Entanglement of Semi-Bell States in Non-Inertial Frames

Abstract

Semi-Bell states are exploited for storing and sending information in non-inertial frames. In this paper, we consider four types of semi-bell states, $|{\varPhi }_{\alpha }^{\pm }\rangle =\alpha |0\rangle |0\rangle \pm \sqrt {1-\alpha ^{2}}|1\rangle |1\rangle$ and $|{\varPsi }_{\alpha }^{\pm }\rangle =\alpha |0\rangle |1\rangle \pm \sqrt {1-\alpha ^{2}}|1\rangle |0\rangle$, and study entanglements and other quantum correlations of these states from the viewpoint of an accelerated and an inertial observers by computing such measures as negativity, quantum coherence, and purity of these states. As expected, these measures degrade for semi-bell states with increasing acceleration. The states, however, exhibit different types of degradation depending on the statistics of the particles. Entanglement, coherence, and purity of bosonic states degrade more rapidly than do states with fermionic statistics. A duality exists in the measures of the two types of semi-bell states and for the maximally entangled states ($\alpha =\frac {1}{\sqrt {2}}$), there is no difference between the measures of $|{\varPhi }_{\alpha }^{\pm }\rangle$ and $|{\varPsi }_{\alpha }^{\pm }\rangle$. In the fermionic case, differences of the measures between the $|{\varPhi }_{\alpha }^{\pm }\rangle$ and $|{\varPsi }_{\alpha }^{\pm }\rangle$ states are greater for large values of acceleration, while in the bosonic case, their subtractions are larger for small values of acceleration.