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Collision models have attracted significant attention in recent years due to their versatility to simulate open quantum systems in different dynamical regimes. They have been used to study various interesting phenomena such as the dynamical emergence of non-Markovian memory effects and the spontaneous establishment of synchronization in open quantum systems. In such models, the repeated pairwise interactions between the system and the environment and also the possible coupling between different environmental units are typically modeled using the coherent partial-swap (PSWAP) operation as it is known to be a universal homogenizer. In this study, we investigate the dynamical behavior of incoherent collision models, where the interactions between different units are modeled by the incoherent controlled-swap (CSWAP) operation, which is also a universal homogenizer. Even though the asymptotic dynamics of the open system in case of both coherent and incoherent swap interactions appear to be identical, its transient dynamics turns out to be significantly different. Here we present a comparative analysis of the consequences of having coherent or incoherent couplings in collision models, namely, PSWAP or CSWAP interactions respectively, for the emergence of memory effects for a single qubit system and for the onset synchronization between a pair of qubits, both of which are strictly determined by the transient dynamics of the open system., Comment: 17 pages, 7 figures

We examine the emergence of dynamical memory effects in quantum processes having indefinite time direction and causal order. In particular, we focus on the class of phase-covariant qubit channels, which encompasses some of the most significant paradigmatic open quantum system models. In order to assess the memory in the time evolution of the system, we utilize the trace distance and the entanglement based measures of non-Markovianity. While the indefinite time direction is obtained through the quantum time flip operation that realizes a coherent superposition of forward and backward processes, the indefinite causal order is achieved via the quantum switch map, which implements two quantum processes in a coherent superposition of their two possible orders. Considering various different families of phase-covariant qubit channels, we demonstrate that, when implemented on memoryless quantum processes, both the quantum time flip and the quantum switch operations can generate memory effects in the dynamics according to the trace distance based measure under certain conditions. On the other hand, with respect to the entanglement based measure, we show that neither the quantum time flip nor the quantum switch could induce dynamical memory for any of the considered phase-covariant channels., Comment: 15 pages, 10 figures

The second law of thermodynamics can be expressed in terms of entropy production, which can be used to quantify the degree of irreversibility of a process. In this Chapter, we consider the standard scenario of open quantum systems, where a system irreversibly interacts with an external environment. We show that the standard approach, based on von Neumann entropy, can be replaced by a phase-space formulation of the problem. In particular, we focus on spin systems that can be described using the so-called spin coherent states. We deploy this formalism to study the interplay between the entropy production rate and the initial quantum coherence available to the system., Comment: 17 pages, 4 figures. Proceedings of the "Crossroad of Maxwell Demon" workshop in Toulouse, March 2023. To appear in Volume 15 of the Springer-Nature Series "Advances in Atom and Single Molecule Machines"

We have applied a machine learning algorithm to predict the emergence of environment-induced spontaneous synchronization between two qubits in an open system setting. In particular, we have considered three different models, encompassing global and local dissipation regimes, to describe the open system dynamics of the qubits. We have utilized the $k$-nearest neighbors algorithm to estimate the long time synchronization behavior of the qubits only using the early time expectation values of qubit observables in these three distinct models. Our findings clearly demonstrate the possibility of determining the occurrence of different synchronization phenomena with high precision even at the early stages of the dynamics using a machine learning-based approach. Moreover, we show the robustness of our approach against potential measurement errors in experiments by considering random errors in qubit expectation values. We believe that the presented results can prove to be useful in experimental studies on the determination of quantum synchronization., Comment: 13 pages, 10 figures

We examine the effectiveness and resilience of achieving quantum gates employing three approaches stemming from quantum control methods: counterdiabatic driving, Floquet engineering, and inverse engineering. We critically analyse their performance in terms of the gate infidelity, the associated resource overhead based on energetic cost, the susceptibility to time-keeping errors, and the degradation under environmental noise. Despite significant differences in the dynamical path taken, we find a broadly consistent behavior across the three approaches in terms of the efficacy of implementing the target gate and the resource overhead. Furthermore, we establish that the functional form of the control fields plays a crucial role in determining how faithfully a gate operation is achieved. Our results are demonstrated for single qubit gates, with particular focus on the Hadamard gate, and we discuss the extension to $N$-qubit operations., Comment: 10 pages, 4 figures. Updated to published version

