arXiv subjects

Adrian A. Budini

Publications and source records attributed to Adrian A. Budini.

At least 19 recordsLinked to original sources

arXiv2025

Superclassical non-Markovian open quantum dynamics

We characterize a class of superclassical non-Markovian open quantum system dynamics that are defined by their lack of measurement invasiveness when the corresponding observable commutates with the pre-measurement state. This diagonal non-invasiveness guarantees that joint probabilities for measurement outcomes fulfill classical Kolmogorov consistency conditions. These features are fulfilled regardless of the previous (measurement) system history and are valid at arbitrary later times after an arbitrary system initialization. It is shown that a subclass of depolarizing dynamics, which are based on a (time-irreversible) non-unitary system-environment coupling, satisfy the required properties. The relationship with other operational [Milz et al., Phys. Rev. X 10, 041049 (2020)] and non-operational [Banacki et al., Phys. Rev. A 107, 032202 (2023)] notions of classicality in non-Markovian open quantum systems is studied in detail and exemplified through different examples.

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arXiv2024

Quantum distinguishability measures: projectors vs. states maximization

The distinguishability between two quantum states can be defined in terms of their trace distance. The operational meaning of this definition involves a maximization over measurement projectors. Here we introduce an alternative definition of distinguishability which, instead of projectors, is based on maximization over normalized states (density matrices). It is shown that this procedure leads to a distance (between two states) that, in contrast to the usual approach based on a 1-norm, is based on an infinite-norm. Properties such as convexity, monotonicity, and invariance under unitary transformations are fulfilled. Equivalent operational implementations based on maximization over classical probabilities and hypothesis testing scenarios are also established. When considering the action of completely positive transformations contractivity is only granted for unital maps. This feature allows us to introduce a measure of the quantumness of non-unital maps that can be written in terms of the proposed distinguishability measure and corresponds to the maximal possible deviation from contractivity. Particular examples sustain the main results and conclusions.

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arXiv2019

Conditional past-future correlation induced by non-Markovian dephasing reservoirs

Memory effects can be studied through a conditional past-future correlation, which measures departure with respect to a conditional past-future independence valid in a memoryless Markovian regime. In a quantum regime this property leads to an operational definition of quantum non-Markovianity based on three consecutive system measurement processes and postselection [Budini, Phys. Rev. Lett. 121, 240401 (2018)]. Here, we study the conditional past-future correlation for a qubit system coupled to different dephasing environments. Exact solutions are obtained for a quantum spin bath as well as for classically fluctuating random Hamiltonian models. The developing of memory effects and departures from Born-Markov or white-noise approximations are related to a measurement back action that changes the system dynamics between consecutive measurements. It is shown that this effect may develop even when the former system evolution is given by a time-independent Lindblad equation. This unusual non-Markovian case arises when the characteristic parameters of the dynamics become Lorentzian random distributed variables.

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arXiv2017

Entropic relations for retrodicted quantum measurements

Given an arbitrary measurement over a system of interest, the outcome of a posterior measurement can be used for improving the statistical estimation of the system state after the former measurement. Here, we realize an informational-entropic study of this kind of (Bayesian) retrodicted quantum measurement formulated in the context of quantum state smoothing. We show that the (average) entropy of the system state after the retrodicted measurement (smoothed state) is bounded from below and above by the entropies of the first measurement when performed in a selective and non-selective standard predictive ways respectively. For bipartite systems the same property is also valid for each subsystem. Their mutual information, in the case of a former single projective measurement, is also bounded in a similar way. The corresponding inequalities provide a kind of retrodicted extension of Holevo bound for quantum communication channels. These results quantify how much information gain is obtained through retrodicted quantum measurements in quantum state smoothing. While an entropic reduction is always granted, in bipartite systems mutual information may be degraded. Relevant physical examples confirm these features.

