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Environment-induced quantum coherence spreading

Mauro Buemo Pozzobom, Jonas Maziero

Published May 16, 2016• 0 citations
OpenAlex

Abstract

We make a thorough study of the spreading of quantum coherence (QC), as quantified by the $l_{1}$-norm QC, when a qubit (a two-level quantum system) is subjected to noise quantum channels commonly appearing in quantum information science. We notice that QC is generally not conserved and that even incoherent initial states can lead to transitory system-environment QC. We show that for the amplitude damping channel the evolved total QC can be written as the sum of local and non-local parts, with the last one being equal to entanglement. On the other hand, for the phase damping channel (PDC) entanglement does not account for all non-local QC, with the gap between them depending on time and also on the qubit's initial state. Besides these issues, the possibility and conditions for time invariance of QC are regarded in the case of bit, phase, and bit-phase flip channels. Here we reveal the qualitative dynamical inequivalence between these channels and the PDC and show that the creation of system-environment entanglement does not necessarily imply in the destruction of the qubit's QC. We also investigate the resources needed for non-local QC creation, showing that while the PDC requires initial coherence of the qubit, for some other channels non-zero population of the excited state (i.e., energy) is sufficient. Related to that, considering the depolarizing channel we notice the qubit's ability to act as a catalyst for the creation of joint QC and entanglement, without need for nonzero initial QC or excited state population.

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We make a thorough study of the spreading of quantum coherence (QC), as quantified by the l1l_{1}l1​-norm QC, when a qubit (a two-level quantum system) is subjected to noise quantum channels commonly appearing in quantum information science. We notice that QC is generally not conserved and that even incoherent initial states can lead to transitory system-environment QC. We show that for the amplitude damping channel the evolved total QC can be written as the sum of local and non-local parts, with the last one being equal to entanglement. On the other hand, for the phase damping channel (PDC) entanglement does not account for all non-local QC, with the gap between them depending on time and also on the qubit's initial state. Besides these issues, the possibility and conditions for time invariance of QC are regarded in the case of bit, phase, and bit-phase flip channels. Here we reveal the qualitative dynamical inequivalence between these channels and the PDC and show that the creation of system-environment entanglement does not necessarily imply in the destruction of the qubit's QC. We also investigate the resources needed for non-local QC creation, showing that while the PDC requires initial coherence of the qubit, for some other channels non-zero population of the excited state (i.e., energy) is sufficient. Related to that, considering the depolarizing channel we notice the qubit's ability to act as a catalyst for the creation of joint QC and entanglement, without need for nonzero initial QC or excited state population.
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.
Abstract This paper systematically investigates the coherence dynamics of a two-qubit system under correlated channels. Through density matrix transformation and operator algebra derivation, we analyze the regulatory effects of memory properties of correlated amplitude damping, phase damping, and depolarization channels on three kinds of coherence, namely l 2 -norm coherence, Tsallis 2-relative entropy coherence, and Rényi 2-relative entropy coherence. The results show that phase damping and depolarization channels induce coherence freezing under perfect memory conditions, where coherence values remain invariant with channel damping rate variations. In partial memory environments, l 2 -norm coherence exhibits superior stability and retains coherence more efficiently than the other two coherence measures. In addition, we quantitatively evaluate the cohering and decohering power of these coherences under the correlated amplitude damping channel. This work provides theoretical support for anti-noise design of quantum technologies in open quantum systems.
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 examine the system-reservoir dynamics of classical and quantum correlations in the decoherence phenomenon within a two-qubit composite system interacting with two independent environments. The most common noise channels (amplitude damping, phase damping, bit flip, bit-phase flip, and phase flip) are analyzed. By analytical and numerical analyses we find that, contrary to what is usually stated in the literature, decoherence may occur without entanglement between the system and the environment. We also show that, in some cases, the bipartite quantum correlation initially present in the system is completely evaporated and not transferred to the environments.
Abstract It is known that the inevitable interaction of the entangled qubits with their environments may result in the degradation of quantum correlation. We study the decoherence of two remote qubits under general local single- and two-sided amplitude-damping channel (ADC). By using concurrence, quantum discord and Clauser–Horne–Shimony–Holt (CHSH) inequality, we find that the relation between the residual quantum correlations and the initial ones are different. Recently, Wang et al. [Int. J. Theor. Phys. 54 (2015) 5] showed that there exist a set of partially entangled states that are more robust than maximally entangled states in terms of the residual quantum correlation measured by concurrence, fully entangled fraction and quantum discord, respectively. Here we find that both in single- and two-sided ADC, only the evolution of CHSH inequality with the initial parameter is proportional to that of the initial nonlocality. That means the initial state with maximally nonlocality will retain its role in the evolution. It implies that the evolution of nonlocality may reveal the characteristics of quantum state better. Furthermore, we discuss the evolutions of the three different quantum measurements with the initial parameter under generalized amplitude damping channel (GADC) and find that they are all proportional to that of the initial state.
We study the dynamics of coherence-induced state ordering under incoherent channels, particularly four specific Markovian channels: amplitude damping channel, phase damping channel, depolarizing channel and bit flit channel for single-qubit states. We show that the amplitude damping channel, phase damping channel, and depolarizing channel do not change the coherence-induced state ordering by l1 norm of coherence, relative entropy of coherence, geometric measure of coherence, and Tsallis relative α-entropies, while the bit flit channel does change for some special cases.