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arXiv:1409.0191 · International Journal of Quantum Information

Continuous quantum measurement in spin environments

Dong Xie, An Min Wang

Published Sep 1, 2015• 0 citations
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Abstract

We derive a stochastic master equation (SME) which describes the decoherence dynamics of a system in spin environments conditioned on the measurement record. Markovian and non-Markovian nature of environment can be revealed by a spectroscopy method based on weak continuous quantum measurement. On account of that correlated environments can lead to a non-local open system which exhibits strong non-Markovian effects although the local dynamics are Markovian, the spectroscopy method can be used to demonstrate that there is correlation between two environments.

DOI
10.1142/s0219749915500409

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We derive a stochastic master equation (SME) which describes the decoherence dynamics of a system in spin environments conditioned on the measurement record. Markovian and non-Markovian nature of environment can be revealed by a spectroscopy method based on weak continuous quantum measurement. On account of that correlated environments can lead to a non-local open system which exhibits strong non-Markovian effects although the local dynamics are Markovian, the spectroscopy method can be used to demonstrate that there is correlation between two environments.
Continuous quantum measurement is the backbone of various methods in quantum control, quantum metrology, and quantum information. Here, we present a generalized formulation of dispersive measurement of a complex quantum systems. We describe the complex system as an open quantum system that is strongly coupled to a non-Markovian environment, enabling the treatment of a broad variety of natural or engineered complex systems. The system is monitored via a probe resonator coupled to a broadband (Markovian) reservoir. Based on this model, we derive a formalism of stochastic hierarchy equations of motion describing the decoherence dynamics of the system conditioned on the measurement record. Furthermore, we demonstrate a spectroscopy method based on weak quantum measurement to reveal the non-Markovian nature of the environment, which we term weak spectroscopy.
In this PHD thesis, I address the study of the evolution of quantum correlations of continuous variable systems interacting with classical environments, portrayed by classical stochastic fields. In particular, the first goal is individuating the working regimes where a full quantum description of the system-environment interaction may be simulated with a stochastic approach. As a paradigmatic example, I consider quantum harmonic oscillators subject to phase diffusion and dissipation decoherence. My results show that the stochastic noise may take over the full quantum description of Markovian dephasing channels, while a stochastic approach to dissipation only works at a high temperature in the early stage of the dynamics. The second goal consists in better exploring the connection between the dynamics of correlations of the system, non-Markovianity and backflow of information. In many situations non-Markovianity cannot be proved but only revealed by means of appropriate witnesses, usually associated to backflow of information. My results show that stochastic phase diffusing and stochastic dissipative environments lead to non-Markovian dynamics, but their non-Markovianity stays unwitnessed unless revivals of correlations as nonclassicality, entanglement or discord are detected. This suggests that non-Markovianity sets the natural framework for revivals of correlations, but the true resource to obtain revivals is the backflow of information. The third goal consists in showing that effects of local or global noise on a bipartite system may easily be distinguished by means of standard laboratory techniques. Indeed, my results show that homodyne-detection-based schemes may discriminate the effects of a global stochastic noise affecting two probes from local perturbation, using as states of the probe ?lab-friendly? states.
The dynamics of an open quantum system is non-Markovian when memory effect is non-negligible. The quantum memory effect is a very complex issue and presently there is no universally accepted method to quantify it. By examining the memory kernel of the Nakajima-Zwanzig master equation, we study the memory effect in a theoretical model consisting of a spin coupled to an environment of an Ising spin chain subject to a transverse field. We find that it can be dictated by either the time correlation in the environment, or the system-environment correlation, depending on the strength of the transverse field and the state of the environment. We analyze the information loss to the environment and backflow from it, and discover that the information flow is not always a reliable indicator for the nature of the dynamics.
We propose a self-contained and accessible derivation of an exact formula for the n -point correlation functions of the signal measured when continuously observing a quantum system. The expression depends on the initial quantum state and on the Stochastic Master Equation (SME) governing the dynamics. This derivation applies to both jump and diffusive evolutions and takes into account common imperfections of realistic measurement devices. We show how these correlations can be efficiently computed numerically for commonly filtered and integrated signals available in practice.
The quantum jump approach allows to characterize the stochastic dynamics associated with an open quantum system submitted to a continuous measurement action. In this paper we show that this formalism can consistently be extended to non-Markovian system dynamics. The results rely on studying a measurement process performed on a bipartite arrangement characterized by a Markovian Lindblad evolution. Both renewal and nonrenewal extensions are found. The general structure of nonlocal master equations that admit an unraveling in terms of the corresponding non-Markovian trajectories is also found. By studying a two-level system dynamics, it is demonstrated that non-Markovian effects such as an environment-to-system flow of information may be present in the ensemble dynamics.
Quantum entanglement is the strange phenomenon first described by Einstein, Podolsky and Rosen in their famous EPR paradox paper. The document, which describes the instantaneous correlation between two particles with spacelike separation when one of the pair is measured by an observer, was meant to criticize quantum theory and regard it incomplete. Antipodal to its objective, entanglement became one of the strengths of quantum mechanics through the proposal of John Bell and the empirical results from the work of Alain Aspect, John Clauser and Anton Zeilinger disproving hidden variables within local realism. Despite these culminations, the “measurement problem” and the “quantum collapse” debates still haunt the physics community. Quantum collapse is so far interpreted as a statistical update rather than a physical occurrence to maintain the relativistic laws in check. With the rising trends and investments in quantum technological research and development in the areas of computation, communication, metrology and sensing, the exploitation of entanglement is indispensable. There is limited research in exploring entanglement dynamics through local subsystem continuous weak measurement with feedback mechanisms. Local measurement with joint correlation inference is a subject of controversy, particularly pertaining to the no signalling theorem. Compliance to this theorem can be achieved through statistics i.e. inference through repeated experimentation thereby keeping causality intact. This thesis proposes a novel method to explore the operational accessibility of local entangled quantum systems. A 4-model approach explores the behaviour of the individual and ensemble trajectories of an entangled system’s temporal evolution. The experimental design uses Kraus operators; the Stochastic Master Equation (SME) and the Lindblad Master Equation (LME) combined with quantum circuit and noise simulations to generate the needed conditional and unconditional statistics of individual and ensemble trajectories of open quantum systems via continuous weak measurement with feedback control. The Operational Accessibility Metric (OAM) defines the quantification to establish reconstruction of local system dynamics by repeated extraction of remote stochastic weak measurement record of the density matrix. The results show Root-Mean-Square Error RMSE values ranging from 0.013706 to 0.231122 and fidelities F(ρ,σ) >0.990 which are accompanied by corresponding Reconstruction Improvement Metric Γrec values from 22.3% to 71.8% correspondingly. These corollaries are supported by p-values with lowest registering at 5.19 x 10-27 and with as high as 0.008083 which still concludes the null hypothesis statistically insignificant. To further strengthen the acceptance of the alternative hypothesis, Cohen’s d effect size and statistical power has been measured indicating effect sizes as high as -7.178 and power >0.999. The experimental results validates that local dynamics is operationally accessible with significant improvement using continuous weak measurement and open feedback control.