arXiv subjects

Sascha Wald

Publications and source records attributed to Sascha Wald.

At least 19 recordsLinked to original sources

arXiv2026

Entanglement capacity of complex networks from quantum walks

Discrete-time quantum walks provide a natural framework for quantum transport on complex networks. On regular structures, coin-walker entanglement has been widely used to characterize quantum transport and to support quantum algorithmic protocols. However, this notion relies on a fixed Hilbert space factorization separating coin and position and is therefore not directly applicable to more complex, irregular structures. Here we introduce an entanglement measure for general networks based on a bipartition that assigns each node two roles, acting as both a source and a target. The resulting bipartition defines the source-target entanglement, a measure for general networks, motivated by coin-walker entanglement. We show that the connectivity of the network imposes an upper bound on this entanglement and identify graph matchings as the underlying structure governing entanglement generation. We further illustrate that in random graphs improving graph connectivity reduces the attainable entanglement, establishing a structure-dependent constraint on quantum correlations.

quant-ph↗

arXiv2026

Nonequilibrium phases and quantum correlations in synthetic transport models

Quantum devices featuring mid-circuit measurement and reset capabilities, such as quantum computers and dual-species Rydberg quantum simulators, enable the realization of quantum cellular automata. These systems evolve in discrete time following local updates implemented by unitary gates, and allow for the realization of both closed and synthetic dissipative dynamics. Here, we focus on quantum cellular automata that implement minimal models of classical and quantum transport. To illustrate our ideas, we focus on a discrete-time totally asymmetric simple exclusion process and investigate how coherent dynamical contributions allow for the emergence of quantum effects and correlations. We find that bipartite entanglement dominates the transient evolution, while stationary states can retain quantum correlations beyond entanglement. Our results suggest viable routes for realizing transport models on quantum devices and characterizing collective quantum correlations in strongly driven systems.

quant-ph↗

arXiv2026

Stochastic resetting induces quantum non-Markovianity

Stochastic resetting describes dynamics which are reinitialized to a reference state at random times. These protocols are attracting significant interest: they can stabilize nonequilibrium stationary states, generate correlations in noninteracting systems, and enable optimal search strategies. While a constant reset probability results in a Markovian dynamics, much less is known about non-Markovian effects in quantum stochastic resetting. Here, we analyze memory effects in these processes -- examining the evolution of quantum states and of observables -- through witnesses of non-Markovianity for open quantum systems. We focus on discrete-time reset processes, which are of particular interest as they can be implemented on existing gate-operated quantum devices. We show that these processes are generically described by non-divisible maps and, in non-classical scenarios where the effective reset probability can become negative, can feature revivals in the state distinguishability. Our results reveal non-Markovian effects in quantum stochastic resetting and show that a time-dependent reset may be exploited to engineer enhanced stationary quantum correlations.

quant-ph↗

arXiv2024

Stochastic resetting in discrete-time quantum dynamics: steady states and correlations in few-qubit systems

Time evolution in several classes of quantum devices is generated through the application of quantum gates. Resetting is a critical technological feature in these systems allowing for mid-circuit measurement and complete or partial qubit reset. The possibility of realizing discrete-time reset dynamics on quantum computers makes it important to investigate the steady-state properties of such dynamics. Here, we explore the behavior of generic discrete-time unitary dynamics interspersed by random reset events. For Poissonian resets, we compute the stationary state of the process and demonstrate, by taking a weak-reset limit, the existence of "resonances" in the quantum gates, allowing for the emergence of steady state density matrices which are not diagonal in the eigenbasis of the generator of the unitary gate. Such resonances are a genuine discrete-time feature and impact on quantum and classical correlations even beyond the weak-reset limit. Furthermore, we consider non-Poissonian reset processes and explore conditions for the existence of a steady state. We show that, when the reset probability vanishes sufficiently rapidly with time, the system does not approach a steady state. Our results highlight key differences between continuous-time and discrete-time stochastic resetting and may be useful to engineer states with controllable correlations on existing devices.

