Experimentally accessible lower bounds for genuine multipartite entanglement and coherence measures

TL;DR

This paper introduces a fidelity-based approach to derive experimentally accessible lower bounds for genuine multipartite entanglement and coherence measures, avoiding complex quantum state tomography.

Contribution

The authors develop a method to estimate lower bounds of entanglement and coherence measures directly from fidelity measurements, applicable to various multipartite entanglement and coherence quantifiers.

Findings

Method provides observable lower bounds for multiple entanglement measures.

Applicable to real experimental states, demonstrating practical utility.

Avoids exponential complexity of full quantum state tomography.

Abstract

Experimentally quantifying entanglement and coherence are extremely important for quantum resource theory. However, because the quantum state tomography requires exponentially growing measurements with the number of qubits, it is hard to quantify entanglement and coherence based on the full information of the experimentally realized multipartite states. Fortunately, other methods have been found to directly measure the fidelity of experimental states without quantum state tomography. Here we present a fidelity-based method to derive experimentally accessible lower bounds for measures of genuine multipartite entanglement and coherence. On the one hand, the method works for genuine multipartite entanglement measures including the convex-roof extended negativity, the concurrence, the G-concurrence, and the geometric measure for genuine multipartite entanglement. On the other hand, the method also delivers observable lower bounds for the convex roof of the $l_{1}$-norm of coherence, the geometric measure of coherence, and the coherence of formation. Furthermore, all the lower bounds are based on the fidelity between the chosen pure state and the target state, and we obtain the lower bounds of several real experimental states as examples of our results.