Observable estimation of entanglement for arbitrary finite-dimensional mixed states

TL;DR

This paper introduces observable upper bounds for squared concurrence, enabling entanglement estimation in unknown finite-dimensional mixed states through minimal experimental measurements.

Contribution

It provides the first observable upper bounds for squared concurrence, complementing existing lower bounds, and relates these bounds to the state's degree of mixing and linear entropy.

Findings

Observable upper bounds for squared concurrence are derived.

Entanglement can be estimated with few measurements on a twofold copy.

Relations between bounds, mixing degree, and linear entropy are established.

Abstract

We present observable upper bounds of squared concurrence, which are the dual inequalities of the observable lower bounds introduced in [F. Mintert and A. Buchleitner, Phys. Rev. Lett. 98, 140505 (2007)] and [L. Aolita, A. Buchleitner and F. Mintert, Phys. Rev. A 78, 022308 (2008)]. These bounds can be used to estimate entanglement for arbitrary experimental unknown finite-dimensional states by few experimental measurements on a twofold copy $\rho\otimes\rho$ of the mixed states. Furthermore, the degree of mixing for a mixed state and some properties of the linear entropy also have certain relations with its upper and lower bounds of squared concurrence.