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arXiv2017

A memory-induced diffusive-superdiffusive transition: ensemble and time-averaged observables

The ensemble properties and time-averaged observables of a memory-induced diffusive-superdiffusive transition are studied. The model consists in a random walker whose transitions in a given direction depend on a weighted linear combination of the number of both right and left previous transitions. The diffusion process is nonstationary and its probability develops the phenomenon of aging. Depending on the characteristic memory parameters, the ensemble behavior may be normal, superdiffusive, or ballistic. In contrast, the time-averaged mean squared displacement is equal to that of a normal undriven random walk, which renders the process non-ergodic. In addition, and similarly to Levy walks [Godec and Metzler, Phys. Rev. Lett. 110, 020603 (2013)], for trajectories of finite duration the time-averaged displacement apparently become random with properties that depend on the measurement time and also on the memory properties. These features are related to the non-stationary power-law decay of the transition probabilities to their stationary values. Time-averaged response to a bias is also calculated. In contrast with Levy walks [Froemberg and Barkai, Phys. Rev. E 87, 030104(R) (2013)], the response always vanishes asymptotically.

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arXiv2016

Inhomogeneous diffusion and ergodicity breaking induced by global memory effects

We introduce a class of discrete random walk model driven by global memory effects. At any time the right-left transitions depend on the whole previous history of the walker, being defined by an urn-like memory mechanism. The characteristic function is calculated in an exact way, which allows us to demonstrate that the ensemble of realizations is ballistic. Asymptotically each realization is equivalent to that of a biased Markovian diffusion process with transition rates that strongly differs from one trajectory to another. Using this "inhomogeneous diffusion" feature the ergodic properties of the dynamics are analytically studied through the time-averaged moments. In the long time regime they becomes random objects. While their mean values recover the corresponding ensemble averages, departure between time and ensemble averages is explicitly shown through their probability densities. For the density of the second time-averaged moment an ergodic limit and the limit of infinite lag times do not commutate. All these effects are induced by the memory effects.

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arXiv2016

Weak ergodicity breaking induced by global memory effects

We study the phenomenon of weak ergodicity breaking for a class of globally correlated random walk dynamics defined over a finite set of states. The persistence in a given state or the transition to another one depends on the whole previous temporal history of the system. A set of waiting time distributions, associated to each state, set the random times between consecutive steps. Their mean value is finite for all states. The probability density of time-averaged observables is obtained for different memory mechanisms. This statistical object explicitly shows departures between time and ensemble averages. While the mean residence time in each state may result divergent, we demonstrate that this condition is in general not necessary for breaking ergodicity. Hence, global memory effects are an alternative mechanism able to induce this property. Analytical and numerical calculations support these results.

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arXiv2016

Central limit theorem for a class of globally correlated random variables

The standard central limit theorem with a Gaussian attractor for the sum of independent random variables may lose its validity in presence of strong correlations between the added random contributions. Here, we study this problem for similar interchangeable globally correlated random variables. Under these conditions, a hierarchical set of equations is derived for the conditional transition probabilities. This result allows us to define different classes of memory mechanisms that depend on a symmetric way on all involved variables. Depending on the correlation mechanisms and single statistics, the corresponding sums are characterized by distinct statistical probability densities. For a class of urn models it is also possible to characterize their domain of attraction which, as in the standard case, is parametrized by the probability density of each random variable. Symmetric and asymmetric $q$-Gaussian attractors $(q<1)$ are a particular case of these models.

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arXiv2015

Symmetries of general non-Markovian Gaussian diffusive unravelings

By using a condition of average trace preservation we derive a general class of non-Markovian Gaussian diffusive unravelings [L. Diosi and L. Ferialdi, Phys. Rev. Lett. \textbf{113}, 200403 (2014)], here valid for arbitrary non-Hermitian system operators and noise correlations. The conditions under which the generalized stochastic Schrodinger equation has the same symmetry properties (invariance under unitary changes of operator base) than a microscopic system-bath Hamiltonian dynamics are determined. While the standard quantum diffusion model (standard noise correlations) always share the same invariance symmetry, the generalized stochastic dynamics can be mapped with an arbitrary bosonic environment only if some specific correlation constraints are fulfilled. These features are analyzed for different non-Markovian unravelings equivalent in average. Results based on quantum measurement theory that lead to specific cases of the generalized dynamics [J. Gambetta and H. M. Wiseman, Phys. Rev. A \textbf{66}, 012108 (2002)]\ are studied from the perspective of the present analysis.

