Universal steering inequalities

TL;DR

This paper introduces a universal framework for steering inequalities that efficiently detect quantum steering across various bipartite states and measurement settings, advancing quantum information theory.

Contribution

It develops a general, data-processing inequality-based framework for universal steering criteria applicable to all bipartite states and measurement scenarios.

Findings

Universal steering inequalities outperform previous criteria in detection efficiency.

Constructed assemblages from mutually unbiased bases show unbounded steering violations.

A single inequality can detect all bipartite pure states of full Schmidt rank.

Abstract

We propose a general framework for constructing universal steering criteria that are applicable to arbitrary bipartite states and measurement settings of the steering party. The same framework is also useful for studying the joint measurement problem. Based on the data-processing inequality for an extended R\'enyi relative entropy, we then introduce a family of universal steering inequalities, which detect steering much more efficiently than those inequalities known before. As illustrations, we show unbounded violation of a steering inequality for assemblages constructed from mutually unbiased bases and establish an interesting connection between maximally steerable assemblages and complete sets of mutually unbiased bases. We also provide a single steering inequality that can detect all bipartite pure states of full Schmidt rank. In the course of study, we generalize a number of results intimately connected to data-processing inequalities, which are of independent interest.