Estimation of Entanglement Negativity of a Two-Qubit Quantum System With Two Measurements

TL;DR

This paper introduces a method to estimate entanglement negativity and concurrence of a two-qubit state using only a single copy and two measurements, simplifying experimental procedures.

Contribution

It establishes a relationship between entanglement negativity and the minimum eigenvalue of a physical approximation, enabling experimental estimation with minimal measurements.

Findings

Entanglement negativity can be estimated via Hong-Ou-Mandel interferometry.

An upper bound of concurrence for two-qubit states is derived and experimentally realizable.

Exact estimation of concurrence is possible for certain pure and rank-2 mixed states.

Abstract

Numerous work had been done to quantify the entanglement of a two-qubit quantum state, but it can be seen that previous works were based on joint measurements on two copies or more than two copies of a quantum state under consideration. In this work, we show that a single copy and two measurements are enough to estimate the entanglement quantifier like entanglement negativity and concurrence. To achieve our aim, we establish a relationship between the entanglement negativity and the minimum eigenvalue of structural physical approximation of partial transpose of an arbitrary two-qubit state. The derived relation make possible to estimate entanglement negativity experimentally by Hong-Ou-Mandel interferometry with only two detectors. Also, we derive the upper bound of the concurrence of an arbitrary two-qubit state and have shown that the upper bound can be realized in experiment. We will further show that the concurrence of (i) an arbitrary pure two-qubit states and (ii) a particular class of mixed states, namely, rank-2 quasi-distillable mixed states, can be exactly estimated with two measurements.