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International Journal of Theoretical Physics

Correlated Effects in Pauli Channels for Quantum Teleportation

Yan‐Ling Li, Chuanjin Zu, Dong-Mei Wei, Chengmin Wang

Published Feb 15, 2019• 11 citations
Publisher
DOI
10.1007/s10773-019-04027-5

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We analytically characterize how the location and the local or correlated structure of stochastic Pauli errors affect a three-qubit coherent quantum-teleportation circuit. Independent local channels and a fully correlated two-qubit channel are inserted separately in six configurations. Propagating each Pauli-error realization through the Clifford circuit yields the effective channel on Bob's qubit and analytical expressions for the average and state-resolved fidelities. Under a common ordered-pair probability convention, the six configurations form three pairs that induce equivalent reduced channels on Bob. Within each pair, corresponding Pauli-error realizations have the same probabilities and produce the same effective Pauli operator on Bob's output state. The equivalence therefore holds for every input state within the stochastic Pauli models considered here, rather than only for the average fidelity. Correlated Z errors do not affect the output for the first pair; local X and Z errors exhibit complementary qubit sensitivity for the second; and correlated same-axis Pauli errors cancel for the third. These results classify the error response of the selected circuit configurations and show that it depends jointly on the error statistics, Pauli axis, and position within the protocol.
Quantum teleportation of an n-qubit state performed using as an entangled resource a general bipartite state of 2n qubits instead of n Bell states is equivalent to a correlated Pauli channel. This yields a new characterization of such channels in terms of many-body correlation functions of the teleporting media. It provides a relatively simple method for determining whether a correlated quantum channel is able to reliably convey quantum messages by studying the entanglement properties of the teleportation mediating system. Our model is then generalized to the continuous-variable case.
Quantum teleportation of an unknown quantum state necessitates the transmission of two classical bits of information; however, when the quantum state is partially known, only a single classical bit is required for the teleportation of its quantum coherence. In this study, we explore the teleportation of quantum coherence through noisy channels utilizing merely one classical bit of information. Our findings reveal that, in contrast to noise-free scenarios, the generalized Bell states POVM (GBS-POVM) and non-maximally entangled states may surpass the performance of Bell states POVM (BS-POVM) and maximally entangled states in enabling probabilistic teleportation of quantum coherence. Nevertheless, when assessing the average amount of quantum coherence that can be teleported, maximally entangled states combined with BS-POVM emerges as the optimal choice, regardless of the type of noise encountered. Moreover, we uncover that for bit-phase-flip (BPF) noise, it is feasible to construct a suitable GBS-POVM that completely mitigates this noise. For other types of noise, we demonstrate that enhancing the teleportation of quantum coherence can be accomplished through entangling two consecutive uses of the same noisy channel, i.e., correlated noise. Notably, correlation effects arising from Pauli channels can entirely negate the detrimental impact of Pauli noises on the teleportation process for quantum coherence.