Local thermal baths composed of harmonic oscillators are allowed to interact with one or more modes of the system and a wide variety of initial Gaussian entangled (NPT as well as PPT) states are studied. The robustness of entanglement is defined as the time duration for which the entanglement of the initial state is preserved under the noisy dynamics. We access the separability by utilizing standard semidefinite programming techniques. While most states lose their entanglement after a certain time across all bipartitions, an exception is observed for a three-parameter family of states which we call the generalized four-mode squeezed vacuum states, which transition to bound entangled states and remain so for a finite window of time. This dynamical onset of bound entanglement in continuous-variable systems is the central observation of our work. We carry out the analysis for Haar-random four-mode states (both pure and mixed) to scan the state space for a transient bound entangled phase.
We investigate the entanglement dynamics of two modes in a common squeezed thermal environment by means of the characteristic function method and the logarithmic negativity. When the two modes are prepared initially in separable squeezed states, we find that the external environment can not only induce but also enhance the two-mode entanglement if their initial squeezing parameters are suitably chosen. When the two modes are initially in a two-mode squeezed vacuum state, we find that whether the initial entanglement is degraded or increased depends strongly on the difference between the squeezing parameters of the considered bath and of a quantum state. Finally, we give a condition of all two-mode entangled Gaussian states to be the decoherence-free state in a given squeezed bath.
Extending the recent work completed by Fan et al. [ Front. Phys. 9(1), 74 (2014)] to a two-mode case, we investigate how a two-mode squeezed vacuum evolves when it undergoes a two-mode amplitude dissipative channel, with the same decay rate κ, using the continuous-variable entangled state approach. Our analytical results show that the initial pure-squeezed vacuum state evolves into a definite mixed state with entanglement and squeezing, decaying over time as a result of amplitude decay. We also investigate the time evolutions of the photon number distribution, the Wigner function, and the optical tomogram in this channel. Our results indicate that the evolved photon number distribution is related to Jacobi polynomials, the Wigner function has a standard Gaussian distribution (corresponding to the vacuum) at long periods, losing its nonclassicality due to amplitude decay, and a larger squeezing leads to a longer decay time.