Inseparable Separation

Zhanyu Ma, Cheolhee Han, Yigal Meir +1 more

We explore sufficient conditions for inseparability in mixed states with a globally conserved charge, such as a particle number. We argue that even separable states may contain entanglement in fixed charge sectors, as long as the state cannot be separated into charge-conserving components. As a witness of symmetric inseparability we study the number entanglement (NE), $\mathrm{\ensuremath{\Delta}}{S}_{m}$, defined as the entropy change due to a subsystem's charge measurement. Whenever $\mathrm{\ensuremath{\Delta}}{S}_{m}>0$, there exist inseparable charge sectors, having finite (logarithmic) negativity, even when the full state either is separable or has vanishing negativity. We demonstrate that the NE is not only a witness of symmetric inseparability, but also an entanglement monotone. Finally, we study the scaling of $\mathrm{\ensuremath{\Delta}}{S}_{m}$ in thermal one-dimensional systems combining high-temperature expansion and conformal field theory.

Adam Miranowicz, Marco Piani, Paweł Horodecki +1 more

Inseparability criteria for continuous and discrete bipartite quantum states based on moments of annihilation and creation operators are studied by developing the idea of Shchukin-Vogel criterion [Phys. Rev. Lett. 95, 230502 (2005)]. If a state is separable, then the corresponding matrix of moments is separable too. Thus, we derive generalized criteria based on the separability properties of the matrix of moments. In particular, a criterion based on realignment of moments in the matrix is proposed as an analog of the standard realignment criterion for density matrices. Other inseparability inequalities are obtained by applying positive maps to the matrix of moments. Usefulness of the Shchukin-Vogel criterion to describe bipartite-entanglement of more than two modes is demonstrated: we obtain various three-mode inseparability criteria, including some previously known ones, which were originally derived from the Cauchy-Schwarz inequality.

Jan Sperling, Ian A. Walmsley

The dynamical behavior of interacting systems plays a fundamental role for determining quantum correlations, such as entanglement. In this Letter, we describe temporal quantum effects of the inseparable evolution of composite quantum states by comparing the trajectories to their classically correlated counterparts. For this reason, we introduce equations of motions describing the separable propagation of any interacting quantum system, which are derived by requiring separability for all times. The resulting Schrödinger-type equations allow for comparing the trajectories in a separable configuration with the actual behavior of the system and, thereby, identifying inseparable and time-dependent quantum properties. As an example, we study bipartite discrete- and continuous-variable interacting systems. The generalization of our developed technique to multipartite scenarios is also provided.

Shengjun Wu, J. Anandan