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Zhongguo kexue. Wulixue Lixue Tianwenxue

Quantum coherence over the noisy quantum channels

Zhengjun Xi

Published Feb 1, 2015• 8 citations
Publisher

Abstract

The coherent superposition of quantum states is one of the characteristic features of quantum mechanics, and it is also physical resource of quantum information processing. The coherence of quantum system can not last a long time as the effect of the noise. How well has the noisy channel preserved the quantum coherence of the quantum system? Based on the relative entropy of coherence, in this paper, we discuss the coherence, entanglement and quantum correlations in the bipartite quantum system. To discuss the effect of the noise, we then give a definition of the decayed amount of the maximal quantum coherence, i.e., the decay of coherence. Then we obtain that the uncertainty relations between entanglement and the coherence with respect to the noisy models. Finally, we used the measure of the decay of coherence to discuss how well several noisy channels preserves the coherence.

DOI
10.1360/sspma2014-00455

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The coherent superposition of quantum states is one of the characteristic features of quantum mechanics, and it is also physical resource of quantum information processing. The coherence of quantum system can not last a long time as the effect of the noise. How well has the noisy channel preserved the quantum coherence of the quantum system? Based on the relative entropy of coherence, in this paper, we discuss the coherence, entanglement and quantum correlations in the bipartite quantum system. To discuss the effect of the noise, we then give a definition of the decayed amount of the maximal quantum coherence, i.e., the decay of coherence. Then we obtain that the uncertainty relations between entanglement and the coherence with respect to the noisy models. Finally, we used the measure of the decay of coherence to discuss how well several noisy channels preserves the coherence.
Quantum coherence is one of the most fundamental features of quantum mechanics that underlines the unique characteristics of quantum technology. Optical cat state is a superposition of two coherent states and has broad applications in quantum information and quantum metrology. In the application of optical cat state, it is essential to investigate the quantum coherence of it when it interacts with the environment. In this manuscript, we present the quantum coherence of an optical cat state in a noisy channel by calculating the relative entropy in Fock basis. We show that the quantum coherence of an optical cat state is robust against loss and noise in a noisy channel. Different from quantum coherence, the negativity of the Wigner function and the fidelity of the cat state are not robust against loss and noise. Our result provides a reference for applying optical cat states in a noisy environment.
Quantum coherence and quantum correlations are of fundamental and practical significance for the development of quantum mechanics.They are also cornerstones of quantum computation and quantum communication theory. Searching physically meaningful and mathematically rigorous quantifiers of them are long-standing concerns of the community of quantum information science, and various faithful measures have been introduced so far. We review in this paper the measures of discordlike quantum correlations for bipartite and multipartite systems, the measures of quantum coherence for any single quantum system, and their relationship in different settings. Our aim is to provide a full review about the resource theory of quantum coherence, including its application in many-body systems, and the discordlike quantum correlations which were defined based on the various distance measures of states. We discuss the interrelations between quantum coherence and quantum correlations established in an operational way, and the fundamental characteristics of quantum coherence such as their complementarity under different basis sets, their duality with path information of an interference experiment, their distillation and dilution under different operations, and some new viewpoints of the superiority of the quantum algorithms from the perspective of quantum coherence. Additionally, we review properties of geometric quantum correlations and quantum coherence under noisy quantum channels. Finally, the main progresses for the study of quantum correlations and quantum coherence in the relativistic settings are reviewed. All these results provide an overview for the conceptual implications and basic connections of quantum coherence, quantum correlations, and their potential applications in various related subjects of physics.
In this paper, we study analytically the skew information-based coherence, and compare its dynamics with that of the l1 norm of coherence for two-qubit Bell-diagonal states under the influence of correlated Pauli channels, such as correlated dephase, depolarizing and classical noisy channels, respectively. The similar as well as different features between the skew information-based coherence and l1 norm of coherence are discussed. In addition, the physical mechanism of preserving quantum coherence based on memory coefficient of correlated channels and non-Markovian memory effect is also expounded.
Criteria of measure quantifying quantum coherence, a unique property of quantum system, are proposed recently. In this paper, we first give an uncertainty-like expression relating the coherence and the entropy of quantum system. This finding allows us to discuss the relations between the entanglement and the coherence. Further, we discuss in detail the relations among the coherence, the discord and the deficit in the bipartite quantum system. We show that, the one-way quantum deficit is equal to the sum between quantum discord and the relative entropy of coherence of measured subsystem.
Quantum dots are nanometer-scale semiconductor particles that exhibit size-dependent quantum mechanical properties. In this work, we investigate the dynamics of quantum correlations, quantified by the concurrence and the quantum coherence, in a bipartite system of coupled double quantum dots. The analysis is carried out within both Markovian and non-Markovian regimes, and further extended to different noisy quantum channels, including amplitude damping, phase flip, and phase damping. Our results show that environmental memory plays a crucial role in the preservation of quantum correlations, leading to oscillatory behavior and partial revivals in the non-Markovian regime, in contrast to the monotonic decay observed under Markovian dynamics. Moreover, distinct decoherence mechanisms induce qualitatively different effects: dissipative channels rapidly suppress correlations, while phase-based channels lead to either redistribution or gradual degradation. A key finding is that quantum coherence exhibits a higher robustness compared to entanglement under all considered conditions, highlighting its relevance as a reliable quantum resource in noisy environments. These results provide valuable insights into the control and protection of quantum correlations in realistic solid-state systems.
Abstract We address the time evolution of quantum correlations (QCs) such as entanglement, purity, and coherence for a model of two non-interacting qubits initially prepared as a maximally entangled bipartite state. We contrast the comparative potential of the classical fields to preserve these QCs in the noisy and noiseless realms. We also disclose the characteristic dynamical behavior of the QCs of the two-qubit state under the static noise effects originating from the common and different configuration models. We show that there is a direct connection between the fluctuations allowed by an environment and the preservation of QCs. Due to the static noise dephasing effects, the QCs are suppressed, resulting in the separability of the two-qubit entangled state after a finite duration. For bipartite QCs preservation, we show that the common configuration is more resourceful than the different configuration. Furthermore, this protection of the QCs under static noise for large intervals is entirely attributable to the existence of the entanglement sudden death and birth phenomenon. Most importantly, we found the bipartite QCs less fragile than the tripartite ones in comparison under the static noise. In addition, we find the concurrence measure to show more evident revivals of entanglement in comparison.