Entanglement in mixed states: the negativity

Mostafa Mansour, Y. Oulouda, A. Sbiri +1 more

Abstract In this paper, we investigate the decay of entanglement of multiqubit randomized entangled states. We start by introducing separable states of collection of n independent qubits. The randomized entangled mixed states are generated from factorisable initial states by coupling the qubits through randomized entangling operators. The bipartite and multipartite entanglement of randomized states are analyzed by employing respectively the concepts of the negativity and the genuine multiparticle negativity as measures of amount of entanglement. The decreases of the amount of entanglement of randomized entangled mixed states is studied in terms of the noisy parameter p .

Sho Sugiura

Adam Miranowicz, Satoshi Ishizaka, Bohdan Horst +1 more

It is well known that for two qubits the upper bounds of the relative entropy of entanglement (REE) for a given concurrence as well as the negativity for a given concurrence are reached by pure states. We show that, by contrast, there are two-qubit mixed states for which the REE for some range of a fixed negativity is higher than that for pure states. Moreover, we demonstrate that a mixture of a pure entangled state and pure separable state orthogonal to it is likely to give the maximal REE. By noting that the negativity is a measure of entanglement cost under operations preserving positivity of partial transpose, our results provide an explicit example of operations such that, even though the entanglement cost for an exact preparation is the same, the entanglement of distillation of a mixed state can exceed that of pure states. This means that the entanglement manipulation via a pure state can result in a larger entanglement loss than that via a mixed state.

Seunghun Lee, Eun-Gook Moon

We investigate 1D and 2D cluster states under local decoherence to assess the robustness of their mixed-state subsystem symmetry-protected topological (SSPT) order. By exactly computing fidelity correlators via dimensional reduction of effective statistical mechanics models, we pinpoint the critical error rate for strong-to-weak spontaneous breaking of strong subsystem symmetry. Without resorting to the replica trick, we demonstrate that mixed-state SSPT order remains remarkably robust up to the maximal decoherence rate when noise respects strong subsystem symmetry. Furthermore, we propose that the mixed-state SSPT order can be detected by a constant correction to the area-law scaling of entanglement negativity, termed spurious topological entanglement negativity. This also highlights that topological entanglement negativity, a widely used diagnostic for mixed-state topological order, is generally not invariant under finite-depth quantum channels.