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Laser Physics Letters

Coherence evolution of bipartite state under decoherent environment

Tao Wu, Qiong Liu, Jiadong Shi

Published Jul 6, 2022• 2 citations
Publisher

Abstract

Abstract We provide an analysis on the quantum coherence (QC) of a general two-qubit pure state interacting with a local decoherent environment. Our results show that the QC in the environment obeys a conservation relation, i.e. the coherence evolution is equal to the product of the coherence contained in the initial state and the environmental action on the maximum entangled state. This means that the coherence dynamics behaviors of the composite quantum-environment system can be observed by analyzing the environmental action. Moreover, within the Markovian environment, the QC damps monotonously, while it exhibits damped oscillations and suffers damped revivals within the non-Markovian environment. These phenomena of damped oscillations and revivals have been interpreted as memory effects of the non-Markovian environment.

DOI
10.1088/1612-202x/ac772b

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Abstract We provide an analysis on the quantum coherence (QC) of a general two-qubit pure state interacting with a local decoherent environment. Our results show that the QC in the environment obeys a conservation relation, i.e. the coherence evolution is equal to the product of the coherence contained in the initial state and the environmental action on the maximum entangled state. This means that the coherence dynamics behaviors of the composite quantum-environment system can be observed by analyzing the environmental action. Moreover, within the Markovian environment, the QC damps monotonously, while it exhibits damped oscillations and suffers damped revivals within the non-Markovian environment. These phenomena of damped oscillations and revivals have been interpreted as memory effects of the non-Markovian environment.
We theoretically study the non-Markovian dynamics of qubit systems coupled to nonequilibrium environments with nonstationary and non-Markovian statistical properties. The reduced density matrix of the single qubit system satisfies a closed third-order differential equation with all the higher-order environmental correlations taken into account and the reduced density matrix of the two qubit system can be expressed as the Kraus representation in terms of the tensor products of the single qubit Kraus operators. We derive the relation between the entanglement and nonlocality of the two qubit system which are both closely associated with the decoherence function. We identify the threshold values of the decoherence function to ensure the existences of the concurrence and nonlocal quantum correlations for a given evolution time when the two qubit system is initially prepared in the composite Bell states and the extended Werner states, respectively. It is shown that the environmental nonstationary feature can suppress the decoherence and disentanglement dynamics and can reduce the coherence and entanglement revivals in non-Markovian dynamics regime. In addition, it is shown that the environmental non-Markovian feature can enhance the coherence revivals in the single decoherence dynamics and the entanglement revivals in the two qubit disentanglement dynamics, respectively. Furthermore, the environmental nonstationary and non-Markovian features can enhance the nonlocality of the two qubit system.
The time evolution of the distribution and shareability of quantum coherence of a tripartite system in a non-Markovian environment is examined. The total coherence can be decomposed into various contributions, ranging from local, global bipartite and global tripartite, which characterize the type of state. We identify coherence revivals for non-Markovian systems for all the contributions of coherence. The local coherence is found to be much more robust under the environmental coupling due to an effective smaller coupling to the reservoir. This allows us to devise a characterization of a quantum state in terms of a coherence tuple on a multipartite state simply by examining various combinations of reservoir couplings. The effect of the environment on the shareability of quantum coherence, as defined using the monogamy of coherence, is investigated and found that the sign of the monogamy is a preserved quantity under the decoherence. We conjecture that the monogamy of coherence is a conserved property under local incoherent processes.
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.
Quantum Coherence (QC) has a fundamental role in Quantum Mechanics (QM). It has been studied since the emergence of QM. However, this quantum feature is easily destroyed when a physical system interacts with the environment. Also, recently the quantum coherence has been highlighted because of the possibility of using its as a resource in the Quantum Information Science (QIS). In this work we study the QC flow of a qubit (two-level system) interacting with the environment modeled by quantum channels of noise that are very common in QIS. These channels represent some physical systems and are widely used for error correction studies. We calculate the QC by the l1-norm, doing this for the different channels seeking to relate it to the entanglement, which is also another key topic in QM. We note that in the amplitude damping channel the total QC is equal to the sum of the local and non-local parts and that the non-local part is equivalent to entanglement. For the phase damping channel, entanglement does not cover all non-local QC. Here there is a gap between them that may depend on the time and on the initial state. Besides, for the bit, phase, and bit phase flip channels the possibility and the conditions for invariance of QC are considered. Also, we notice that for the depolarizing channel we can use the qubit as a catalyst for the creation of non-local QC and entanglement. We, as well, observed that even initial states incoherent can lead to transient quantum coherence between system and environment. We also showed that the emergence of entanglement does not necessarily imply the destruction of QC. Furthermore, we investigated whether QC is lost or changed into other types of correlations and besides which initial conditions allow making quantum coherence robust to decoherence.
We theoretically study the non-Markovian disentanglement dynamics of a two-qubit system coupled to nonequilibrium environments with nonstationary and non-Markovian random telegraph noise statistical properties. The reduced density matrix of the two-qubit system can be expressed as the Kraus representation in terms of the tensor products of the single qubit Kraus operators. We derive the relation between the entanglement and nonlocality of the two-qubit system which are both closely associated with the decoherence function. We identify the threshold values of the decoherence function to ensure the existences of the concurrence and nonlocal quantum correlations for an arbitrary evolution time when the two-qubit system is initially prepared in the composite Bell states and the Werner states, respectively. It is shown that the environmental nonequilibrium feature can suppress the disentanglement dynamics and reduce the entanglement revivals in non-Markovian dynamics regime. In addition, the environmental nonequilibrium feature can enhance the nonlocality of the two-qubit system. Moreover, the entanglement sudden death and rebirth phenomena and the transition between quantum and classical nonlocalities closely depend on the parameters of the initial states and the environmental parameters in nonequilibrium environments.
How quantum coherence influences thermodynamic behavior remains an open question in quantum thermodynamics. Here we investigate this relation within the pure dephasing framework, where a central qubit interacts with a finite Ising-like spin environment. Although the system's internal energy remains constant, the interaction induces decoherence and gives rise to nontrivial thermodynamic features. Within the two-point measurement approach, we show that the heat dissipated into the environment matches the coherent energy contribution appearing in a reformulated first law of quantum thermodynamics. Numerical calculations reveal oscillatory coherence dynamics, with revivals associated with information backflow and non-Markovian effects, as quantified by the Breuer-Laine-Piilo measure. We find that heat and coherence exhibit intertwined temporal behavior, with enhanced heat dissipation during coherence decay and reduced heat during revivals. These results suggest a connection between coherence dynamics and thermodynamic quantities in finite, closed composite systems undergoing pure dephasing.