Initial System-environment Correlations Research Articles

Enhance the coherence of open two-level system through the superposition of environments

Dynamics of a two-level system in the superposition of two dephasing environments with Ohmic-like spectral density is studied when considering initial system-environment correlations. The quantum system and one environment are treated as whole thermal equilibrium state, while the other environment is at thermal equilibrium state alone. Which environment the system interacts with is determined by an ancillary two-level system. When the system interacts with mixture of two sub-Ohmic environments, initial correlations can make the mixed dynamics non-Markovian. For two identical sub-Ohmic environments, if performing the projective measurement on the ancillary two-level system at the special time points, whatever the initial state of the system is, the coherence can be enhanced. For two different environments with βħω0/2>>, we get the approximate expression about the coherence of the system when measuring the ancillary two-level system.

The role of initial system–environment correlations with a spin environment

Open quantum systems are a subject of immense interest as their understanding is crucial in the implementation of modern quantum technologies. In the study of their dynamics, the role of the initial system–environment correlations is commonly ignored. In this work, to gain insights into the role of these correlations, we solve an exactly solvable model of a single two-level system interacting with a spin environment, with the initial system state prepared by a suitable unitary operation. By solving the dynamics exactly for arbitrary system–environment coupling strength while taking into account the initial system–environment correlations, we show that the effect of the initial correlations is, in general, very significant and nontrivial. To further highlight the importance of the initial system–environment correlations, we also extend our study to investigate the dynamics of the entanglement between two two-level systems interacting with a common spin environment.

Initial correlations in open quantum systems: constructing linear dynamical maps and master equations

We investigate the dynamics of open quantum systems which are initially correlated with their environment. The strategy of our approach is to analyze how given, fixed initial correlations modify the evolution of the open system with respect to the corresponding uncorrelated dynamical behavior with the same fixed initial environmental state, described by a completely positive dynamical map. We show that, for any predetermined initial correlations, one can introduce a linear dynamical map on the space of operators of the open system which acts like the proper dynamical map on the set of physical states and represents its unique linear extension. Furthermore, we demonstrate that this construction leads to a linear, time-local quantum master equation with generalized Lindblad structure involving time-dependent, possibly negative transition rates. Thus, the general non-Markovian dynamics of an open quantum system can be described by means of a time-local master equation even in the case of arbitrary, fixed initial system–environment correlations. We present some illustrative examples and explain the relation of our approach to several other approaches proposed in the literature.

Master equation incorporating the system-environment correlations present in the joint equilibrium state

We present a general master equation, correct to second order in the system-environment coupling strength, that takes into account the initial system-environment correlations. We assume that the system and its environment are in a joint thermal equilibrium state, and thereafter a unitary operation is performed to prepare the desired initial system state, with the system Hamiltonian possibly changing thereafter as well. We show that the effect of the initial correlations shows up in the second-order master equation as an additional term, similar in form to the usual second-order term describing relaxation and decoherence in quantum systems. We apply this master equation to a generalization of the paradigmatic spin-boson model, namely a collection of two-level systems interacting with a common environment of harmonic oscillators, as well as a collection of two-level systems interacting with a common spin environment. We demonstrate that, in general, the initial system-environment correlations need to be accounted for in order to accurately obtain the system dynamics.

Detecting initial system-environment correlations in open systems

Correlations between a system and its environment lead to errors in an open quantum system. Detecting those correlations would be valuable for avoiding and/or correcting those errors. Here we show that we can detect correlations by only measuring the system itself if we know the cause of the interaction between the two, for example in the case of a dipole-dipole interaction. We investigate the unitary $U$ which is associated with the exchange Hamiltonian and examine the ability to detect initial correlations between a system and its environment for various types of initial states. The states we select are motivated by realistic experimental conditions and we provide bounds for when we can state with certainty that there are initial system-environment correlations given experimental data.

