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.
Highlights
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
We will investigate the performance of quantum steering, nonlocality and entanglement for the evolution state described by a trace-preserving quantum operation ε(ρ), which is given by ε(ρ) = ∑i=0,1(I A ⊗ EiB)ρ (I A ⊗ EiB)†, where {Ei} is the set of Kraus operators associated to a decohering process of a single qubit, with the trace-preserving condition reading44 ∑i Ei†Ei = I
We define that the entangled evolution states (EESs) are damped states, which the subsystem B of the initial bipartite state suffers from the quantum noisy channels
Summary
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. Shortly after that, quantum steering experiences a recovery with the increase of decoherence strength in bit flip (BF) and phase flip (PF) channels 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 When they initially share an entangled mixed state, the outcome is different from that of the pure state. Some problems of that Alice can distantly steer Bob are investigated, and we consider two different types of bipartite states (entangled pure state and entangled mixed state) as the initial states. Our analytical results indicate that: (i) All entangled pure states and maximally entangled evolution states are steerable. (ii) Not every entangled evolution state is steerable and some steerable states cannot violate Bell-CHSH inequality. (iii) Decoherence can rapidly induce the degradation of quantum steering, and the steerability of entangled pure states is stronger than that of entangled mixed states
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