Entanglement measures of W-state in noninertial frames

In this work we present the entanglement measures of a tripartite W-State entangled system in noninertial frame through the coordinate transformation between Minkowski and Rindler. Two cases are considered, i.e., when one qubit goes in a uniform acceleration a and the others remain stationary and when two qubits undergo in a uniform acceleration and while the other is stationary. The analytical negativities for one-tangle, two-tangle and pi-tangle in total are not written out explicitly except for some special cases due to complicated expressions, but we illustrate them in graphics and study their dependencies on the acceleration parameters r(b) and r(c). We find that the negativities of the one-tangle, two-tangle and pi-tangle decrease with the acceleration parameters except for the constant N-AB = N-BA. The negativity N-CI(AB) and the pi(CI), decrease faster than N-A(BCI) and pi(A)(pi(B)). The negativities N-ACI (N-B(ACI))and N-BICI decrease faster than those N-AB and N-ABI, respectively. It is interesting to see there exist turning points for the negativity N-A(BICI) at the coordinate position (r(b), r(c)) with r(b) = r(c), which implies that the N-A(BICI) has minimum value when Bob and Charlie are on the same position and the degree of the entanglement of the subsystem rho(A(BICI)) becomes smallest. The von Neumann entropy of tripartite system densities rho(ABCI) and rho(ABICI) are obtained analytically. We notice that they all increase with the acceleration parameters r(b) and r(c). C) 2018 The Author(s). Published by Elsevier B.V.