# Separability criteria via some classes of measurements

## TL;DR

This paper develops new separability criteria for quantum systems using generalized measurements like MUMs and GSIC, which are more effective and experimentally feasible than previous methods.

## Contribution

It introduces novel separability criteria based on MUMs and GSIC measurements applicable to diverse quantum systems, improving detection efficiency.

## Key findings

- Criteria outperform previous methods in mixed-dimension systems
- No full quantum state tomography needed for implementation
- Effective for bipartite and multipartite multi-level systems

## Abstract

Mutually unbiased bases (MUBs) and symmetric informationally complete (SIC) positive operator-valued measurements (POVMs) are two related topics in quantum information theory. They are generalized to mutually unbiased measurements (MUMs) and general symmetric informationally complete (GSIC) measurements, respectively, that are both not necessarily rank 1. We study the quantum separability problem by using these measurements and present separability criteria for bipartite systems with arbitrary dimensions and multipartite systems of multi-level subsystems. These criteria are proved to be more effective than previous criteria especially when the dimensions of the subsystems are different. Furthermore, full quantum state tomography is not needed when these criteria are implemented in experiment.