1307.5779 (Elie Wolfe et al.)

Certifying Separability in Symmetric Mixed States of N qudits, and
Superradiance    [PDF]

Elie Wolfe, S. F. Yelin

In this paper we present a sufficient condition for separability applicable to all "diagonally symmetric" mixed states of N qubits. Separability criteria are typically of the necessary-but-not-sufficient variety, in that satisfying some separability criterion, such as demanding positivity of all eigenvalues under partial transpose, does not strictly imply separability. In contrast this work provides explicit separability certification based on algorithmically decomposing the target state into a convex combination of separable states. "Successful" termination of the algorithm thus acts as a sufficient separability condition. We further conjecture and give evidence that our decomposition succeeds for all genuinely separable N qubit diagonally symmetric states, in which case the condition derived here is both necessary and sufficient for establishing separability. We use the sufficiency of the condition to prove that, contrary to instinct, Dicke model superradiance time evolution does not lead to entangled states, and we explore various ramifications implied by the apparent necessity as well.

View original: http://arxiv.org/abs/1307.5779