Tetrapartite entanglement measures of W-class in noninertial frames*

Abstract

We present the entanglement measures of a tetrapartite W-Class entangled system in noninertial frame, where the transformation between Minkowski and Rindler coordinates is applied. Two cases are considered. First, when one qubit has uniform acceleration whilst the other three remain stationary. Second, when two qubits have nonuniform accelerations and the others stay inertial. The 1 − 1 tangle, 1 − 3 tangle and whole entanglement measurements (π4 and Π4), are studied and illustrated with graphics through their dependency on the acceleration parameter r d for the first case and rc and r d for the second case. It is found that the Negativities (1 − 1 tangle and 1 − 3 tangle) and π-tangle decrease when the acceleration parameter r d or in the second case rc and r d increase, remaining a nonzero entanglement in the majority of the results. This means that the system will be always entangled except for special cases. It is shown that only the 1−1 tangle for the first case, vanishes at infinite accelerations, but for the second case the 1 − 1 tangle disappears completely when r > 0.472473. It is found an analytical expression for von Neumann information entropy of the system and we notice that it increases with the acceleration parameter.

The entropy of systems

“…Moreover, as the relativistic effects of infinite accelerations affect the entanglement, there exists interest in investigating the entanglement of quantum states in non-inertial frames. The entropy of von Neumann can be used to measure the loss of entanglement in a multipartite quantum systems because the density matrix tends to mix as become more non-inertial [35]. For example, in a tetrapartite quantum system of a GHZ state in a non-inertial frame the loss of entanglement when one, two, three and all parties are non-inertial can be described as function of a parameter r ∈ [0, infty] associated to the acceleration (see Fig.…”

Efficient Mediated Quantum Secret Sharing Protocol in a Restricted Quantum Environment

“…Additionally, in the QSS protocol, secret shadows can be distributed securely to each agent, regardless of the length of the secret shadows (similar to the quantum key distribution protocol), and the protocol's participants can detect eavesdroppers actively, which is an impossible task in CSS protocols. Subsequently, the properties of various quantum resources, including the single photon, Bell state, [ 6 ] W state, [ 7–9 ] etc. were adopted to develop numerous QSS protocols.…”

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 ].…”

“…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 ]. This was realized by studying the -tangle, including the 1-4, 1-1 tangles and the von Neumann entropy.…”