Revisiting maximal average fidelity of teleportation

TL;DR

This paper calculates the maximum average fidelity of quantum teleportation for various input state distributions and resource states, revealing that even non-entangled states can outperform classical fidelity under certain measurement conditions.

Contribution

It extends the analysis of teleportation fidelity to arbitrary isotropic input distributions and resource states, including non-entangled states, highlighting the role of measurement correlations.

Findings

Quantum teleportation can surpass classical fidelity with non-entangled resources.

Maximum fidelity depends on measurement basis correlations.

Classical fidelity is only not exceeded when measurement basis is uncorrelated.

Abstract

We obtain the maximal average fidelity corresponding to the standard quantum teleportation protocol for an arbitrary isotropic distribution of input states and an arbitrary resource state. We extend this result to a family of von Neumann measurements, which includes the projections onto the computational and Bell basis, considering a Bell-diagonal resource state. We focus on three specific isotropic distributions of input states: 1) completely mixed input states, 2) states with a certain (fixed) degree of purity, and 3) quasi-pure input states. We show that the standard quantum teleportation protocol can teleport arbitrary mixed states with higher average fidelity than its classical counterpart even when the resource of the protocol is a non-entangled state, specifically, a separable Werner state. Moreover, we find that the maximum average fidelity obtained with classical-quantum states used as a resource in a standard teleportation protocol also exceeds the classical fidelity. To establish the role played by the presence or absence of quantum correlations in the resource state and their relation with the correlations present in the von Neumann measurement performed by Alice, we analyze in detail the case of Bell diagonal resource states employing a family of monoparametric basis for which both the Bell and the computational (non-correlated) basis are included. Only in the case where the basis on which Alice measures is completely uncorrelated (computational basis) the maximum average fidelity does not exceed the classical fidelity for any resource state. In all other cases, the maximum average fidelity exceeds the classical one for a certain range of parameters describing the resource state, evidencing the importance of the correlations present in the measurements.