quant-ph↗

arXiv2023

Coined quantum walks on the line: Disorder, entanglement, and localization

Disorder in coined quantum walks generally leads to localization. We investigate the influence of the localization on the entanglement properties of coined quantum walks. Specifically, we consider quantum walks on the line and explore the effects of quenched disorder in the coin operations. After confirming that our choice of disorder localizes the walker, we study how the localization affects the properties of the coined quantum walk. We find that the mixing properties of the walk are altered nontrivially with mixing being improved at short time scales. Special focus is given to the influence of coin disorder on the properties of the quantum state and the coin-walker entanglement. We find that disorder alters the quantum state significantly even when the walker probability distribution is still close to the nondisordered case. We observe that, generically, coin disorder decreases the coin-walker entanglement and that the localization leaves distinct traces in the entanglement entropy and the entanglement negativity of the coined quantum walk.

quant-ph↗

arXiv2023

Active quantum flocks

Flocks of animals represent a prominent archetype of collective behavior in the macroscopic classical world, where the constituents, such as birds, concertedly perform motions and actions as if being one single entity. Here, we address the so far open question of whether flocks can also form in the microscopic world at the quantum level. For that purpose, we introduce the concept of active quantum matter by formulating a class of models of active quantum particles on a one-dimensional lattice. We provide both analytical and large-scale numerical evidence that these systems can give rise to quantum flocks. A key finding is that these quantum flocks exhibit distinct quantum properties by developing strong quantum coherence over long distances. We propose that quantum flocks could be experimentally observed in Rydberg atom arrays.

quant-ph↗

arXiv2023

Entanglement gap in 1D long-range quantum spherical models

We investigate the finite-size scaling of the entanglement gap in the one dimensional long-range quantum spherical model (QSM). We focus on the weak long-range QSM, for which the thermodynamic limit is well-defined. This model exhibits a continuous phase transition, separating a paramagnetic from a ferromagnet phase. The universality class of the transition depends on the long-range exponent $α$. We show that in the thermodynamic limit the entanglement gap is finite in the paramagnetic phase, and it vanishes in the ferromagnetic phase. In the ferromagnetic phase the entanglement gap is understood in terms of standard magnetic correlation functions. The entanglement gap decays as $δξ\simeq C_αL^{-(1/2-α/4)}$, where the constant $C_α$ depends on the low-energy properties of the model. This reflects that the lower part of the dispersion is affected by the long range physics. Finally, multiplicative logarithmic corrections are absent in the scaling of the entanglement gap, in contrast with the higher-dimensional case.

cond-mat.stat-mech↗

arXiv2023

Entanglement in the Quantum Spherical Model -- a Review

We review some recent results on entanglement in the Quantum Spherical Model (QSM). The focus lays on the physical results rather than the mathematical details. Specifically, we study several entanglement-related quantities, such asentanglement entropies, and logarithmic negativity, in the presence of quantum and classical critical points, and in magnetically ordered phases. We consider both the short as well as the long-range QSM. The study of entanglement properties of the QSM is feasible because the model is mappable to a Gaussian system in any dimension. Despite this fact the QSM is an ideal theoretical laboratory to investigate a wide variety of physical scenarios, such as non mean field criticality, the effect of long-range interactions, the interplay between finite-temperature fluctuations and genuine quantum ones.

cond-mat.stat-mech↗

arXiv2022

Stochastic Representation of the Quantum Quartic Oscillator

Recent experimental advances have inspired the development of theoretical tools to describe the non-equilibrium dynamics of quantum systems. Among them an exact representation of quantum spin systems in terms of classical stochastic processes has been proposed. Here we provide first steps towards the extension of this stochastic approach to bosonic systems by considering the one-dimensional quantum quartic oscillator. We show how to exactly parameterize the time evolution of this prototypical model via the dynamics of a set of classical variables. We interpret these variables as stochastic processes, which allows us to propose a novel way to numerically simulate the time evolution of the system. We benchmark our findings by considering analytically solvable limits and providing alternative derivations of known results.

quant-ph↗

arXiv2022

Entanglement dynamics of a hard-core quantum gas during a Joule expansion

We study the entanglement dynamics of a one-dimensional hard-core quantum gas initially confined in a box of size $L$ with saturated density $ρ=1$. The gas is suddenly released into a region of size $2L$ by moving one of the box edges. We show that the analytic prediction for the entanglement entropy obtained from quantum fluctuating hydrodynamics holds quantitatively true even after several reflections of the gas against the box edges. We further investigate the long time limit $t/L\gg 1$ where a Floquet picture of the non-equilibrium dynamics emerges and hydrodynamics eventually breaks down.

