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Laser Physics Letters

Mitigating decoherence effect on teleportation and dense coding by reservoir engineering

Ling-shan Xu

Published Dec 1, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1612-202x/ae1e6b

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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.
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.
In order to understand the resourcefulness of a natural quantum system in quantum communication tasks, we study the dense coding capacity (DCC) and teleportation fidelity of Haar uniformly generated random multipartite states of various ranks. We prove that when a rank-2 two-qubit state, a Werner state, and a pure state possess the same amount of entanglement, the DCC of a rank-2 state belongs to the envelope made by pure and Werner states. In a similar way, we obtain an upper bound via the generalized Greenberger-Horne-Zeilinger state for rank-2 three-qubit states when the dense coding with two senders and a single receiver is performed and entanglement is measured in the senders:receiver bipartition. The normalized frequency distributions of DCC for randomly generated two-, three-, and four-qubit density matrices with global as well as local decodings at the receiver's end are reported. The estimation of mean DCC for two-qubit states is found to be in good agreement with the numerical simulations. Universally, we observe that the performance of random states for dense coding as well as teleportation decreases with the increase of the rank of states, which we have shown to be surmounted by the local preprocessing operations performed on the shared states before starting the protocols, irrespective of the rank of the states. The local preprocessing employed here is based on positive operator valued measurements along with classical communication and we show that unlike dense coding with two-qubit random states, the senders' operations are always helpful to probabilistically enhance the capabilities of implementing dense coding as well as teleportation.
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.
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.
We investigate measurement uncertainty of two incompatible observables, dense coding capacity, teleportation fidelity, and quantum Fisher information for two qubits traversing sequentially a dephasing channel modeled by the multimode bosonic field. Using a memory factor determined by the time separation between two channel uses and the transmit time of each qubit, it is shown that the memory effect of this channel on these four quantum characteristics is state-dependent. It is beneficial for some initial states and detrimental for the other states. There is also circumstance in which the memory effects with different origins have different influences on these quantum characteristics. These results may enrich our comprehension on the interplay between memory effect of a channel and decoherence process of a multi-qubit system.
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.