Several Trade off Features of Quantum Steering in Distributed Scenario

TL;DR

This paper investigates the distribution and limitations of quantum steering violations in multi-qubit systems, revealing trade-offs and complementarity relations that constrain how steering can be shared among subsystems.

Contribution

It derives a trade-off relation for bipartite steering violations in multi-qubit systems and explores the complementarity between entanglement and steering violations.

Findings

Maximal steering violation in one pair limits violations in others.

Not all pairs can violate steering simultaneously in a three-qubit system.

A complementarity relation links entanglement and steering violations.

Abstract

In the present work, we address the question of how bipartite steering violation takes place among multi-partite systems (where each sub-system have Hilbert space dimension restricted to two) based on the maximal violations of the bipartite steering inequality of the reduced pairwise qubit systems. We have derived a trade-off relation which is satisfied by those pairwise bipartite maximal steering violations, which physically can be understood as providing restrictions on the distribution of steering among subsystems. For a three-qubit system, it is impossible that all pairs of qubits violate the steering inequality, and once a pair of qubits violates the steering inequality maximally, the other two pairs of qubits must both obey the steering inequality. We also present a complementarity relation between genuine entanglement present in a tripartite state and maximum bipartite steering violation by its reduced states.