The high energy transfer efficiency of photosynthetic complexes has been a topic of research across many disciplines. Several attempts have been made in order to explain this energy transfer enhancement in terms of quantum mechanical resources such as energetic and vibration coherence and constructive effects of environmental noise. The developments in this line of research have inspired various biomimetic works aiming to use the underlying mechanisms in biological light harvesting complexes for improvement of synthetic systems. In this article we explore the effect of an auxiliary hierarchically structured environment interacting with a system on the steady-state heat transport across the system. The cold and hot baths are modeled by a series of identically prepared qubits in their respective thermal states, and we use collision model to simulate the open quantum dynamics of the system. We investigate the effects of system-environment, inter-environment couplings and coherence of the structured environment on the steady state heat flux and find that such a coupling enhances the energy transfer. Our calculations reveal that there exists a non-monotonic and non-trivial relationship between the steady-state heat flux and the mentioned parameters., Comment: 10 pages, 6 figures

We investigate the irreversible entropy production of a qubit in contact with an environment modelled by a microscopic collision model both in Markovian and non-Markovian regimes. Our main goal is to contribute to the discussions on the relationship between non-Markovian dynamics and negative entropy production rates. We employ two different types of collision models that do or do not keep the correlations established between the system and the incoming environmental particle, while both of them pertain to their non-Markovian nature through information backflow from the environment to the system. We observe that as the former model, where the correlations between the system and environment is preserved, gives rise to negative entropy production rates in the transient dynamics, the latter one always maintains positive rates, even though the convergence to the steady-state value is slower as compared to the corresponding Markovian dynamics. Our results suggest that the mechanism underpinning the negative entropy production rates is not solely non-Markovianity through information backflow, but rather the contribution to it through established system-environment correlations., Comment: 7 pages, 2 figures. Close to published version

Recent experiments at the nanoscales confirm that thermal rectifiers, the thermal equivalent of electrical diodes, can operate in the quantum regime. We present a thorough investigation of the effect of different particle exchange statistics, coherence, and collective interactions on the quantum heat transport of rectifiers with two-terminal junctions. Using a collision model approach to describe the open system dynamics, we obtain a general expression of the nonlinear heat flow that fundamentally deviates from the Landauer formula whenever quantum statistical or coherence asymmetries are present in the bath particles. Building on this, we show that heat rectification is possible even with symmetric medium-bath couplings if the two baths differ in quantum statistics or coherence. Furthermore, the associated thermal conductance vanishes exponentially at low temperatures as in the Coulomb-blockade effect. However, at high temperatures it acquires a power-law behavior depending on the quantum statistics. Our results can be significant for heat management in hybrid open quantum systems or solid-state thermal circuits., Comment: 11 pages, 4 figures. Close to the published version

We investigate the implications of quantum Darwinism in a composite quantum system with interacting constituents exhibiting a decoherence-free subspace. We consider a two-qubit system coupled to an $N$-qubit environment via a dephasing interaction. For excitation preserving interactions between the system qubits, an analytical expression for the dynamics is obtained. It demonstrates that part of the system Hilbert space redundantly proliferates its information to the environment, while the remaining subspace is decoupled and preserves clear non-classical signatures. For measurements performed on the system, we establish that a non-zero quantum discord is shared between the composite system and the environment, thus violating the conditions of strong Darwinism. However, due to the asymmetry of quantum discord, the information shared with the environment is completely classical for measurements performed on the environment. Our results imply a dichotomy between objectivity and classicality that emerges when considering composite systems., Comment: 10 pages, 2 figures. v2 matches published version

