Mutually Unbiased Bases and Bound Entanglement

TL;DR

This paper explores the relationship between mutually unbiased bases and bound entanglement, demonstrating that MUBs can serve as a practical tool for detecting complex entangled states in quantum systems.

Contribution

It introduces a MUB-based criterion for identifying bound entanglement in certain quantum states, highlighting its potential for experimental detection and theoretical analysis.

Findings

MUB criterion detects bound entanglement across various dimensions and particle numbers

The geometry of bound entangled states is similar across different system sizes

MUBs provide a feasible method for investigating the typicality of bound entanglement

Abstract

In this contribution we relate two different key concepts: mutually unbiased bases (MUBs) and entanglement; in particular we focus on bound entanglement, i.e. highly mixed states which cannot be distilled by local operations and classical communications. For a certain class of states --for which the state-space forms a "magic" simplex-- we analyze the set of bound entangled states detected by the MUB criterion for different dimensions d and number of particles n. We find that the geometry is similar for different d and n, consequently, the MUB criterion opens possibilities to investigate the typicality of PPT-bound and multipartite bound entanglement deeper and provides a simple experimentally feasible tool to detect bound entanglement.