Measuring entanglement of a rank-2 mixed state prepared on a quantum computer

TL;DR

This paper introduces a protocol to measure entanglement in rank-2 mixed quantum states on a quantum computer, relating geometric entanglement to correlations, and applies it to Schrödinger cat states.

Contribution

It proposes a new method linking geometric entanglement with correlations and demonstrates its application on IBM quantum hardware for mixed states.

Findings

Measured geometric entanglement for 2- and 4-qubit states.

Established relation between concurrence and geometric entanglement.

Analyzed entanglement dependence on state parameters.

Abstract

We study the entanglement between a certain qubit and the remaining system in rank- 2 mixed states prepared on the quantum computer. The protocol, which we propose for this purpose, is based on the relation of geometric measure of entanglement with correlations between qubits. As a special case, we consider a two-qubit rank-2 mixed state and find the relation of concurrence with the geometric measure of entanglement. On the ibmq-melbourne quantum computer we measure the geometric measure of entanglement in the cases of 2- and 4-qubit mixed quantum states which consist of Schr\"odinger cat states. We study the dependence of the value of entanglement on the parameter which defines the weight of pure states. Finally, we determine the concurrence of 2-qubit mixed state.