Exploration quantum steering, nonlocality and entanglement of two-qubit X-state in structured reservoirs

TL;DR

This paper investigates quantum steering, nonlocality, and entanglement of two-qubit X-states in structured reservoirs, revealing how decoherence affects steerability and Bell nonlocality in satellite-based quantum communication.

Contribution

It provides analytical insights into the dynamics of quantum steering and nonlocality of two-qubit X-states under various decoherence channels, highlighting conditions for steerability and Bell inequality violations.

Findings

All entangled pure states and maximally entangled states are steerable.

Quantum steering can experience sudden death and recovery depending on decoherence strength.

Steerability is weaker in entangled mixed states compared to pure states.

Abstract

In this work, there are two parties, Alice on Earth and Bob on the satellite, which initially share an entangled state, and some open problems, which emerge during quantum steering that Alice remotely steers Bob, are investigated. Our analytical results indicate that all entangled pure states and maximally entangled evolution states (EESs) are steerable, and not every entangled evolution state is steerable and some steerable states are only locally correlated. Besides, quantum steering from Alice to Bob experiences a "sudden death" with increasing decoherence strength. However, shortly after that, quantum steering experiences a recovery with the increase of decoherence strength in bit flip (BF) and phase flip (PF) channels. Interestingly, while they initially share an entangled pure state, all EESs are steerable and obey Bell nonlocality in PF and phase damping channels. In BF channels, all steerable states can violate Bell-CHSH inequality, but some EESs are unable to be employed to realize steering. However, when they initially share an entangled mixed state, the outcome is different from that of the pure state. Furthermore, the steerability of entangled mixed states is weaker than that of entangled pure states. Thereby, decoherence can induce the degradation of quantum steering, and the steerability of state is associated with the interaction between quantum systems and reservoirs.