Construction of optimal witness for unknown two-qubit entanglement

TL;DR

This paper presents a new efficient method to detect, quantify, and distill entanglement in two-qubit photon pairs without full state reconstruction, using an optimal entanglement witness.

Contribution

It introduces a scheme to construct the optimal entanglement witness for two-qubit states, enabling direct entanglement detection and quantification without full tomography.

Findings

Efficient detection and quantification of entanglement using the witness.

Maximal entanglement distillation with tunable polarization filters.

Extension of the method to multiqubit GHZ entanglement.

Abstract

Whether entanglement in a state can be detected, distilled, and quantified without full state reconstruction is a fundamental open problem. We demonstrate a new scheme encompassing these three tasks for arbitrary two-qubit entanglement, by constructing the optimal entanglement witness for polarization-entangled mixed-state photon pairs without full state reconstruction. With better efficiency than quantum state tomography, the entanglement is maximally distilled by newly developed tunable polarization filters, and quantified by the expectation value of the witness, which equals the concurrence. This scheme is extendible to multiqubit Greenberger-Horne-Zeilinger entanglement.