Informationally complete measures of quantum entanglement

TL;DR

This paper introduces a new family of entanglement measures called informationally complete entanglement measures (ICEMs) that can more accurately characterize quantum entanglement, distinguish states better, and be efficiently estimated on quantum computers.

Contribution

The paper establishes a novel correspondence between the characteristic polynomial of reduced states and their trace, introducing ICEMs that outperform existing measures in characterizing and detecting quantum entanglement.

Findings

ICEMs provide finer entanglement characterization.

ICEMs can be efficiently estimated on quantum computers.

ICEMs can detect separability and multipartite entanglement faithfully.

Abstract

Although quantum entanglement has already been verified experimentally and applied in quantum computing, quantum sensing and quantum networks, most of the existing measures cannot characterize the entanglement faithfully. In this work, by exploiting the Schmidt decomposition of a bipartite state $|\psi\rangle_{AB}$, we first establish a one-to-one correspondence relation between the characteristic polynomial of the reduced state $\rho_A$ and the polynomials its trace. Then we introduce a family of entanglement measures which are given by the complete eigenvalues of the reduced density matrices of the system. Specific measures called informationally complete entanglement measures (ICEMs) are presented to illustrate the advantages. It is demonstrated that such ICEMs can characterize finer and distinguish better the entanglement than existing well-known entanglement measures. They also give rise to criteria of state transformations under local operation and classical communication. Moreover, we show that the ICEMs can be efficiently estimated on a quantum computer. The fully separability, entanglement and genuine multipartite entanglement can detected faithfully on quantum devices.