Hierarchical-environment-assisted non-Markovian and its effect on thermodynamic properties

We consider a microscopic collision model, i.e., a quantum system interacts with a hierarchical environment consisting of an auxiliary system and a reservoir. We show how the non-Markovian character of the system is influenced by the coupling strength of system-auxiliary system and auxiliary system-reservoir, coherence of environment and initial system-environment correlations. And we study the non-Markovianity induced by coherence of environment from the perspective of energy, further the relationship between information backflow and energy flux is obtained. Then we study the effect of non-Markovianity on thermodynamic properties. By studying the entropy change of system especially that from heat exchanges with the environment, we reveal the essence of entropy change between positive and negative values during non-Markovian evolution is due to the contribution of heat flux induced by coherence. And compared with the case of Markovian dynamics, we observe that the entropy production decreases in some specific time intervals under non-Markovian dynamics induced by the coupling strength. And this is different to the case of non-Markovianity caused by initial system-environment correlation, that we show the possibility of positive entropy production during the whole dynamics.

Dynamical decoupling with initial system-environment correlations

Dynamical decoupling (DD) technique is one of the most successful methods to suppress decoherence in qubit systems. In this paper, we studied a solvable pure dephasing model and investigated how DD sequences and initial correlations affect this system. We gave the analytical expressions of decoherence functions and compared the decoherence suppression effects of DD pulses in Ohmic, sub-Ohmic and super-Ohmic environments. Our results show that (1) The initial system-environment correlation will cause additional decoherence. In order to control the dynamic process of open quantum system more accurately and effectively, the initial correlation between the system and reservoir must be considered. (2) High frequency DD pulses can significantly reduce the amplitude of the decoherence function even in the presence of initial system-environment correlations.

Correlation-Picture Approach to Open-Quantum-System Dynamics

We introduce a new dynamical picture, referred to as correlation picture,' which connects a correlated state to its uncorrelated counterpart. Using this picture allows us to derive an exact dynamical equation for a general open-system dynamics with system--environment correlations included. This exact dynamics is in the form of a Lindblad-like equation even in the presence of initial system-environment correlations. For explicit calculations, we also develop a weak-correlation expansion formalism that allows us to perform systematic perturbative approximations. This expansion provides approximate master equations which can feature advantages over existing weak-coupling techniques. As a special case, we derive a Markovian master equation, which is different from existing approaches. We compare our equations with corresponding standard weak-coupling equations by two examples, where our correlation picture formalism is more accurate, or at least as accurate as weak-coupling equations.

Time-Convolutionless Master Equation for Multi-Level Open Quantum Systems with Initial System-Environment Correlations

Time-Convolutionless Master Equation for Multi-Level Open Quantum Systems with Initial System-Environment Correlations

Quantum Error Correction in the Presence of Initial System-Environment Correlations

Quantum error correction is studied in a framework consisting of an open quantum system and its environment, jointly subjected to a unitary action, and an interaction-free reference system. It has been shown that coherent information between the initially correlated open system and reference system is conserved in the transmission stage of any quantum communication process, provided that the tripartite input is any pure Markov state and the overall evolution preserves its form. This conservation constitutes the necessary and sufficient condition for accomplishment of perfect error correction by a recovery channel even in the presence of initial system-environment correlations. Explicit expressions of the recovery operators and examples of the joint unitary evolution preserving the form of inputs are given for all classes of pure Markov states.

Photonic dephasing dynamics and the role of initial correlations

Dynamics of open quantum systems depends on different types of initial correlations. On the one hand, when system and environment are both inherently multipartite, initial correlations between the parties of the composite environment make the dynamical map non-local, despite of local nature of the interaction between each party of the system and the environment. On the other hand, initial correlations between the open system and its environment prevents one from defining a completely positive dynamical map. Recently, dephasing dynamics of photons has been used in both of these frameworks - theoretically and experimentally - to demonstrate some fundamental and applicable aspects of open system dynamics and memory effects. However, the earlier studies in this context are often based solely on the concept of decoherence functions. Therefore, we still lack explicit master equation descriptions for dynamics induced by correlated composite initial environmental states. Also, a detailed understanding how initial system-environment correlations influence qubit dynamics in the photonic context is missing. In this paper, we derive generic master equations for the reduced dephasing dynamics of the two-photon polarization state when the bipartite environmental frequency degrees of freedom are initially correlated. We thereby show the explicit dependence of the operator form and the decay rates of the master equation on the initial frequency correlations and the influence of various types of frequency distributions. Furthermore, we use recently developed bath positive decomposition method to treat initially correlated polarization-frequency state of a photon, and demonstrate how this allows new insight and detailed information on how the contributions of different origin influence the photonic dephasing.

