We explore the impact of non-Markovian channels on the quantum correlations (QCs) of Haar uniformly generated random two-qubit input states with different ranks -- either one of the qubits (single-sided) or both the qubits independently (double-sided) are passed through noisy channels. Under dephasing and depolarizing channels with varying non-Markovian strength, entanglement and quantum discord of the output states collapse and revive with the increase of noise. We find that in case of the depolarizing double-sided channel, both the QCs of random states show a higher number of revivals on average than that of the single-sided ones with a fixed non-Markovianity strength, irrespective of the rank of the states -- we call such a counter-intuitive event as a constructive feedback of non-Markovianity. Consequently, the average noise at which QCs of random states show first revival decreases with the increase of the strength of non-Markovian noise, thereby indicating the role of non-Markovian channels on the regenerations of QCs even in presence of a high amount of noise. However, we observe that non-Markovianity does not play any role to increase the robustness in random quantum states which can be measured by the mean value of critical noise at which quantum correlations first collapse. Moreover, we observe that the tendency of a state to show regeneration increases with the increase of average QCs of the random input states along with non-Markovianity.
We investigate the relation between two approaches to the characterisation of quantum Markovianity, divisibility and lack of information backflow. We show that a bijective dynamical map is completely-positive-divisible if and only if a monotonic non-increase of distinguishability is observed for two equiprobable states of the evolving system and an ancilla. Moreover our proof is constructive: given any such map that is not completely-positive-divisible, we give an explicit construction of two states that, when taken with the same a priori probability, exhibit information back-flow. Finally, wh…
Quantum mechanics, in principle, allows for processes with indefinite causal order. However, most of these causal anomalies have not yet been detected experimentally. We show that every such process can be simulated experimentally by means of non-Markovian dynamics with a measurement on additional degrees of freedom. Explicitly, we provide a constructive scheme to implement arbitrary acausal processes. Furthermore, we give necessary and sufficient conditions for open system dynamics with measurement to yield processes that respect causality locally, and find that tripartite entanglement and no…
We show that applying feedback and weak measurements to a quantum system induces phase transitions beyond the dissipative ones. Feedback enables controlling essentially quantum properties of the transition, i.e., its critical exponent, as it is driven by the fundamental quantum fluctuations due to measurement. Feedback provides the non-Markovianity and nonlinearity to the hybrid quantum-classical system, and enables simulating effects similar to spin-bath problems and Floquet time crystals with tunable long-range (long-memory) interactions.
Based on recent work on the asymptotic behavior of controlled quantum Markovian dynamics, we show that any generic quantum state can be stabilized by devising constructively a simple Lindblad-GKS generator that can achieve global asymptotic stability at the desired state. The applications of such result is demonstrated by designing a direct feedback strategy that achieves global stabilization of a qubit state encoded in a noise-protected subspace.
We consider the unitary time evolution of continuous quantum mechanical systems confined to a cavity in contact with a finite bath of variable size. Measures for Markovianity for such finite system-bath configurations are developed in terms of Hilbert-Schmidt distances of time evolving wave packets. The relevant time scales are identified, which characterize pseudo-Markovian transient behavior, boundary scattering induced non-Markovian oscillations at intermediate times, and non-Markovian rephasing events at long time scales. It is shown how these time scales can be controlled by tunable param…
A comparative study of a qutrit (three-level atomic system) coupled to a classical field in a typical Markovian reservoir (free space) and in a photonic band-gap (PBG) crystal is carried out. The aim of the study is to assess the collective impact of structured environment and classical control of the system on the dynamics of quantum coherence, non-Markovianity, and estimation of parameters which are initially encoded in the atomic state. We show that the constructive interplay of PBG material as a medium and classical driving field as a part of system results in a significant enhancement of …
It is hoped that quantum computers will offer advantages over classical computers for combinatorial optimization. Here, we introduce a feedback-based strategy for quantum optimization, where the results of qubit measurements are used to constructively assign values to quantum circuit parameters. We show that this procedure results in an estimate of the combinatorial optimization problem solution that improves monotonically with the depth of the quantum circuit. Importantly, the measurement-based feedback enables approximate solutions to the combinatorial optimization problem without the need f…
In this paper we investigate parametrization-free solutions of the problem of quantum pure state preparation and subspace stabilization by means of Hamiltonian control, continuous measurement and quantum feedback, in the presence of a Markovian environment. In particular, we show that whenever suitable dissipative effects are induced either by the unmonitored environment or by non Hermitian measurements, there is no need for feedback control to accomplish the task. Constructive necessary and sufficient conditions on the form of the open-loop controller can be provided in this case. When open-l…
We investigate the non-Markovian dynamics of two giant artificial atoms interacting with a continuum of bosonic modes in a one-dimensional (1D) waveguide. Based on the diagrammatic method, we present the exact analytical solutions, which predict the rich phenomena of collective radiance. For the certain collective states, the decay rates are found to be far beyond that predicted in the the Dicke model and standard Markovian framework, which indicates the occurrence of super-superradiance. The superadiance-to-subradiance transition could be realized by adjusting the exchange symmetry of giant a…
We propose a general framework for investigating a large class of stabilization problems in Markovian quantum systems. Building on the notions of invariant and attractive quantum subsystem, we characterize attractive subspaces by exploring the structure of the invariant sets for the dynamics. Our general analysis results are exploited to assess the ability of open-loop Hamiltonian and output-feedback control strategies to synthesize Markovian generators which stabilize a target subsystem, subspace, or pure-state. In particular, we provide an algebraic characterization of the manifold of stabil…
Starting from the paradigmatic spin-boson model (SBM), we investigate the static and dynamical properties of a system of two distant two-level emitters coupled to a one-dimensional Ohmic waveguide beyond the rotating wave approximation. Employing static and dynamical polaron Ansätze we study the effects of finite separation distance on the behavior of the photon-mediated Ising-like interaction, qubit frequency renormalization, ground-state magnetization, and entanglement entropy of the two-qubit system. Based on previous works we derive an effective approximate Hamiltonian for the two-impurity…
Constructive realization of self-referential prediction limits in quantum control: Resource bounds and Gödel-safe architectures
Qatar Center for Quantum Computing, College of Science and Engineering, Hamad Bin Khalifa University（哈马德·本·哈利法大学科学与工程学院量子计算中心）；Computer Engineering Department, Polytechnic School, Universidad de Alcalá（阿尔卡拉大学理工学院计算机工程系）；Canadian Quantum Research Center（加拿大量子研究中心）；Irving K. Barber School of Arts and Sciences, University of British Columbia Okanagan（不列颠哥伦比亚大学奥肯纳根分校欧文·K·巴伯艺术与理学院）；Department of Mathematical Sciences, Durham University（杜伦大学数学科学系）；Faculty of Sciences, Hasselt University（哈瑟尔特大学理学院）
