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

Abstract

We discover a new class of Gaussian bound entangled states of four-mode continuous-variable systems. These states appear as a transient phase when certain NPT-entangled Gaussian states are evolved under a noisy environment. A thermal bath comprising of harmonic oscillators is allowed to interact with one or 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 semi-definite programming techniques. While most states lose their entanglement after a certain time across all bi-partitions, an exception is observed for a three-parameter family of states which we call the generalized four-mode squeezed vacuum (gFMSV) states, which transitions to a bound entangled state, and remains 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 transient bound entangled phase

12 pages, 3 figures revtex

References in corpus (16)

• Continuous-variable quantum key distribution system: past, present, and future
• Non-Markovian entanglement dynamics of noisy continuous variable quantum channels
• Unitarily localizable entanglement of Gaussian states
• Quantum Teleportation with Continuous Variables: a survey
• Semidefinite programming relaxations for quantum correlations
• Improved composable key rates for CV-QKD
• Coexistence of unlimited bipartite and genuine multipartite entanglement: Promiscuous quantum correlations arising from discrete to continuous variable systems
• Entanglement dynamics of bipartite system in squeezed vacuum reservoirs
• Verifying bound entanglement of dephased Werner states
• Analytical evaluation of the coefficients of the Hu-Paz-Zhang master equation: Ohmic spectral density, zero temperature, and consistency check
• Increasing distillable key rate from bound entangled states by using local filtration
• Gaussian entanglement witness and refined Werner-Wolf criterion for continuous variables
• Numerical detection of Gaussian entanglement and its application to the identification of bound entangled Gaussian states
• Evolution of two-mode quantum states under a dissipative environment: which quantum resource survives better, squeezing or entanglement?
• Positivity and entanglement of polynomial Gaussian integral operators
• Generating random Gaussian states