Non-Markovian master equation for a damped driven two-state system

We present a detailed microscopic derivation for a non-Markovian master equation for a driven two-state system interacting with a general structured reservoir. The master equation is derived using the time-convolutionless projection operator technique in the limit of weak coupling between the two-state quantum system and its environment. We briefly discuss the Markov approximation, the secular approximation and their validity.Comment: 6 pages, submitted to proceedings of CEWQO200

Two-qubit non-Markovianity induced by a common environment

We study non-Markovianity as backflow of information in two-qubit systems. We consider a setting where, by changing the distance between the qubits, one can interpolate between independent reservoir and common reservoir scenarios. We demonstrate that non-Markovianity can be induced by the common reservoir and single out the physical origin of this phenomenon. We show that two-qubit non-Markovianity coincides with instances of non-divisibility of the corresponding dynamical map, and we discuss the pair of states maximizing information flowback. We also discuss the issue of additivity for the measure we use and in doing so, give an indication of its usefulness as a resource for multipartite quantum systems.Comment: 9 pages, 5 figures, Published version with minor modification

Non-Markovianity, Loschmidt echo and criticality: a unified picture

A simple relationship between recently proposed measures of non-Markovianity and the Loschmidt echo is established, holding for a two-level system (qubit) undergoing pure dephasing due to a coupling with a many-body environment. We show that the Loschmidt echo is intimately related to the information flowing out from and occasionally back into the system. This, in turn, determines the non-Markovianity of the reduced dynamics. In particular, we consider a central qubit coupled to a quantum Ising ring in the transverse field. In this context, the information flux between system and environment is strongly affected by the environmental criticality; the qubit dynamics is shown to be Markovian exactly and only at the critical point. Therefore non-Markovianity is an indicator of criticality in the model considered here

Invariant quantum discord in qubit-qutrit systems under local dephasing

We investigate the dynamics of quantum discord and entanglement for a class of mixed qubit-qutrit states assuming that only the qutrit is under the action of a dephasing channel. We demonstrate that even though the entanglement in the qubit-qutrit state disappears in a finite time interval, partial coherence left in the system enables quantum discord to remain invariant throughout the whole time evolution

Non-Markovian dynamics for an open two-level system without rotating wave approximation: Indivisibility versus backflow of information

By use of the two measures presented recently, the indivisibility and the backflow of information, we study the non-Markovianity of the dynamics for a two-level system interacting with a zero-temperature structured environment without using rotating wave approximation (RWA). In the limit of weak coupling between the system and the reservoir, and by expanding the time-convolutionless (TCL) generator to the forth order with respect to the coupling strength, the time-local non-Markovian master equation for the reduced state of the system is derived. Under the secular approximation, the exact analytic solution is obtained and the sufficient and necessary conditions for the indivisibility and the backflow of information for the system dynamics are presented. In the more general case, we investigate numerically the properties of the two measures for the case of Lorentzian reservoir. Our results show the importance of the counter-rotating terms to the short-time-scale non-Markovian behavior of the system dynamics, further expose the relations between the two measures and their rationality as non-Markovian measures. Finally, the complete positivity of the dynamics of the considered system is discussed

Negativity and quantum discord in Davies environments

We investigate the time evolution of negativity and quantum discord for a pair of non-interacting qubits with one being weakly coupled to a decohering Davies--type Markovian environment. At initial time of preparation, the qubits are prepared in one of the maximally entangled pure Bell states. In the limiting case of pure decoherence (i.e. pure dephasing), both, the quantum discord and negativity decay to zero in the long time limit. In presence of a manifest dissipative dynamics, the entanglement negativity undergoes a sudden death at finite time while the quantum discord relaxes continuously to zero with increasing time. We find that in dephasing environments the decay of the negativity is more propitious with increasing time; in contrast, the evolving decay of the quantum discord proceeds weaker for dissipative environments. Particularly, the slowest decay of the quantum discord emerges when the energy relaxation time matches the dephasing time.Comment: submitted for publicatio

