Measurable Concurrence of Mixed States

TL;DR

This paper demonstrates that key entanglement measures like bipartite concurrence for rank-2 qubit states and 3-tangle for tripartite pure states can be directly measured experimentally using local projective measurements on multiple copies, simplifying entanglement detection.

Contribution

It introduces a method to directly measure bipartite concurrence and 3-tangle in qubit systems using local projective measurements on multiple copies, providing a practical approach for entanglement quantification.

Findings

Bipartite concurrence for rank-2 qubit states is measurable via local projective measurements on four copies.

3-tangle for tripartite pure qubit states can be measured using reduced density matrices conditioned on four copies.

The method enables direct experimental access to entanglement measures without full state tomography.

Abstract

We show that bipartite concurrence for rank-2 mixed states of qubits is written by an observable which can be exactly and directly measurable in experiment by local projective measurements, provided that four copies of the composite quantum system are available. In addition, for a tripartite quantum pure state of qubits, the 3-tangle is also shown to be measurable only by projective measurements on the reduced density matrices of a pair of qubits conditioned on four copies of the state.