Einstein-Podolsky-Rosen Steering for Mixed Entangled Coherent States.

Kamal Berrada,Mariam Algarni,Sayed Abdel-Khalek,Hichem Eleuch

doi:10.3390/e23111442

Abstract

By using the Born Markovian master equation, we study the relationship among the Einstein–Podolsky–Rosen (EPR) steering, Bell nonlocality, and quantum entanglement of entangled coherent states (ECSs) under decoherence. We illustrate the dynamical behavior of the three types of correlations for various optical field strength regimes. In general, we find that correlation measurements begin at their maximum and decline over time. We find that quantum steering and nonlocality behave similarly in terms of photon number during dynamics. Furthermore, we discover that ECSs with steerability can violate the Bell inequality, and that not every ECS with Bell nonlocality is steerable. In the current work, without the memory stored in the environment, some of the initial states with maximal values of quantum steering, Bell nonlocality, and entanglement can provide a delayed loss of that value during temporal evolution, which is of interest to the current study.

Highlights

Entanglement is a crucial physical resource in the development of the necessary tasks for the processing and transmission of quantum information (PTQI) [1,2,3,4,5,6,7]
We find that the quantum steering and nonlocality have similar behavior with respect to the photon number during dynamics
Without the memory encoded in the environment, certain of the initial states with maximal values of quantum steering, Bell nonlocality, and entanglement can provide a delayed loss of that value during the temporal evolution, which is of interest to the current study

Summary

Introduction

Entanglement is a crucial physical resource in the development of the necessary tasks for the processing and transmission of quantum information (PTQI) [1,2,3,4,5,6,7]. We find that the ECSs with the steerability can violate the Bell inequality, and not every ECS is steerable with Bell nonlocality These correlations can be preserved during the evolution and resist against environment, exhibiting an important feature of quantum steerability and nonlocality in the present model. Following the references [26,30], by using the positivity of the continuous entropies, Walborn et al [25] discussed the observR ables in states that verify local hidden state model (LHSM) h( x b | x a ) ≥ dλρ(λ)hq ( x b |λ), where λ represents the HV, ρ(λ) is the probability density, and hq ( x b |λ) is the continuous. Entanglement is measured in terms of E , which ranges from 0 for factorizable states to 1 for maximally entangled states

Physical System and Dynamics

Conclusions