cond-mat.stat-mech↗

arXiv2022

Mathematical Characterization of Private and Public Immune Repertoire Sequences

Diverse T and B cell repertoires play an important role in mounting effective immune responses against a wide range of pathogens and malignant cells. The number of unique T and B cell clones is characterized by T and B cell receptors (TCRs and BCRs), respectively. Although receptor sequences are generated probabilistically by recombination processes, clinical studies found a high degree of sharing of TCRs and BCRs among different individuals. In this work, we use a general probabilistic model for T/B cell receptor clone abundances to define "publicness" or "privateness" and information-theoretic measures for comparing the frequency of sampled sequences observed across different individuals. We derive mathematical formulae to quantify the mean and the variances of clone richness and overlap. Our results can be used to evaluate the effect of different sampling protocols on abundances of clones within an individual as well as the commonality of clones across individuals. Using synthetic and empirical TCR amino acid sequence data, we perform simulations to study expected clonal commonalities across multiple individuals. Based on our formulae, we compare these simulated results with the analytically predicted mean and variances of the repertoire overlap. Complementing the results on simulated repertoires, we derive explicit expressions for the richness and its uncertainty for specific, single-parameter truncated power-law probability distributions. Finally, the information loss associated with grouping together certain receptor sequences, as is done in spectratyping, is also evaluated. Our approach can be, in principle, applied under more general and mechanistically realistic clone generation models.

q-bio.QM↗

arXiv2021

Non-equilibrium dynamics of the open quantum $O(n)$-model with non-Markovian noise: exact results

The collective and purely relaxational dynamics of quantum many-body systems after a quench at temperature $T=0$, from a disordered state to various phases is studied through the exact solution of the quantum Langevin equation of the spherical and the $O(n)$-model in the limit $n\to\infty$. The stationary state of the quantum dynamics is shown to be a non-equilibrium state. The quantum spherical and the quantum $O(n)$-model for $n\to\infty$ are in the same dynamical universality class. The long-time behaviour of single-time and two-time correlation and response functions is analysed and the universal exponents which characterise quantum coarsening and quantum ageing are derived. The importance of the non-Markovian long-time memory of the quantum noise is elucidated by comparing it with an effective Markovian noise having the same scaling behaviour and with the case of non-equilibrium classical dynamics.

cond-mat.stat-mech↗

arXiv2020

From classical to quantum walks with stochastic resetting on networks

Random walks are fundamental models of stochastic processes with applications in various fields including physics, biology, and computer science. We study classical and quantum random walks under the influence of stochastic resetting on arbitrary networks. Based on the mathematical formalism of quantum stochastic walks, we provide a framework of classical and quantum walks whose evolution is determined by graph Laplacians. We study the influence of quantum effects on the stationary and long-time average probability distribution by interpolating between the classical and quantum regime. We compare our analytical results on stationary and long-time average probability distributions with numerical simulations on different networks, revealing differences in the way resets affect the sampling properties of classical and quantum walks.

cond-mat.stat-mech↗

arXiv2020

Closure of the entanglement gap at quantum criticality: The case of the Quantum Spherical Model

The study of entanglement spectra is a powerful tool to detect or elucidate universal behaviour in quantum many-body systems. We investigate the scaling of the entanglement (or Schmidt) gap $δξ$, i.e., the lowest laying gap of the entanglement spectrum, at a two-dimensional quantum critical point. We focus on the paradigmatic quantum spherical model, which exhibits a second-order transition, and is mappable to free bosons with an additional external constraint. We analytically show that the Schmidt gap vanishes at the critical point, although only logarithmically. For a system on a torus and the half-system bipartition, the entanglement gap vanishes as $π^2/\ln(L)$, with $L$ the linear system size. The entanglement gap is nonzero in the paramagnetic phase and exhibits a faster decay in the ordered phase. The rescaled gap $δξ\ln(L)$ exhibits a crossing for different system sizes at the transition, although logarithmic corrections prevent a precise verification of the finite-size scaling. Interestingly, the change of the entanglement gap across the phase diagram is reflected in the zero-mode eigenvector of the spin-spin correlator. At the transition quantum fluctuations give rise to a non-trivial structure of the eigenvector, whereas in the ordered phase it is flat. We also show that the vanishing of the entanglement gap at criticality can be qualitatively but not quantitatively captured by neglecting the structure of the zero-mode eigenvector.