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arXiv2015

Extended q-Gaussian and q-exponential distributions from Gamma random variables

The family of q-Gaussian and q-exponential probability densities fit the statistical behavior of diverse complex self-similar non-equilibrium systems. These distributions, independently of the underlying dynamics, can rigorously be obtained by maximizing Tsallis "non-extensive" entropy under appropriate constraints, as well as from superstatistical models. In this paper we provide an alternative and complementary scheme for deriving these objects. We show that q-Gaussian and q-exponential random variables can always be expressed as function of two statistically independent Gamma random variables with the same scale parameter. Their shape index determine the complexity q-parameter. This result also allows to define an extended family of asymmetric q-Gaussian and modified $q$-exponential densities, which reduce to the previous ones when the shape parameters are the same. Furthermore, we demonstrate that simple change of variables always allow to relate any of these distributions with a Beta stochastic variable. The extended distributions are applied in the statistical description of different complex dynamics such as log-return signals in financial markets and motion of point defects in fluid flows.

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arXiv2014

Post-Markovian quantum master equations from classical environment fluctuations

In this paper we demonstrate that two commonly used phenomenological post-Markovian quantum master equations can be derived without using any perturbative approximation. A system coupled to an environment characterized by self-classical configurational fluctuations, the latter obeying a Markovian dynamics, defines the underlying physical model. Both Shabani-Lidar equation [A. Shabani and D. A. Lidar, Phys. Rev. A 71, 020101(R) (2005)] and its associated approximated integro-differential kernel master equation are obtained by tracing out two different bipartite Markovian Lindblad dynamics where the environment fluctuations are taken into account by an ancilla system. Furthermore, conditions under which the non-Markovian system dynamics can be unravelled in terms of an ensemble of measurement trajectories are found. In addition, a non-Markovian quantum jump approach is formulated. Contrary to recent analysis [L. Mazzola, E. M. Laine, H. P. Breuer, S. Maniscalco, and J. Piilo, Phys. Rev. A 81, 062120 (2010)], we also demonstrate that these master equations, even with exponential memory functions, may lead to non-Markovian effects such as an environment-to-system backflow of information if the Hamiltonian system does not commutate with the dissipative dynamics.

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arXiv2013

Bipartite entanglement induced by classically-constrained quantum dissipative dynamics

The properties of some complex many body systems can be modeled by introducing in the dissipative dynamics of each single component a set of kinetic constraints that depend on the state of the neighbor systems. Here, we characterize this kind of dynamics for two quantum systems whose independent dissipative evolutions are defined by a Lindblad equation. The constraints are introduced through a set of projectors that restrict the action of each single dissipative Lindblad channel to the state of the other system. Conditions that guaranty a classical interpretation of the kinetic constraints are found. The generation and evolution of entanglement is studied for two optical qubits systems. Classically constrained dissipation leads to a stationary state whose degree of entanglement depends on the initial state. Nevertheless, independently of the initial conditions, a maximal entangled state is generated when both systems are subjected to the action of local Hamiltonian fields that do not commutate with the constraints. The underlying physical mechanism is analyzed in detail.

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arXiv2013

Non-Markovian quantum jumps from measurements in bipartite Markovian dynamics

The quantum jump approach allows to characterize the stochastic dynamics associated to 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 in studying a measurement process performed on a bipartite arrangement characterized by a Markovian Lindblad evolution. Both a renewal and non-renewal extensions are found. The general structure of non-local master equations that admit an unravelling in terms of the corresponding non-Markovian trajectories are also found. 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.

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arXiv2013

Markovian embedding of non-Markovian quantum collisional models

A wide class of non-Markovian completely positive master equations can be formulated on the basis of quantum collisional models. In this phenomenological approach the dynamics of an open quantum system is modeled through an ensemble of stochastic realizations that consist in the application at random times of a (collisional) completely positive transformation over the system state. In this paper, we demonstrate that these kinds of models can be embedded in bipartite Markovian Lindblad dynamics consisting of the system of interest and an auxiliary one. In contrast with phenomenological formulations, here the stochastic ensemble dynamics an the inter-event time interval statistics are obtained from a quantum measurement theory after assuming that the auxiliary system is continuously monitored in time. Models where the system inter-collisional dynamics is non-Markovian [B. Vacchini, Phys. Rev. A 87, 030101(R) (2013)] are also obtained from the present approach. The formalism is exemplified through bipartite dynamics that leads to non-Markovian system effects such as an environment-to-system back flow of information.

