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Quantum Information Processing

Protecting tripartite entanglement in non-Markovian environments via quantum partially collapsing measurements

Zhiyong Ding, Juan He, Ye Liu

Published May 27, 2016• 2 citations
Publisher
DOI
10.1007/s11128-016-1342-8

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We investigate the effects of the time-dependent magnetic field (TDMF) and partial-collapse quantum measurements (PCQMs) on the information flow of a superconducting flux qubit coupled to a reservoir and find that the information flow is equivalent to the quantum Fisher information flow in the resonant case. A scheme is proposed to preserve the quantum correlations of two uncoupled flux qubits interacting with independent reservoirs via PCQMs and TDMFs, and steady amount of entanglement can be achieved by the PCQMs. We also discuss the effect of TDMF on the dynamics of the entanglement and show distinct behaviors in the Markovian and non-Markovian regimes. Finally, we explore the influence of non-Markovian effect on the dynamics of entanglement under the combined action of TDMFs and PCQMs and show that the combined action of TDMFs and PCQMs can protect entanglement better for some situations.
Abstract In this work, a scheme to protect quantum entanglement from a non‐Markovian noisy environment is proposed. By applying two quantum weak measurements before and after sending the quantum state into the noisy channel, the quantum state can be “pushed” closer to a decoherence‐free state, reducing decoherence during the time evolution. Then, the second weak measurement can partially retrieve the initial quantum state from the state corrupted by the noisy environment. The study involves a non‐Markovian dynamic equation to examine the impact of the memory effect on the protection scheme's performance. Various factors affecting the residual entanglement and the success probability are analyzed. The results suggest that two measurement strengths shall be chosen approximately in a linear relation, with the best ratio determined by the memory time of the environment. Additionally, it is demonstrated that the memory effect significantly enhances the protection efficiency. Lastly, the scheme's robustness against systematic errors is evaluated.
We study how to control the dynamics of tripartite entanglement among optical cavities using non-Markovian baths. In particular, we demonstrate how the reservoir engineering through the utilization of non-Markovian baths with different types of Lorentzian and ohmic spectral densities can lead to an entanglement survival for longer times and in some cases considerable regain of seemingly lost entanglement. Both of these behaviours indicate a better sustainability of entanglement (in time) compared to the usual Markovian bath situations which assumes a flat spectrum of the bath around the system resonant frequency. Our scheme shows these effects in the context of optical cavities starting off in a maximally entangled W and Greenberger–Horne–Zeilinger tripartite states. In Lorentzian cases, we find that the far detuned double Lorentzian baths with small coupling strengths and for ohmic-type baths super-ohmic environments with smaller cutoff frequencies are the best candidates for preserving entanglement among cavities for significant amount of time. A non-Markovian quantum jump approach is employed to understand the entanglement dynamics in these cases, especially to recognize the collapse and revival of the entanglement in both W and GHZ states.