ENTCALC: Toolkit for calculating geometric entanglement in multipartite quantum systems

TL;DR

This paper introduces entcalc, a Python and MATLAB toolkit for estimating the geometric entanglement of multipartite quantum states, providing accurate bounds and applying it to various quantum systems to analyze entanglement properties.

Contribution

The paper presents a new software package that efficiently estimates geometric entanglement in multipartite quantum states, including methods for bounds and error estimation, with practical applications.

Findings

Accurate bounds on geometric entanglement for tested states.

Signatures of quantum phase transitions detected via entanglement measures.

Entanglement activation between non-neighbouring sites by external magnetic field.

Abstract

We present entcalc, a Python and MATLAB package for estimating the geometric entanglement of multipartite quantum states. The package operates as follows: given a multipartite quantum state as input, it outputs an estimate of its geometric entanglement. For pure states, it computes the geometric entanglement together with an estimation error. For mixed states, it provides both lower and upper bounds on the geometric entanglement, thereby identifying an interval in which the true value lies. We provide several methods to compute the lower bound, enabling users to balance accuracy against computational cost. We apply entcalc to several representative examples, including for $3\otimes3$ PPT entangled states, mixtures of GHZ and W states, thermal states of selected three-qubit spin chains, and noisy GHZ and W states. We observe signatures of quantum phase transitions by quantifying entanglement in spin chains. We also demonstrate that entanglement between non-neighbouring sites can be activated by tuning the external magnetic field. In all tested cases, the gap between the lower and upper bounds is found to be very small, indicating that entcalc provides highly accurate estimates of the geometric entanglement for these states.