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 π-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 rb and rc. We find that the negativities of the one-tangle, two-tangle and π-tangle decrease with the acceleration parameters except for the constant NAB=NBA. The negativity NCI(AB) and the πCI decrease faster than NA(BCI) and πA(πB). The negativities NACI (NB(ACI))and NBICI decrease faster than those NAB and NABI, respectively. It is interesting to see there exist turning points for the negativity NA(BICI) at the coordinate position (rb,rc) with rb=rc, which implies that the NA(BICI) has minimum value when Bob and Charlie are on the same position and the degree of the entanglement of the subsystem ρA(BICI) becomes smallest. The von Neumann entropy of tripartite system densities ρABCI and ρABICI are obtained analytically. We notice that they all increase with the acceleration parameters rb and rc. Keywords: W-state, Entanglement, Dirac field, Noninertial frames