Geometric phase corrected by initial system-environment correlations

We find the geometric phase of a two-level system undergoing pure dephasing via interaction with an arbitrary environment, taking into account the effect of the initial system-environment correlations. We use our formalism to calculate the geometric phase for the two-level system in the presence of both harmonic oscillator and spin environments, and we consider the initial state of the two-level system to be prepared by a projective measurement or a unitary operation. The geometric phase is evaluated for a variety of parameters such as the system-environment coupling strength to show that the initial correlations can affect the geometric phase very significantly even for weak and moderate system-environment coupling strengths. Moreover, the correction to the geometric phase due to the system-environment coupling generally becomes smaller (and can even be zero) if initial system-environment correlations are taken into account, thus implying that the system-environment correlations can increase the robustness of the geometric phase.

Time-Convolutionless Master Equation for Multi-Level Open Quantum Systems with Initial System-Environment Correlations

Time-Convolutionless Master Equation for Multi-Level Open Quantum Systems with Initial System-Environment Correlations

Why initial system-environment correlations do not imply the failure of complete positivity: A causal perspective

The common wisdom in the field of quantum information theory is that when a system is initially correlated with its environment, the map describing its evolution may fail to be completely positive. If true, this would have practical and foundational significance. We here demonstrate, however, that the common wisdom is mistaken. We trace the error to the standard argument for how the evolution map ought to be defined. We show that it sometimes fails to define a linear map or any map at all and that these pathologies persist even in completely classical examples. Drawing inspiration from the framework of classical causal models, we argue that the correct definition of the evolution map is obtained by considering a counterfactual scenario wherein the system is reprepared independently of any systems in its causal past while the rest of the circuit remains the same, yielding a map that is always completely positive. In a post-mortem on the standard argument, we highlight two distinct mistakes that retrospectively become evident (in its application to completely classical examples): (i) the types of constraints to which it appealed are constraints on what one can infer about the final state of a system based on its initial state, where such inferences are based not just on the cause-effect relation between them-which defines the correct evolution map-but also on the common cause of the two; (ii) in a (retrospectively unnecessary) attempt to introduce variability in the input state, it inadvertently introduced variability in the inference map itself, then tried to fit the input-output pairs associated to these different maps with a single map.

Dynamics of Multi-Level Open Quantum Systems with Initial System-Environment Correlations

Exact and approximate master equations were derived by the projection operator method for the reduced statistical operator of a multi-level open quantum system with finite number $$N$$ of quantum eigenstates interacting with arbitrary external deterministic fields and dissipative environment simultaneously. Unlike conventional master equations derived by the projection operator method for the quantum systems of this kind so far, these equations are homogeneous in the reduced statistical operator while, at the same time, taking into account initial correlations between the multi-level system and the environment. Consistent representation of the multi-level system evolution in terms of the $$SU(N)$$ operator algebra facilitates efficient numerical analysis of these equations derived for various physically realistic quantum models.

Effect of initial system–environment correlations with spin environments

Understanding the dynamics of open quantum systems is a highly important task for the implementation of emerging quantum technologies. To make the problem tractable theoretically, it is common to neglect initial system-environment correlations. However, this assumption is questionable in situations where the system is interacting strongly with the environment. In particular, the system state preparation can then influence the dynamics of the system via the system-environment correlations. To gain insight into the effect of these correlations, we solve an exactly solvable model of a quantum spin interacting with a spin environment both with and without initial correlations for arbitrary system-environment coupling strengths. We show that the effect of the system state preparation may or may not be significant in the strong system-environment coupling regime at low temperatures. We also study the dynamics of the entanglement between two spins interacting with a common spin environment with and without initial system-environment correlations to demonstrate that the correlations can play a significant role in the dynamics of two-qubit systems as well.

