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Quantum Information Processing

Dynamical evolution of entanglement of a three-qubit system driven by a classical environmental colored noise

Lionel Tenemeza Kenfack, Martin Tchoffo, Georges Collince Fouokeng, Lukong Cornelius Fai

Published Feb 21, 2018• 12 citations
Publisher
DOI
10.1007/s11128-018-1839-4

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We use a system of three non-interacting qubits as a quantum probe to classify three classical non-Gaussian noises (namely the static, colored (pink and brown) and random telegraph noise), according to their detrimental effects on the evolution of entanglement of the latter. The probe system is initially prepared in the GHZ state and coupled to the noises in independent environments. Seven configurations for the qubit-noise coupling (QNC) are considered. To estimate the destructive influence of each kind of noise, we employ the tripartite negativity to compare the evolution of entanglement in these QNC configurations to each other with the same noise parameters. The results show that the evolution of entanglement is drastically impacted by the QNC configuration considered as well as the properties of the environmental noises and that the SN is more detrimental to the survival of entanglement than the RTN and CN, regardless of the Markov or non-Markov character of the RTN and the color of the CN. We also observed that pink noise is more fatal to the system than the RTN and that the situation is totally reversed in the case of brown noise. Finally, we show that these noises, in descending order of destructive influence, can be classified as follows: SN>pink noise>RTN>brown noise.
We address the dynamics of entanglement and quantum discord for two noninteracting qubits initially prepared in a maximally entangled state and then subjected to a classical colored noise, i.e., coupled with an external environment characterized by a noise spectrum of the form $1/{f}^{\ensuremath{\alpha}}$. More specifically, we address systems in which the Gaussian approximation fails, i.e., mere knowledge of the spectrum is not enough to determine the dynamics of quantum correlations. We thus investigate the dynamics for two different configurations of the environment: in the first case, the noise spectrum is due to the interaction of each qubit with a single bistable fluctuator with an undetermined switching rate, whereas in the second case we consider a collection of classical fluctuators with fixed switching rates. In both cases, we found analytical expressions for the time dependence of entanglement and quantum discord, which may also be extended to a collection of fluctuators with random switching rates. The environmental noise is introduced by means of stochastic time-dependent terms in the Hamiltonian, and this allows us to describe the effects of both separate and common environments. We show that the non-Gaussian character of the noise may lead to significant effects, e.g., environments with the same power spectrum, but different configurations give rise to the opposite behavior for quantum correlations. In particular, depending on the characteristics of the environmental noise considered, both entanglement and discord display either a monotonic decay or the phenomena of sudden death and revivals. Our results show that the microscopic structure of the environment, in addition to its noise spectrum, is relevant for the dynamics of quantum correlations and may be a valid starting point for the engineering of non-Gaussian colored environments.
We propose a quantum model consisting of two remote qubits interacting with two correlated colored noises and establish an exact stochastic Schr\"odinger equation for this open quantum system. It is shown that the quantum dynamics of the qubit system is profoundly modulated by the mutual correlation between baths and the bath memory capability through dissipation and fluctuation. We report a physical effect on generating inner correlation and entanglement of two distant qubits arising from the strong bath-bath correlation.