https://doi.org/10.1140/epjd/e2010-00017-8
Teleportation via a mixture of a two qubit subsystem of a N-qubit W and GHZ state
1
Heritage Institute of Technology, 700107, Kolkata, West Bengal, India
2
Institute of Physics, Sachivalaya Marg, 751005, Bhubaneswar, Orissa, India
Corresponding author: indranilc@indiainfo.com
Received:
6
May
2009
Revised:
3
September
2009
Published online:
26
January
2010
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)]
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 ![$p\in(0.75,1]$](/articles/epjd/abs/2010/05/d09215/d09215_tex_eq2.png)
, this entangled state can be used as a teleportation channel without
violating Bell's inequality.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2010