It is an established fact that quantum coherences have thermodynamic value. The natural question arises, whether other genuine quantum properties such as entanglement can also be exploited to extract thermodynamic work. In the present analysis, we show that the ergotropy can be expressed as a function of the quantum mutual information, which demonstrates the contributions to the extractable work from classical and quantum correlations. More specifically, we analyze bipartite quantum systems with locally thermal states, such that the only contribution to the ergotropy originates in the correlations. Our findings are illustrated for a two-qubit system collectively coupled to a thermal bath., Comment: 16 pages, 3 figures. Eq. 2 in the published version has a typo, please see the current arXiv version for the correct form

We propose a quantum Otto cycle in a two spin-$1/2$ anisotropic XY model in a transverse external magnetic field. We first characterize the parameter regime that the working medium operates as an engine in the adiabatic regime. Then, we consider finite-time behavior of the engine with and without utilizing a shortcut to adiabaticity (STA) technique. STA schemes guarantee that the dynamics of a system follows the adiabatic path, at the expense of introducing an external control. We compare the performance of the non-adiabatic and STA engines for a fixed adiabatic efficiency but different parameters of the working medium. We observe that, for certain parameter regimes, the irreversibility, as measured by the efficiency lags, due to finite-time driving is so low that non-adiabatic engine performs quite close to the adiabatic engine, leaving the STA engine only marginally better than the non-adiabatic one. This suggests that by designing the working medium Hamiltonian one may spare the difficulty of dealing with an external control protocol., Comment: 10 pages, 5 figures. An extension on the previous work arXiv:1812.00969. Comments are always welcome. v2: fixed some typos and updated the reference list. Close to published version

We theoretically show that the dynamics of a driven quantum harmonic oscillator subject to non-dissipative noise is formally equivalent to the single-particle dynamics propagating through an experimentally feasible dynamically-disordered photonic network. Using this correspondence, we find that noise assisted energy transport occurs in this network and, if the noise is Markovian or delta-correlated, we can obtain an analytical solution for the maximum amount of transferred energy between all network's sites at a fixed propagation distance. Beyond the Markovian limit, we further consider two different types of non-Markovian noise and show that it is possible to have efficient energy transport for larger values of the dephasing rate., Comment: 12 pages, 4 figures

Detuned systems can spontaneously achieve a synchronous dynamics and display robust quantum correlations in different local and global dissipation regimes. Beyond the Markovian limit, information backflow from the environment becomes a crucial mechanism whose interplay with spontaneous synchronization is unknown. Considering a model of two coupled qubits, one of which interacts with a dissipative environment, we show that non-Markovianity is highly detrimental for the emergence of synchronization, for the latter can be delayed and hindered because of the presence of information backflow. The results are obtained considering both a master equation approach and a collision model based on repeated interactions, which represents a very versatile tool to tailor the desired kind of environment., Comment: 10 pages, 8 figures. v2 includes discussions on a hybrid noise model relevant for superconducting qubits, and the relationship between synchronization and different measures of non-Markovianity

We show that it is possible to have non-zero ergotropy in the steady-states of an open quantum system consisting of qubits that are collectively coupled to a thermal bath at a finite temperature. The dynamics of our model leads the qubits into a steady-state that has coherences in the energy eigenbasis when the number of qubits in the system is more than one. We observe that even though the system do not have inverted populations, it is possible to extract work from the coherences and analytically show that in the high temperature limit, ergotropy per unit energy is equal to the $l_1$ norm of coherence for the two qubit case. Further, we analyze the scaling of coherence and ergotropy as a function of the number of qubits in the system for different initial states. Our results suggest that one can design a quantum battery that is charged by a dissipative thermal bath in the weak coupling regime., Comment: 12 pages, 4 figures. v3 includes a new appendix on the relationship between ergotropy and quantum correlations, together with updated main text and references. Matches the published version

We investigate the steady state properties arising from the open system dynamics described by a memoryless (Markovian) quantum collision model, corresponding to a master equation in the ultra-strong coupling regime. By carefully assessing the work cost of switching on and off the system-environment interaction, we show that only a coupling Hamiltonian in the energy-preserving form drives the system to thermal equilibrium, while any other interaction leads to non-equilibrium steady states that are supported by steady-state currents. These currents provide a neat exemplification of the housekeeping work and heat. Furthermore, we characterize the specific form of system-environment interaction that drives the system to a steady-state exhibiting coherence in the energy eigenbasis, thus, giving rise to families of states that are non-passive., Comment: 11 pages, 3 figures. Substantially revised and expanded in v2; v3 close to published version

