Fidelity deviation in quantum teleportation with a two-qubit state

Abstract

We derive an exact computable formula for fidelity deviation in quantum teleportation with an arbitrary state of two qubits. As an application, we obtain the condition for universality: the condition that all input states are teleported equally well and provide a necessary and sufficient condition for a state to be both useful and universal for quantum teleportation. We illustrate these results with examples from well-known classes of two-qubit states. * Electronic address: a.

Optimal two-qubit states for quantum teleportation vis-à-vis state properties

“…The fidelity deviation is defined as the standard deviation of fidelity over all input states [7,8,9]:…”

“…The fidelity deviation corresponding to the optimal protocol mentioned above is defined as ∆ ρ = δ ̺ [9]. In general, the minimum of δ ρ , where the minimum is taken over all local unitary strategies, is not the same as ∆ ρ .…”

“…A protocol that achieves this maximal value is said to be optimal. Fidelity deviation, however, is something one would like to minimize but not at the expense of maximal fidelity, as pointed out in [9]. The authors argued that a protocol that achieves the minimal fidelity deviation is not guaranteed to achieve the maximal fidelity; hence, one should compute fidelity deviation only for optimal protocols; in particular, they obtained an exact formula for the fidelity deviation in optimal quantum teleportation [6] with a two-qubit state.…”

“…Because we want fidelity deviation to be as small as possible, the best performing states are clearly those with the minimum fidelity deviation. In fact, it has been shown [9] that within a set of states having the same maximal fidelity, larger than the classical bound, one can always find states with zero fidelity deviation. Here we take this idea forward and apply it to a more general setting.…”

“…For our analysis, we rely on the the canonical representation [6,9] of a two-qubit state, which is known to be quite useful in studying two-qubit nonlocal properties [2,4,6,12,14]. The canonical form is related to the Hilbert-Schmidt representation [2,4,6,12,14] of a two-qubit state via an appropriate local unitary transformation [6] and can be described with fewer state parameters.…”