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arXiv2012

A generalized fluctuation relation for power-law distributions

Strong violations of existing fluctuation theorems may arise in nonequilibrium steady states characterized by distributions with power-law tails. The ratio of the probabilities of positive and negative fluctuations of equal magnitude behaves in an anomalous nonmonotonic way [H. Touchette and E.G.D. Cohen, Phys. Rev. E \textbf{76}, 020101(R) (2007)]. Here, we propose an alternative definition of fluctuation relation (FR) symmetry that, in the power-law regime, is characterized by a monotonic linear behavior. The proposal is consistent with a large deviation-like principle. As example, it is studied the fluctuations of the work done on a dragged particle immersed in a complex environment able to induce power-law tails. When the environment is characterized by spatiotemporal temperature fluctuations, distributions arising in nonextensive statistical mechanics define the work statistics. In that situation, we find that the FR symmetry is solely defined by the average bath temperature. The case of a dragged particle subjected to a Lévy noise is also analyzed in detail.

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arXiv2011

Large deviations of ergodic counting processes: a statistical mechanics approach

The large-deviation method allows to characterize an ergodic counting process in terms of a thermodynamic frame where a free energy function determines the asymptotic non-stationary statistical properties of its fluctuations. Here, we study this formalism through a statistical mechanics approach, i.e., with an auxiliary counting process that maximizes an entropy function associated to the thermodynamic potential. We show that the realizations of this auxiliary process can be obtained after applying a conditional measurement scheme to the original ones, providing is this way an alternative measurement interpretation of the thermodynamic approach. General results are obtained for renewal counting processes, i.e., those where the time intervals between consecutive events are independent and defined by a unique waiting time distribution. The underlying statistical mechanics is controlled by the same waiting time distribution, rescaled by an exponential decay measured by the free energy function. A scale invariance, shift closure, and intermittence phenomena are obtained and interpreted in this context. Similar conclusions apply for non-renewal processes when the memory between successive events is induced by a stochastic waiting time distribution.

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arXiv2011

Fluctuation relations with intermittent non-Gaussian variables

Non-equilibrium stationary fluctuations may exhibit a special symmetry called fluctuation relations (FR). Here, we show that this property is always satisfied by the subtraction of two random and independent variables related by a thermodynamic-like change of measure. Taking one of them as a modulated Poisson process, it is demonstrated that intermittence and FR are compatibles properties that may coexist naturally. Strong non-Gaussian features characterize the probability distribution and its generating function. Their associated large deviation functions (LDF) develop a kink at the origin and a plateau regime respectively. Application of this model in different stationary nonequilibrium situations is discussed.

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arXiv2010

Thermodynamics of quantum jump trajectories in systems driven by classical fluctuations

The large-deviation method can be used to study the measurement trajectories of open quantum systems. For optical arrangements this formalism allows to describe the long time properties of the (non-equilibrium) photon counting statistics in the context of a (equilibrium) thermodynamic approach defined in terms of dynamical phases and transitions between them in the trajectory space [J.P. Garrahan and I. Lesanovsky, Phys. Rev. Lett. 104, 160601 (2010)]. In this paper, we study the thermodynamic approach for fluorescent systems coupled to complex reservoirs that induce stochastic fluctuations in their dynamical parameters. In a fast modulation limit the thermodynamics corresponds to that of a Markovian two-level system. In a slow modulation limit, the thermodynamic properties are equivalent to those of a finite system that in an infinite-size limit is characterized by a first-order transition. The dynamical phases correspond to different intensity regimes, while the size of the system is measured by the transition rate of the bath fluctuations. As a function of a dimensionless intensive variable, the first and second derivative of the thermodynamic potential develop an abrupt change and a narrow peak respectively. Their scaling properties are consistent with a double-Gaussian probability distribution of the associated extensive variable.

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