With the advent of quantum technologies comes the requirement of building quantum components able to store energy to be used whenever necessary, i.e. quantum batteries. In this paper we exploit an adiabatic protocol to ensure a stable charged state of a three-level quantum battery which allows to avoid the spontaneous discharging regime. We study the effects of the most relevant sources of noise on the charging process and, as an experimental proposal, we discuss superconducting transmon qubits. In addition we study the self-discharging of our quantum battery where it is shown that spectrum engineering can be used to delay such phenomena., Comment: 9 pages, 4 figures. Close to published version

We show that certain coherences, termed as heat-exchange coherences, which contribute to the thermalization process of a quantum probe in a repeated interactions scheme, can modify the spectral response of the probe system. We suggest to use the power spectrum as a way to experimentally assess the apparent temperature of non-thermal atomic clusters carrying such coherences and also prove that it is useful to measure the corresponding thermalization time of the probe, assuming some information is provided on the nature of the bath. We explore this idea in two examples in which the probe is assumed to be a single-qubit and a single-cavity field mode. Moreover, for the single-qubit case, we show how it is possible to perform a quantum simulation of resonance fluorescence using such repeated interactions scheme with clusters carrying different class of coherences., Comment: 14 pages, 5 figures, Close to published version

We examine the emergence of objectivity via quantum Darwinism through the use of a collision model, i.e. where the dynamics is modeled through sequences of unitary interactions between the system and the individual constituents of the environment, termed "ancillas". By exploiting versatility of this framework, we show that one can transition from a "Darwinistic" to an "encoding" environment by simply tuning their interaction. Furthermore we establish that in order for a setting to exhibit quantum Darwinism we require a mutual decoherence to occur between the system and environmental ancillas, thus showing that system decoherence alone is not sufficient. Finally, we demonstrate that the observation of quantum Darwinism is sensitive to a non-uniform system-environment interaction., Comment: 7 pages, 3 figures. Close to published version

We consider a finite-time quantum Otto cycle with single and two-spin-$1/2$ systems as its working medium. In order to mimic adiabatic dynamics at a finite-time, we employ a shortcut-to-adiabaticity technique and evaluate the performance of the engine including the cost of the shortcut. We compare our results with the true adiabatic and non-adiabatic performances of the same cycle. Our findings clearly indicate that the use of shortcut-to-adiabaticity scheme significantly enhances the performance of the quantum Otto engine as compared to its adiabatic and non-adiabatic counterparts for different figures of merit., Comment: 11 pages, 3 figures. Close to published version

We investigate the evolution of a target qubit caused by its multiple random collisions with $N$-qubit clusters. Depending on the cluster state, the evolution of the target qubit may correspond to its effective interaction with a thermal bath, a coherent (laser) drive, or a squeezed bath. In cases where the target qubit relaxes to a thermal state its dynamics can exhibit a quantum advantage, whereby the target-qubit temperature can be scaled up proportionally to $N^2$ and the thermalization time can be shortened by a similar factor, provided the appropriate coherence in the cluster is prepared by non-thermal means. We dub these effects quantum super-thermalization due to its analogies to super-radiance. Experimental realizations of these effects are suggested., Comment: 9 pages, 8 figures

We examine a simple scheme to generate genuine multipartite entangled states across disjoint qubit registers. We employ a shuttle qubit that is sequentially coupled, in an energy preserving manner, to the constituents within each register through rounds of interactions. We establish that stable $W$-type entanglement can be generated among all qubits within the registers. Furthermore, we find that the entanglement is sensitive to how the shuttle is treated, showing that a significantly larger degree is achieved by performing projective measurements on it. Finally, we assess the resilience of this entanglement generation protocol to several types of noise and imperfections, showing that it is remarkably robust., Comment: 11 pages, 7 figures. Close to published version