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

TL;DR

This paper investigates a mixed quantum state derived from N-qubit W and GHZ states, analyzing its entanglement, teleportation fidelity, and Bell inequality violations for different qubit numbers and mixture probabilities.

Contribution

It introduces a detailed analysis of a mixed state combining W and GHZ states, establishing conditions for teleportation and entanglement without Bell inequality violation.

Findings

For N=3 and p in (0.75,1], the state can teleport without Bell violation.

Relationships between N, p, and entanglement criteria are established.

The state exhibits useful teleportation fidelity under certain mixture probabilities.

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 [14,15]), non violation of Bell's inequality [6]($M(\rho)<1$)and teleportation fidelity [1,2,3,4] ($(F_{max}>{2/3})$) 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 $p\in(.75,1]$, this entangled state can be used as a teleportation channel without violating Bell's inequality.