Negative entanglement measure for bipartite separable mixed states

TL;DR

This paper introduces a negative entanglement measure for bipartite separable states, quantifying the minimal entanglement needed to convert a separable state into an entangled one, with applications in quantum phase transitions.

Contribution

It defines and formulates a negative entanglement measure for separable states, providing explicit formulas and bounds, and demonstrates its usefulness in analyzing quantum phase transitions.

Findings

Negative entanglement measure vanishes for pure separable states.

Divergence of derivatives of NEM near quantum critical points.

NEM changes from zero to negative near phase transition points.

Abstract

We define a negative entanglement measure for separable states which shows that how much entanglement one should compensate the unentangled state at least for changing it into an entangled state. For two-qubit systems and some special classes of states in higher-dimensional systems, the explicit formula and the lower bounds for the negative entanglement measure have been presented, and it always vanishes for bipartite separable pure states. The negative entanglement measure can be used as a useful quantity to describe the entanglement dynamics and the quantum phase transition. In the transverse Ising model, the first derivatives of negative entanglement measure diverge on approaching the critical value of the quantum phase transition, although these two-site reduced density matrices have no entanglement at all. In the 1D Bose-Hubbard model, the NEM as a function of $t/U$ changes from zero to negative on approaching the critical point of quantum phase transition.