Tetrapartite entanglement measures of generalized GHZ state in the noninertial frames

Abstract

Using a single-mode approximation, we carry out the entanglement measures, e.g., the negativity and von Neumann entropy when a tetrapartite generalized GHZ state is treated in a noninertial frame, but only uniform acceleration is considered for simplicity. In terms of explicit negativity calculated, we notice that the difference between the algebraic average π 4 and geometric average Π 4 is very small with the increasing accelerated observers and they are totally equal when all four qubits are accelerated simultaneously. The entanglement properties are discussed from one accelerated observer to all four accelerated observers. It is shown that the entanglement still exists even if the acceleration parameter r goes to infinity. It is interesting to discover that all 1-1 tangles are equal to zero, but 1-3 and 2-2 tangles always decrease when the acceleration parameter r increases. We also study the von Neumann entropy and find that it increases with the number of the accelerated observers. In addition, we find that the von Neumann entropy S ABCDI, S ABCIDI, S ABICIDI and S AIBICIDI always decrease with the controllable angle θ, while the entropies S 3 – 3 non, S 3 – 2 non, S 3 – 1 non and S 3 – 0 non first increase with the angle θ and then decrease with it.

Visualizing and witnessing first-order coherence, Bell nonlocality and purity by using a quantum steering ellipsoid in the non-inertial frame

“…[58] Relevant explorations in the non-inertial frame have been widely carried out. [59][60][61][62][63][64][65][66][67][68][69][70][71][72][73][74] There has been a lot of effort made to investigate nonlocality under non-inertial frames. [75][76][77][78] Friis et al [75] explored entanglement of accelerated fermions.…”

Pentapartite Entanglement Measures of GHZ and W-Class State in the Noninertial Frame

“…Compared with the well-known entangled stated-GHZ state [ 15 , 36 , 37 , 38 , 39 , 40 , 41 ], the authors paid less attention to the W-class state because its density matrix cannot be written as an X matrix form. Nevertheless, we have employed a special technique to study the density matrix in the non-X matrix form and carried out the tripartite and tetrapartite W-class state cases [ 42 , 43 , 44 ], except for the generalized GHZ state in the noninertial frame [ 45 , 46 , 47 , 48 ]. After studying, we find that the degree of entanglement of the W-class state is more robust than the GHZ and generalized GHZ states.…”

“…The three tangle has interesting properties, but its analytical calculation becomes a nontrivial task because its calculation depends on the negativities of bipartite and tripartite systems. Similarly, four tangle has been proposed when we studied the tetrapartite systems, which include 1-3 and 2-2 tangles [ 42 , 44 , 45 , 47 , 48 ]. Recently, stimulated by the study of the tripartite and tetrapartite W-class state [ 42 , 43 , 44 ], Sun and her coauthors studied the entanglement property of a pentapartite W-class state in the noninertial frame and showed how the acceleration parameter and the number of the accelerated qubits affect the entanglement property of the pentapartite W-class entangled system [ 51 ].…”