Teleportation fidelity and its deviation for an arbitrary two-qubit state when the classical communication is noisy

Abstract

In this work, we consider the following teleportation protocol: There is an arbitrary two-qubit resource state, shared between two spatially separated parties, Alice and Bob. Applying local unitary operators, they transform the resource state into the canonical form. To teleport an unknown qubit, Alice now measures her qubits in the Bell basis. Then, the measurement outcome is communicated by Alice to Bob via noisy classical channel(s). Finally, after receiving the classical message, Bob applies the necessary unitary operator to his qubit. Under this protocol, we find the exact formulae of teleportation fidelity and its deviation. We further find conditions for non-classical fidelity within this protocol. If the classical communication is noiseless in the above protocol then there are resource states which can lead to zero fidelity deviation. However, we show that such states may not lead to zero fidelity deviation when the classical communication is noisy in the same protocol. We also explore the opposite case, i.e., the states, which cannot lead to zero fidelity deviation in the above protocol when the classical communication is noiseless, may lead to zero fidelity deviation when the classical communication is noisy in the same protocol without compromising the non-classical fidelity. Moreover, we exhibit scenarios within the present protocol, where the fidelity deviation increases if the entanglement of the resource state is increased.

Characterizing qubit channels in the context of quantum teleportation

“…At first, let us take the nonunital channel nu having the Kraus operators given by Eq. (21). It can be checked that the maximal average fidelity and fidelity deviation of the final shared state are given by…”

“…In such cases, all input states may not be teleported equally well, and dispersion or fluctuation in fidelity over the input states may arise [16,17]. Although the average fidelity is the standard quantifier for QT, it does not contain any information about the fluctuation in fidelity or fidelity deviation [16][17][18][19][20][21]. Hence, average fidelity associated with fidelity deviation can completely characterize QT.…”