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Entropy

Quantum Teleportation and Dense Coding in Multiple Bosonic Reservoirs

Yu Wang, Ming‐Liang Hu

Published Aug 12, 2022• 8 citations
Publisher

Abstract

The effect of a reservoir on quantum communication depends on its spectral density. The efficiency of quantum teleportation and dense coding is explored when each one of the channel qubits is coupled simultaneously to multiple bosonic reservoirs. It is shown that the non-Markovianity triggered by increasing the reservoir number can induce revivals of quantum advantages of the two protocols after their disappearance. However, the backflow of information to the system that signifies non-Markovianity does not always induce immediate revivals of the quantum advantages. There may be a delayed effect for some initial states, and only as the backflow of information accumulates to a certain extent can the revivals of quantum advantages be triggered.

DOI
10.3390/e24081114

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The effect of a reservoir on quantum communication depends on its spectral density. The efficiency of quantum teleportation and dense coding is explored when each one of the channel qubits is coupled simultaneously to multiple bosonic reservoirs. It is shown that the non-Markovianity triggered by increasing the reservoir number can induce revivals of quantum advantages of the two protocols after their disappearance. However, the backflow of information to the system that signifies non-Markovianity does not always induce immediate revivals of the quantum advantages. There may be a delayed effect for some initial states, and only as the backflow of information accumulates to a certain extent can the revivals of quantum advantages be triggered.
Quantum teleportation and dense coding are well-known quantum protocols that have been widely explored in the field of quantum computing. In this paper, the efficiency of quantum teleportation and dense coding protocols is examined in two-level atoms with two-photon transitions via the Stark shift effect, where each atom is separately coupled to a dissipative reservoir at zero temperature. Our results show that non-Markovianity and Stark shift can play constructive roles in restoring the quantum advantages of these protocols after they are diminished. These findings could offer a potential solution to preserving the computational and communicative advantages of quantum technologies.
Abstract Reservoir engineering is an efficient technique for mitigating the adverse effects of decoherence. We consider teleportation and dense coding protocols with the two channel qubits being disturbed by their respective bosonic reservoirs, and show that both the average teleportation fidelity (ATF) and dense coding capacity (DCC) of the channel can be well preserved by adding auxiliary qubits into each reservoir or by detuning the central frequency of the reservoir from the qubit’s transition frequency. For the initial Bell states, the ATF and DCC progressively approach their respective maxima with an increasing number of auxiliary qubits and frequency detuning.
Decoherence of quantum information of qubits is investigated under the influence of the non-Markovian quantum channel, where the correlation time of reservoir variables takes a finite value. Degradation of purity, distinguishability and entanglement of qubit states are evaluated. It is found that the non-Markov effect makes the coherence time of quantum information longer than that obtained for the Markovian quantum channel. Furthermore, the quantum teleportation and quantum dense coding of qubits are considered under the influence of non-Markov channels. The fidelity between teleported and original states and the Holevo capacity are obtained.
The uncertainty principle imposes a limitation on the measurement accuracy of two incompatible observables and has potential applications in quantum information science. We explore the bipartite entropic uncertainty relation and dense coding for two qubits coupled via dipole–dipole interaction and subject to a bosonic reservoir. It is shown that there exists a trade-off between the uncertainty bound and the dense coding capacity which results in their opposite dynamical behaviors. Moreover, the behaviors of the measurement uncertainty and the dense coding capacity rely crucially on the initial system–reservoir correlation, the strength of the dipole–dipole interaction, and the degree of non-Markovianity, and one can reduce the measurement uncertainty and enhance the dense coding capacity by tuning these parameters to appropriate values.
Quantum teleportation of the quantum correlated states via noisy channels is investigated. The noisy channels are realized by a couple of two-level atoms (qubits) embedded in a zero-temperature bosonic bath. The entanglement of the channels is provided by the interqubit interaction and/or through the memory of the environment. Especially for the case of noninteracting qubits, the resource of the teleportation can be supplied by the entangled state of the channel, which is provided by information backflow in the non-Markovian regime of the evolution. More non-Markovianity of the dynamics generates a higher amount of induced entanglement and hence enhances the quality of the quantum correlation teleportation process. When the degree of non-Markovianity of dynamics is sufficiently high, quantum teleportation, which is superior to classical communication, is achievable.
We investigate the fidelity and the linear entropy of teleportation using a shared two qubit initially maximally entangled state as a quantum channel, in which one qubit interacts with a two-state system named as the probe particle in a reservoir by dispersive atom-field coupling. Without the coupling of the probe particle with the reservoir, the quantum channel state is a pure state but not an initially maximally entangled state under the influence of the probe particle, and thus Bob obtains a pure state with an average fidelity fluctuating between 2/3 and 1 with time t. In the cases of the probe particle coupling with the reservoir the Markovian and non-Markovian dynamics of such a quantum channel are discussed in detail to show the influence of the reservoir on teleportation. The quantum channel state is a mixed state, but its entanglement does not die under the influence of the reservoir. It is found that, for a given teleported state, the fidelity and the linear entropy both evolve asymptotically to their fixed values, respectively, which are relative to the decay rate γ (Markovian) or to the pseudomode decay rate Γ (non-Markovian). Furthermore, when time t ≫ γ^(-1) and t ≫ Γ^(-1), the average fidelity increases with the augments of γ and Γ, while it decreases with the aggrandizement of the dispersive interaction strength κ.