Global Passivity in Microscopic Thermodynamics

The main thread that links classical thermodynamics and the thermodynamics of small quantum systems is the celebrated Clausius inequality form of the second law. However, its application to small quantum systems suffers from two cardinal problems: (i) The Clausius inequality does not hold when the system and environment are initially correlated - a commonly encountered scenario in microscopic setups. (ii) In some other cases, the Clausius inequality does not provide any useful information (e.g. in dephasing scenarios). We address these deficiencies by developing the notion of global passivity and employing it as a tool for deriving thermodynamic inequalities on observables. For initially uncorrelated thermal environments the global passivity framework recovers the Clausius inequality. More generally, global passivity provides an extension of the Clausius inequality that holds even in the presences of strong initial system-environment correlations. Crucially, the present framework provides additional thermodynamic bounds on expectation values. To illustrate the role of the additional bounds we use them to detect unaccounted heat leaks and weak feedback operations ("Maxwell's demons") that the Clausius inequality cannot detect. In addition, it is shown that global passivity can put practical upper and lower bounds on the buildup of system-environment correlation for dephasing interactions. Our findings are highly relevant for experiments in various systems such as ion traps, superconducting circuits, atoms in optical cavities and more.

Initial system-environment correlations via the transfer-tensor method

Open quantum systems exhibiting initial system-environment correlations are notoriously difficult to simulate. We point out that given a sufficiently long sample of the exact short-time evolution of the open system dynamics, one may employ transfer tensors for the further propagation of the reduced open system state. This approach is numerically advantageous and allows for the simulation of quantum correlation functions in hardly accessible regimes. We benchmark this approach against analytically exact solutions and exemplify it with the calculation of emission spectra of multichromophoric systems as well as for the reverse temperature estimation from simulated spectroscopic data. Finally, we employ our approach for the detection of spectral signatures of electromagnetically induced transparency in open three-level systems.

Reduced quantum dynamics with initial system-environment correlations characterized by pure Markov states

Any tripartite state which saturates the strong subadditivity relation for the quantum entropy is defined as the Markov state.A tripartite pure state describing an open system, its environment and their purifying system isa pure Markov state iff the bipartite marginal state of purifying system and environment is a product state. It has been shown that as long as the purification of the input system-environment state is a pure Markov state the reduced dynamics of the open system can be described, on the support of initial system state, by a quantum channel for every joint unitary evolution of the system-environment composite even in the presence of initial correlations. Entanglement, discord and classical correlations of the initial system-environment states implied by the pure Markov state are analyzed and it has been shown that all these correlations are entirely specified by the entropy of the environment. Some implications concerning perfect quantum error correction procedure and quantum Markovian dynamics are presented.

Environment and initial state engineered dynamics of quantum and classical correlations

Based on an open exactly solvable system coupled to an environment with nontrivial spectral density, we connect the features of quantum and classical correlations with some features of the environment, initial states of the system, and the presence of initial system–environment correlations. Some interesting features not revealed before are observed by changing the structure of environment, the initial states of system, and the presence of initial system–environment correlations. The main results are as follows. (1) Quantum correlations exhibit temporary freezing and permanent freezing even at high temperature of the environment, for which the necessary and sufficient conditions are given by three propositions. (2) Quantum correlations display a transition from temporary freezing to permanent freezing by changing the structure of environment. (3) Quantum correlations can be enhanced all the time, for which the condition is put forward. (4) The one-to-one dependency relationship between all kinds of dynamic behaviors of quantum correlations and the initial states of the system as well as environment structure is established. (5) In the presence of initial system–environment correlations, quantum correlations under local environment exhibit temporary multi-freezing phenomenon. While under global environment they oscillate, revive, and damp, an explanation for which is given.