Teleportation with a mixed state of four qubits and the generalized singlet fraction

Abstract

Recently, an explicit protocol E0 for faithfully teleporting arbitrary two-qubit states using genuine four-qubit entangled states was presented by us. Here, we show that E0 with an arbitrary four-qubit mixed-state resource Ξ is equivalent to a generalized depolarizing bichannel with probabilities given by the maximally entangled components of the resource. These are defined in terms of our four-qubit entangled states. We define the generalized singlet fraction G [Ξ] and illustrate its physical significance with several examples. We argue that in order to teleport arbitrary two-qubit states with average fidelity better than is classically possible, we have to demand that G [Ξ] > 2. In addition, we conjecture that when G [Ξ] < 4, then no entanglement could be teleported. It is shown that to determine the usefulness of Ξ for E0, it is necessary to analyze G [Ξ]. © 2006 The American Physical Society.