Robust non-Markovianity in ultracold gases

We study the effect of thermal fluctuations on a probe qubit interacting with a Bose-Einstein condensed (BEC) reservoir. The zero-temperature case was studied in [Haikka P et al 2011 Phys. Rev. A 84 031602], where we proposed a method to probe the effects of dimensionality and scattering length of a BEC based on its behavior as an environment. Here we show that the sensitivity of the probe qubit is remarkably robust against thermal noise. We give an intuitive explanation for the thermal resilience, showing that it is due to the unique choice of the probe qubit architecture of our model.Comment: Submitted to FQMT11 topical issue of the Physica Script

The Rotating-Wave Approximation: Consistency and Applicability from an Open Quantum System Analysis

We provide an in-depth and thorough treatment of the validity of the rotating-wave approximation (RWA) in an open quantum system. We find that when it is introduced after tracing out the environment, all timescales of the open system are correctly reproduced, but the details of the quantum state may not be. The RWA made before the trace is more problematic: it results in incorrect values for environmentally-induced shifts to system frequencies, and the resulting theory has no Markovian limit. We point out that great care must be taken when coupling two open systems together under the RWA. Though the RWA can yield a master equation of Lindblad form similar to what one might get in the Markovian limit with white noise, the master equation for the two coupled systems is not a simple combination of the master equation for each system, as is possible in the Markovian limit. Such a naive combination yields inaccurate dynamics. To obtain the correct master equation for the composite system a proper consideration of the non-Markovian dynamics is required.Comment: 17 pages, 0 figures

Automated operative workflow analysis of endoscopic pituitary surgery using machine learning: development and preclinical evaluation (IDEAL stage 0)

OBJECTIVE: Surgical workflow analysis involves systematically breaking down operations into key phases and steps. Automatic analysis of this workflow has potential uses for surgical training, preoperative planning, and outcome prediction. Recent advances in machine learning (ML) and computer vision have allowed accurate automated workflow analysis of operative videos. In this Idea, Development, Exploration, Assessment, Long-term study (IDEAL) stage 0 study, the authors sought to use Touch Surgery for the development and validation of an ML-powered analysis of phases and steps in the endoscopic transsphenoidal approach (eTSA) for pituitary adenoma resection, a first for neurosurgery. METHODS: The surgical phases and steps of 50 anonymized eTSA operative videos were labeled by expert surgeons. Forty videos were used to train a combined convolutional and recurrent neural network model by Touch Surgery. Ten videos were used for model evaluation (accuracy, F1 score), comparing the phase and step recognition of surgeons to the automatic detection of the ML model. RESULTS: The longest phase was the sellar phase (median 28 minutes), followed by the nasal phase (median 22 minutes) and the closure phase (median 14 minutes). The longest steps were step 5 (tumor identification and excision, median 17 minutes); step 3 (posterior septectomy and removal of sphenoid septations, median 14 minutes); and step 4 (anterior sellar wall removal, median 10 minutes). There were substantial variations within the recorded procedures in terms of video appearances, step duration, and step order, with only 50% of videos containing all 7 steps performed sequentially in numerical order. Despite this, the model was able to output accurate recognition of surgical phases (91% accuracy, 90% F1 score) and steps (76% accuracy, 75% F1 score). CONCLUSIONS: In this IDEAL stage 0 study, ML techniques have been developed to automatically analyze operative videos of eTSA pituitary surgery. This technology has previously been shown to be acceptable to neurosurgical teams and patients. ML-based surgical workflow analysis has numerous potential uses-such as education (e.g., automatic indexing of contemporary operative videos for teaching), improved operative efficiency (e.g., orchestrating the entire surgical team to a common workflow), and improved patient outcomes (e.g., comparison of surgical techniques or early detection of adverse events). Future directions include the real-time integration of Touch Surgery into the live operative environment as an IDEAL stage 1 (first-in-human) study, and further development of underpinning ML models using larger data sets

Frozen and Invariant Quantum Discord under Local Dephasing Noise

In this chapter, we intend to explore and review some remarkable dynamical properties of quantum discord under various different open quantum system models. Specifically, our discussion will include several concepts connected to the phenomena of time invariant and frozen quantum discord. Furthermore, we will elaborate on the relation of these two phenomena to the non-Markovian features of the open system dynamics and to the usage of dynamical decoupling protocols.Comment: 29 pages, 8 figure