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arXiv:2403.10551

Impact of Decoherence on Average Correlation

A. M. Silva

Published Mar 13, 2024• 0 citations
arXivHTMLPDF

Abstract

This article presents a comprehensive study of the impact of decoherence on the average correlation for pure quantum states. We explore two primary mechanisms of decoherence: phase damping and amplitude damping, each having distinct effects on quantum systems. Phase damping, which describes the loss of quantum coherence without energy loss, primarily affects the phase relationships between the components of a quantum system while amplitude damping involves energy dissipation and also affects the state's occupation probabilities. We show that the average correlation follows a predictable decaying pattern in both scenarios. Our analysis can be understood in the context of quantum computing, by focusing on how phase damping influences the entanglement and correlation between qubits, key factors in quantum computational efficiency and error correction protocols.

DOI
10.48550/arxiv.2403.10551

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This article presents a comprehensive study of the impact of decoherence on the average correlation for pure quantum states. We explore two primary mechanisms of decoherence: phase damping and amplitude damping, each having distinct effects on quantum systems. Phase damping, which describes the loss of quantum coherence without energy loss, primarily affects the phase relationships between the components of a quantum system while amplitude damping involves energy dissipation and also affects the state's occupation probabilities. We show that the average correlation follows a predictable decaying pattern in both scenarios. Our analysis can be understood in the context of quantum computing, by focusing on how phase damping influences the entanglement and correlation between qubits, key factors in quantum computational efficiency and error correction protocols.
Cooperative effects in the loss (the amplitude damping) and decoherence (the phase damping) of the qubits (two-state quantum systems) due to the inevitable coupling to the same environment are investigated. It is found that the qubits undergo the dissipation coherently in this case. In particular, for a special kind of input states (called the coherence-preserving states), whose form depends on the type of the coupling, loss and decoherence in quantum memory are much reduced. Based on this phenomenon, a scheme by encoding the general input states of the qubits into the corresponding coherence-preserving states is proposed for reducing the cooperative loss and decoherence in quantum computation or communication.
Quantum entanglement manifests as a distinctive correlation between particles that transcends classical boundaries when their quantum states cannot be described independently. On the other hand, as quantum systems interact with their surroundings, decoherence emerges, leading to the gradual decay of quantum coherence and entanglement. In the case of entanglement, this is known as entanglement sudden death (ESD). Decoherence mechanisms are examined, focusing on how various environmental factors, such as thermal, electromagnetic, and collisional decoherence, influence the integrity of entangled states. The role of quantum noise, such as amplitude damping, phase damping, and depolarizing, is also analyzed. By integrating theoretical insights with experimental findings, this study highlights the delicate balance between maintaining entanglement and mitigating decoherence. The findings have significant implications for the development of quantum technologies, including quantum computing and quantum communication, where preserving entanglement is crucial for achieving robust and reliable performance.
Quantum correlations between two or more different degrees of freedom of the same particle are sometimes referred to as intraparticle entanglement. In this work, we study these intraparticle correlations between two different degrees of freedom under various decoherence channels, viz. amplitude damping, depolarizing, and phase damping channels. We mainly focus on the amplitude-damping channel for which we obtain an exact analytical expression for the concurrence of an arbitrary initial pure state. In this channel, we observe the unique feature of entanglement arising from a separable initial state. We show that this channel allows for a revival of entanglement with an increasing damping parameter, including from a zero value of the concurrence. We also consider the amplitude-damping channel for interparticle entanglement and show that it does not display any of the above-mentioned interesting features. Further, for comparable parameters, the decay of entanglement in the interparticle system is much greater than in the intraparticle system, which we also find to be true for the phase damping and depolarizing channels. Thus, intraparticle entanglement subjected to damping is much more robust than interparticle entanglement.
We investigate the effects of error correction on non-local quantum coherence as a function of time, extending the study by Sainz and Bjork. We consider error correction of amplitude damping, pure phase damping and combinations of amplitude and phase damping as they affect both fidelity and quantum entanglement. Initial two-qubit entanglement is encoded in arbitrary real superpositions of both Φ\PhiΦ-type and Ψ\PsiΨ-type Bell states. Our main focus is on the possibility of delay or prevention of ESD (early stage decoherence, or entanglement sudden death). We obtain the onset times for ESD as a function of the state-superposition mixing angle. Error correction affects entanglement and fidelity differently, and we exhibit initial entangled states for which error correction increases fidelity but decreases entanglement, and vice versa.
We investigate the effects of error correction on non-local quantum coherence as a function of time, extending the study by Sainz and Björk. We consider error correction of amplitude damping, pure phase damping and combinations of amplitude and phase damping as they affect both fidelity and quantum entanglement. Initial two-qubit entanglement is encoded in arbitrary real superpositions of both Φ-type and Ψ-type Bell states. Our main focus is on the possibility of delay or prevention of ESD (early stage decoherence, or entanglement sudden death). We obtain the onset times for ESD as a function of the state-superposition mixing angle. Error correction affects entanglement and fidelity differently, and we exhibit initial entangled states for which error correction increases fidelity but decreases entanglement, and vice versa.
The combined effects of memory effects due to correlated actions of the amplitude damping channel on two qubits and temporal correlations in the time evolution of each qubit on the average steered coherence (ASC) are explored. For the input Bell states, it is shown that the two kinds of memory effects are beneficial for enhancing ASC of the output states in a wide time region. In particular, the ASC is immune to decoherence for some input states if the actions of the amplitude damping channel are fully correlated. Moreover, in the infinite-time limit, the positive role of the non-Markovian effect on the steady-state ASC disappears, whereas the correlated actions of the channel are still beneficial to certain input states.