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Communications in Theoretical Physics

Steady-state teleportation fidelity and Bell nonlocality in dissipative environments

Yu-Xia Xie

Published Apr 22, 2021• 3 citations
Publisher

Abstract

Abstract We investigate quantum teleportation and Bell nonlocality for two channel qubits coupled via the Heisenberg interaction and subject to two independent dissipative environments. Compared with the case of two uncoupled qubits, it is shown that the interaction Hamiltonian is beneficial for enhancing the teleportation fidelity and Bell nonlocality, and remarkably, it can also be used to create nonclassical teleportation fidelity and Bell nonlocality even from the initial product states. Moreover, the interaction Hamiltonian guarantees the generation of steady-state nonclassical teleportation fidelity, which is independent of the initial state and therefore one can take any state as the initial channel state.

DOI
10.1088/1572-9494/abfa85

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Abstract We investigate quantum teleportation and Bell nonlocality for two channel qubits coupled via the Heisenberg interaction and subject to two independent dissipative environments. Compared with the case of two uncoupled qubits, it is shown that the interaction Hamiltonian is beneficial for enhancing the teleportation fidelity and Bell nonlocality, and remarkably, it can also be used to create nonclassical teleportation fidelity and Bell nonlocality even from the initial product states. Moreover, the interaction Hamiltonian guarantees the generation of steady-state nonclassical teleportation fidelity, which is independent of the initial state and therefore one can take any state as the initial channel state.
Abstract We investigate how the correlations between consecutive actions of the two-qubit noisy channels affect quantum teleportation, entanglement, and Bell nonlocality. For the initial Bell and Werner states used for teleportation, we established connections among these three quantities, and obtained the minimum correlation strengths for achieving the nonclassical teleportation fidelity, nonvanishing entanglement, and Bell-nonlocal states. It was found that these three quantities can be noticeably enhanced due to the existence of the channel correlations. By considering a colored dephasing channel, we further investigated the combined effects of the channel correlation and the (non-)Markovianity of the channel on the teleportation fidelity, entanglement, and Bell nonlocality. The result shows that while they decrease monotonically with time in the Markovian regime, their strengths can be further enhanced due to the non-Markovian memory effect in a wide time region.
We investigate quantum teleportation of a single unknown qubit state for the dissipative situation in which both qubits of the entangled channels that are formed by the pure and mixed maximally entangled states are subjected to local structured reservoirs. We consider the dissipative factors in Markovian and non-Markovian regimes on the average fidelity of the teleportation by solving the quantum master equation. It is shown that the fidelity of teleportation decreases exponentially over time in Markovian environments and attenuates oscillatorily in non-Markovian ones. In addition, when the non-Markovian and detuning conditions are satisfied simultaneously, the fidelity increases as the detuning increases. Even with a lower purity of entanglement, fidelity can be preserved effectively at comparatively high levels.
For single-qubit teleportation, it has been shown that there is a family of two-qubit mixed states whose teleportation fidelity can be enhanced by subjecting one of the qubits to an amplitude damping channel. This is an interesting result, since noise in general degrades quantum entanglement. It is believed that this enhancement is due to an improvement in the classical correlations of the two-qubit states. Here, we consider two-qubit teleportation using a family of four-qubit mixed states as a resource. In this context, we show that one can again achieve enhancement in teleportation fidelity via dissipative interactions with the local environment. For a rather general class of input states, we find that this improvement implies an enhancement in the quantum discord of some teleported states. We conjecture that an improvement in some quantum property of the four-qubit mixed states could have resulted from the local interactions. We expect that our analysis will make an important case study for future investigations on the different aspects of composite quantum systems.
We investigate quantum teleportation through dissipative channels and calculate teleportation fidelity as a function of damping rates. It is found that the average fidelity of teleportation and the range of states to be teleported depend on the type and rate of the damping in the channel. Using the fully entangled fraction, we derive two bounds on the damping rates of the channels: one is to beat the classical limit and the second is to guarantee the nonexistence of any other copy with better fidelity. The effect of the initially distributed maximally entangled state on the process is presented; the concurrence and the fully entangled fraction of the shared states are discussed. We intend to show that prior information on the dissipative channel and the range of qubit states to be teleported is helpful for the evaluation of the success of teleportation, where success is defined as surpassing the fidelity limit imposed by the fidelity of the 1-to-2 optimal cloning machine for the specific range of qubits.
We show how an interaction with the environment can enhance fidelity of quantum teleportation. To this end, we present examples of states which cannot be made useful for teleportation by any local unitary transformations; nevertheless, after being subjected to a dissipative interaction with the local environment, the states allow for teleportation with genuinely quantum fidelity. The surprising fact here is that the necessary interaction does not require any intelligent action from the parties sharing the states. In passing, we produce some general results regarding optimization of teleportation fidelity by local action. We show that bistochastic processes cannot improve fidelity of two-qubit states. We also show that in order to have their fidelity improvable by a local process, the bipartite states must violate the so-called reduction criterion of separability.
We study quantum teleportation via two two-level atoms coupled collectively to a multimode vacuum field and prepared initially in different atomic states. We concentrated on the influence of the spontaneous emission, collective damping and dipole–dipole interaction of the atoms on fidelity dynamics of quantum teleportation and obtained the region of spatial distance between the two atoms over which the state can be teleported nonclassically. Moreover, we showed through concrete examples that entanglement of the channel state is the prerequisite but not the only essential quantity for predicting the teleportation fidelity.