Conditional steering under von-Neumann scenario

TL;DR

This paper investigates whether tripartite mixed entangled states can exhibit quantum steering through conditional bipartite states after projective measurements, expanding the understanding of nonlocality beyond pure states.

Contribution

It introduces the concept of conditional steering in tripartite mixed states and compares it with existing tripartite correlation notions, showing that genuine entanglement isn't necessary.

Findings

Conditional steering can occur in tripartite mixed states.

Tripartite states need not be genuinely entangled to show conditional steering.

The study extends nonlocality characterization to mixed states.

Abstract

In [\href{http://www.sciencedirect.com/science/article/pii/037596019290711T}{Phys. Lett. A {\bf 166}, 293 (1992)}] Popescu characterized nonlocality of pure $n$-partite entangled systems by studying bipartite violation of local realism when $n-2$ number of parties perform projective measurements on their particles. A pertinent question in this scenario is whether similar characterization is possible for $n$-partite mixed entangled states also. In the present work we have followed an analogous approach so as to explore whether given a tripartite mixed entangled state the conditional bipartite states obtained by performing projective measurement on the third party, demonstrate a weaker form of nonlocality, quantum steering. We also compare this new phenomenon of conditional steering with existing notions of tripartite correlations. Interestingly the tripartite state need not be genuinely entangled to demonstrate conditional steering.