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arXiv:1908.01097 · Physical Review A

High-dimensional quantum teleportation under noisy environments

Alejandro Fonseca

Published Dec 9, 2019• 102 citations
arXivHTMLPDF

Abstract

We study the protocol of qudit teleportation using quantum systems subjected to several kinds of noise for arbitrary dimensionality $d$. We consider four classes of noise: dit-flip, $d$-phase-flip, dit-phase-flip, and depolarizing noise, each of them corresponding to a family of Weyl operators, introduced via Kraus formalism. We derive a general expression for the average fidelity of teleportation in arbitrary dimension $d$ for any combination of noise on the involved qudits. Under a different approach we derive the average fidelity of teleportation for a more general scenario involving the $d$-dimensional generalization of amplitude damping noise as well. We show that all possible scenarios may be classified in four different behaviors and discuss the cases in which it is possible to improve the fidelity by increasing the associated noise fractions. All our results are in agreement with previous analysis for the case of qubits [R. Fortes and G. Rigolin, Phys. Rev. A 92, 012338 (2015)].

DOI
10.1103/physreva.100.062311

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We study the protocol of qudit teleportation using quantum systems subjected to several kinds of noise for arbitrary dimensionality ddd. We consider four classes of noise: dit-flip, ddd-phase-flip, dit-phase-flip, and depolarizing noise, each of them corresponding to a family of Weyl operators, introduced via Kraus formalism. We derive a general expression for the average fidelity of teleportation in arbitrary dimension ddd for any combination of noise on the involved qudits. Under a different approach we derive the average fidelity of teleportation for a more general scenario involving the ddd-dimensional generalization of amplitude damping noise as well. We show that all possible scenarios may be classified in four different behaviors and discuss the cases in which it is possible to improve the fidelity by increasing the associated noise fractions. All our results are in agreement with previous analysis for the case of qubits [R. Fortes and G. Rigolin, Phys. Rev. A 92, 012338 (2015)].
In the actual quantum communication process, there will inevitably be noise in the quantum channel. In this chapter, we consider teleportation protocols in noisy environment. There are different types of noises, which are amplitude-damping, bit-flip, phase-flip, phase-damping, depolarizing noise, etc. Throughout this chapter, four types of noises are considered, namely amplitude-damping, bit-flip, phase-flip, phase-damping, under which teleportation without and with control are presented. The analysis of fidelity of the process against the variation of noise parameters are also discussed. Teleportation through noisy environment have been discussed in a good number of papers like [ 43 , 57 , 60 , 63 , 69 , 79 , 92 , 96 , 114 , 178 , 198 , 204 ].
We investigate how the efficiency of the quantum teleportation protocol is affected when the qubits involved in the protocol are subjected to noise or decoherence. We study all types of noise usually encountered in real-world implementations of quantum communication protocols, namely, the bit-flip, phase-flip (phase damping), depolarizing, and amplitude-damping noise. Several realistic scenarios are studied in which a part or all of the qubits employed in the execution of the quantum teleportation protocol are subjected to the same or different types of noise. We find noise scenarios not yet known in which more noise or less entanglement lead to more efficiency. Furthermore, we show that if noise is unavoidable it is better to subject the qubits to different noise channels in order to obtain an increase in the efficiency of the protocol.
The concept of quantum teleportation is fundamental in the theory of quantum communication. Developing models of quantum teleportation in different physical scenario is a modern trend of research in this direction. This work is at the interface of hypergraph theory and quantum teleportation. We propose a new teleportation protocol for qutrit states in a noisy environment. This protocol utilizes a shared quantum hypergraph state between parties as quantum channels, to carry quantum information. During the preparation of the shared state different quantum noise may act on it. In this article, we consider six types of noises which are generalized for qutrits using Wyel operators. They are the qutrit-flip noise, qutrit-phase-flip noise, depolarizing noise, Markovian and non-Markovian amplitude damping channel, Markovian and non-Markovian dephasing channel, and non-Markovian depolarization noise. There are only five qutrit hypergraph states which satisfies our requirements to be used as a channel. We consider all of them in this work. For different hypergraph states and different noises we work out the analytical expressions of quantum teleportation fidelity.
Noise is a major challenge in quantum computing, affecting the reliability of quantum protocols. In this work, we analytically study the impact of various noise processes, such as depolarization, bit flip, and phase flip, on the quantum state teleportation protocol. Each noise process is modeled as a quantum channel and is applied individually to all qubits after the corresponding unitary operations to simulate realistic conditions. We evaluate the fidelity between the ideal and noisy teleported states to quantify the effect of noise. Our analysis shows that the fidelity decreases polynomially, in general, as the noise strength increases for all noise types, highlighting the sensitivity of state teleportation to different noise mechanisms. However, in the low noise regime, the fidelity decreases only linearly, indicating the robustness of the teleportation protocol. These results provide insight into error characterization and can inform strategies for noise mitigation in practical quantum computing applications.
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