Teleportation via a mixture of a two qubit subsystem of a N-qubit W and GHZ state

Abstract

In this work we study a state which is a random mixture of a two qubit subsystem of a N-qubit W state and GHZ state. We analyze several possibilities like separability criterion (Peres-Horodecki criterion [M. Horodecki, P. Horodecki, R. Horodecki, Phys. Lett. A 223, 1 (1996); A. Peres, Phys. Rev. Lett. 77, 1413 (1996)]), non violation of Bell’s inequality [J.F. Clauser, M.A. Horne, A. Shimony, R.A. Holt, Phys. Rev. Lett. 23, 80 (1969)] (M(ρ)<1) and teleportation fidelity [N. Gisin, Phys. Lett. A 210, 157 (1996); R. Horodecki, P. Horodecki, M. Horodecki, Phys. Lett. A 200, 340 (1995); S. Massar, S. Popescu, Phys. Rev. Lett. 74, 1259 (1995); S. Popescu, Phys. Rev. Lett. 72, 797 (1994); C.H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, W.K. Wootters, Phys. Rev. Lett. 70, 1895 (1993)] $(F_{max}>\frac{2}{3})$ for this state. We also obtain a relationship between N (number of qubits) and p (the classical probability of random mixture) for each of these possibilities. Finally we present a detailed analysis of all these possibilities for N=3,4,5 qubit systems. We also report that for N=3 and $p\in(0.75,1]$ , this entangled state can be used as a teleportation channel without violating Bell’s inequality.