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Europhysics Letters (EPL)

Effects of Pauli channels and noisy quantum operations on standard teleportation

Ye Yeo, Zhe-Wei Kho, Lixian Wang

Published May 1, 2009• 34 citations
Publisher

Abstract

Quantum noises generated by non-commuting Pauli operators may also cause entanglement sudden death (ESD). In this work, stimulated by this observation, we show how a Pauli- X or - Y gate could also destroy entanglement in a finite time when they are executed in the presence of dephasing noise. Motivated by the fact that they are basic to quantum information processing, we analyze the impact of noisy operations and non-commuting noises on single- and two-qubit teleportation —archetype of quantum communication. By considering the decoherence dynamics during establishment of the channel states and noisy recovery operations, we show that there is a finite lifetime for a standard teleportation to be completed before it loses the quantum advantage over purely classical communication.

DOI
10.1209/0295-5075/86/40009

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Quantum noises generated by non-commuting Pauli operators may also cause entanglement sudden death (ESD). In this work, stimulated by this observation, we show how a Pauli- X or - Y gate could also destroy entanglement in a finite time when they are executed in the presence of dephasing noise. Motivated by the fact that they are basic to quantum information processing, we analyze the impact of noisy operations and non-commuting noises on single- and two-qubit teleportation —archetype of quantum communication. By considering the decoherence dynamics during establishment of the channel states and noisy recovery operations, we show that there is a finite lifetime for a standard teleportation to be completed before it loses the quantum advantage over purely classical communication.
Maintaining quantum coherence and entanglement in the presence of environmental noise, particularly within non-Markovian contexts, represents a significant challenge for the progression of quantum information science and technology. This study offers a substantial advancement by investigating the dynamics of a two-qubit system subjected to diverse noise conditions, encompassing relaxation, dephasing, and their cumulative effects. By employing quantum-state-diffusion equations specifically crafted for non-Markovian environments, we introduce an innovative strategy to counteract the detrimental influences of environmental noise on quantum teleportation fidelity and entanglement concurrence. Our results underscore the potential for external interventions to markedly improve the resilience of quantum information processing tasks over prolonged durations, especially in settings where dephasing noise prevails. A key revelation is the intricate relationship between dephasing noise and the initial state of entanglement, which profoundly impacts the occurrence of entanglement sudden death. This research not only deepens our comprehension of quantum system dynamics under noisy circumstances but also furnishes practical directives for engineering robust quantum systems, a necessity for the development of scalable quantum technologies.
We show how noncommuting noises could cause a Bell state ${\ensuremath{\chi}}_{0}$ to suffer entanglement sudden death (ESD). ESD may similarly occur when a noisy operation acts, if the corresponding Hamiltonian and Lindblad operator do not commute. We study the implications of these in special dense coding S\mathcal{S}S. When noises that cause ESD act, we show that ${\ensuremath{\chi}}_{0}$ may lose its capacity for S\mathcal{S}S before ESD occurs. Similarly, ${\ensuremath{\chi}}_{0}$ may fail to yield information transfer better than classically possible when the encoding operations are noisy, though entanglement is not destroyed in the process.
This study compares the effects of Markovian and non-Markovian noise channels on a standard Bell state-based quantum teleportation protocol. Amplitude damping, phase damping, depolarising, and time-dependent (non-Markovian) channels were analysed within the same simulation framework, and teleportation fidelity was calculated as a function of noise intensity. Critical noise parameters were determined with reference to the classical threshold value (F=2/3), entanglement dynamics were evaluated using concurrence, and entanglement sudden death (ESD) points were identified. Non-Markovian behaviour was quantitatively analysed using the Breuer–Laine–Piilo (BLP) metric. The results show that different noise mechanisms significantly affect teleportation performance, and that entanglement conservation and operational teleportation advantages do not always coincide. Numerical results were validated by analytical comparison
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.
Abstract Quantum teleportation exemplifies how the transmission of quantum information starkly differs from that of classical information and serves as a key protocol for quantum communication and quantum computing. While an ideal teleportation protocol requires noiseless quantum channels to share a pure maximally entangled state, the reality is that shared entanglement is often severely degraded due to various decoherence mechanisms. Although the quantum noise induced by the decoherence is indeed a major obstacle to realizing a near-term quantum network or processor with a limited number of qubits, the methodologies considered thus far to address this issue are resource-intensive. Here, we demonstrate a protocol that allows optimal quantum teleportation via noisy quantum channels without additional qubit resources. By analyzing teleportation in the framework of generalized quantum measurement, we optimize the teleportation protocol for noisy quantum channels. In particular, we experimentally demonstrate that our protocol enables to teleport an unknown qubit even via a single copy of an entangled state under strong decoherence that would otherwise preclude any quantum operation. Our work provides a useful methodology for practically coping with decoherence with a limited number of qubits and paves the way for realizing noisy intermediate-scale quantum computing and quantum communication.