Chaos in quantum steering in high-dimensional systems

TL;DR

This paper explores chaotic behavior in quantum steering within high-dimensional and infinite-dimensional systems, revealing states with counterintuitive steering properties that have potential cryptographic applications.

Contribution

It demonstrates the existence of chaos effects in quantum steering in high-dimensional systems and identifies states with identical density matrices but no steerability, challenging previous assumptions.

Findings

Chaos effect in high-dimensional quantum steering

States with identical density matrices but no steerability

Potential applications in quantum cryptography

Abstract

Quantum steering means that in some bipartite quantum systems, the local measurements on one side can determine the state of the other side. Here we show that in high-dimensional systems, there exists a specific entangled state which can display a kind of chaos effect when being adopted for steering. That is, a subtle difference in the measurement results on one side can steer the other side into completely orthogonal states. Moreover, by expanding the result to infinite-dimensional systems, we find two sets of states for which, contrary to common belief, even though their density matrices approach being identical, the steering between them is impossible. This property makes them very useful for quantum cryptography.