cond-mat.stat-mech↗

arXiv2020

In and out of equilibrium quantum metrology with mean-field quantum criticality

We study the influence that collective transition phenomena have on quantum metrological protocols. The single spherical quantum spin (SQS) serves as stereotypical toy model that allows analytical insights on a mean-field level. First, we focus on equilibrium quantum criticality in the SQS and obtain the quantum Fisher information analytically, which is associated with the minimum lower bound for the precision of estimation of the parameter driving the phase transition. We compare it with the Fisher information for a specific experimental scenario where photoncounting-like measurements are employed. We find how quantum criticality and squeezing are useful resources in the metrological scenario. Second, we obtain the quantum Fisher information for the out of equilibrium transition in the dissipative non-equilibrium steady state (NESS), and investigate how the presence of dissipation affects the parameter estimation. In this scenario, it is known that the critical point is shifted by an amount which depends on the dissipation rate. This is used here to design high precision protocols for a whole range of the transition-driving parameter in the ordered phase. In fact, for certain values of the parameter being estimated, dissipation may be used to obtain higher precision when compared to the equilibrium scenario.

quant-ph↗

arXiv2019

Entanglement and classical fluctuations at finite-temperature critical points

We investigate several entanglement-related quantities at finite-temperature criticality in the three-dimensional quantum spherical model, both as a function of temperature $T$ and of the quantum parameter $g$, which measures the strength of quantum fluctuations. While the von Neumann and the Rényi entropies exhibit the volume-law for any $g$ and $T$, the mutual information obeys an area law. The prefactors of the volume-law and of the area-law are regular across the transition, reflecting that universal singular terms vanish at the transition. This implies that the mutual information is dominated by nonuniversal contributions. This hampers its use as a witness of criticality, at least in the spherical model. We also study the logarithmic negativity. For any value of $g,T$, the negativity exhibits an area-law. The negativity vanishes deep in the paramagnetic phase, it is larger at small temperature, and it decreases upon increasing the temperature. For any $g$, it exhibits the so-called sudden death, i.e., it is exactly zero for large enough $T$. The vanishing of the negativity defines a "death line", which we characterise analytically at small $g$. Importantly, for any finite $T$ the area-law prefactor is regular across the transition, whereas it develops a cusp-like singularity in the limit $T\to 0$. Finally, we consider the single-particle entanglement and negativity spectra. The vast majority of the levels are regular across the transition. Only the larger ones exhibit singularities. These are related to the presence of a zero mode, which reflects the symmetry breaking. This implies the presence of sub-leading singular terms in the entanglement entropies. Interestingly, since the larger levels do not contribute to the negativity, sub-leading singular corrections are expected to be suppressed for the negativity.

cond-mat.stat-mech↗

arXiv2019

Dynamical chaotic phases and constrained quantum dynamics

In classical mechanics, external constraints on the dynamical variables can be easily implemented within the Lagrangian formulation. Conversely, the extension of this idea to the quantum realm, which dates back to Dirac, has proven notoriously difficult due to the noncommutativity of observables. Motivated by recent progress in the experimental control of quantum systems, we propose a framework for the implementation of quantum constraints based on the idea of work protocols, which are dynamically engineered to enforce the constraints. As a proof of principle, we consider the dynamical mean-field approach of the many-body quantum spherical model, which takes the form of a quantum harmonic oscillator plus constraints on the first and second moments of one of its quadratures. The constraints of the model are implemented by the combination of two work protocols, coupling together the first and second moments of the quadrature operators. We find that such constraints affect the equations of motion in a highly nontrivial way, inducing nonlinear behavior and even classical chaos. Interestingly, Gaussianity is preserved at all times. A discussion concerning the robustness of this approach to possible experimental errors is also presented.

quant-ph↗

arXiv2019

Axiomatic construction of quantum Langevin equations

A phenomenological construction of quantum Langevin equations, based on the physical criteria of (i) the canonical equal-time commutators, (ii) the Kubo formula, (iii) the virial theorem and (iv) the quantum fluctuation-dissipation theorem is presented. The case of a single harmonic oscillator coupled to a large external bath is analysed in detail. This allows to distinguish a markovian semi-classical approach, due to Bedeaux and Mazur, from a non-markovian full quantum approach, due to to Ford, Kac and Mazur. The quantum-fluctuation-dissipation theorem is seen to be incompatible with a markovian dynamics. Possible applications to the quantum spherical model are discussed.

cond-mat.stat-mech↗