arXiv subjects

Katarzyna Macieszczak

Publications and source records attributed to Katarzyna Macieszczak.

At least 19 recordsLinked to original sources

arXiv2026

Supermartingales in Quantum Resources Theories: Where do quantum resources go when you're watching?

We establish a connection between quantum resource theory and probability theory, under repeated application of free operations. We show that strong monotonicity of a resource measure implies that the resource is a supermartingale. We then use the optional stopping and martingale convergence theorems to derive bounds on the efficiency of post-selection, and other free adaptive strategies. We also describe the asymptotic dynamics of the conditional state, where resource fluctuations are necessarily absent, showing one of two distinct phenomena occurs: resource vanishing or resource freezing.

quant-ph↗

arXiv2025

Gauge freedoms in unravelled quantum dynamics: When do different continuous measurements yield identical quantum trajectories?

Quantum trajectories of a Markovian open quantum system arise from the back-action of measurements performed in the environment with which the system interacts. In this work, we consider counting measurements of quantum jumps, corresponding to different representations of the same quantum master equation. We derive necessary and sufficient conditions under which these different measurements give rise to the same unravelled quantum master equation, which governs the dynamics of the probability distribution over pure conditional states of the system. Since that equation uniquely determines the stochastic dynamics of a conditional state, we also obtain necessary and sufficient conditions under which different measurements result in identical quantum trajectories. We then consider the joint stochastic dynamics for the conditional state and the measurement record. We formulate this in terms of labelled quantum trajectories, and derive necessary and sufficient conditions under which different representations lead to equivalent labelled quantum trajectories, up to permutations of labels. As those conditions are generally stricter, we finish by constructing coarse-grained measurement records, such that equivalence of the corresponding partially-labelled trajectories is guaranteed by equivalence of the trajectories alone. These general results are illustrated by two examples that demonstrate permutation of labels, and equivalence of different quantum trajectories.

quant-ph↗

arXiv2025

Weak unitary symmetries of open quantum dynamics: beyond quantum master equations

We consider Markovian open quantum dynamics with weak unitary symmetries. Starting from the quantum master equation for the system alone, it is known that the joint dynamics of the system and its environment can be obtained by dilation, leading to a closed dynamics for a continuous matrix product state. Performing counting measurements on the environment gives rise to stochastic dynamics of quantum trajectories for the system, which when averaged yield back the quantum master equation. In this work, we identify necessary and sufficient conditions under which the dynamics of these different descriptions retain the weak symmetry of the quantum master equation and we characterise the resulting symmetries of the different descriptions in terms of their generators. We find that the joint dynamics always features a separable symmetry directly related to that of the quantum master equation, but for quantum trajectories the corresponding symmetry is present only if the counting measurement satisfies certain conditions.

quant-ph↗

arXiv2024

Occupation Uncertainty Relations

We introduce occupation uncertainty relations (OURs) for dynamics of a Markov process over discrete configurations. Those are lower bounds on uncertainties of system observables that are time-integrated along stochastic trajectories. The uncertainty is defined as the ratio of the variance to the square of the average, with the latter necessarily shifted by the average in a reference distribution. The derived bounds are observable independent, but rely on the reference choice. We show, however, that all OURs originate from a matrix bound on correlations between times spent in different system configurations, i.e., occupation times. This result is reference independent, and expressed only in terms of stationary probability and lifetimes of individual configurations. Any dynamics that saturates the matrix bound, is optimal in approximating stationary distribution by occupation times; this always occurs for unidirectional cycles. Furthermore, using this bound, dynamic correlations can be asymptotically bounded in terms of static correlations, in turn leading to the positivity of dynamic exponents in the thermodynamic limit. While at a finite size the matrix bound generally saturates away from equilibrium, we demonstrate detailed-balance dynamics can still saturate it asymptotically, by leading to vanishing dynamic exponents and optimal simulations in that context.

cond-mat.stat-mech↗

arXiv2024

Ultimate Kinetic Uncertainty Relation and Optimal Performance of Stochastic Clocks

For Markov processes over discrete configurations, an asymptotic bound on the uncertainty of stochastic fluxes is derived in terms of the harmonic mean of decay rates with respect to the stationary distribution. This bound is necessarily tighter than the bound in terms of the arithmetic mean, i.e., the activity, known as the kinetic uncertainty relation. What is more, it can always be saturated. In turn, an exact limit for the uncertainty of first-passage times as well as the optimal long-time performance of stochastic clocks are established. The results generalise to semi-Markov processes, including quantum reset processes, where it can be determined when clock performance improves thanks to coherent driving.

cond-mat.stat-mech↗

arXiv2024

Unravelling Metastable Markovian Open Quantum Systems

We analyse the dynamics of metastable Markovian open quantum systems by unravelling their average dynamics into stochastic trajectories. We use quantum reset processes as examples to illustrate metastable phenomenology, including a simple three-state model whose metastability is of classical type, and a two-qubit model that features a metastable decoherence free subspace. In the three-state model, the trajectories exhibit classical metastable phenomenology: fast relaxation into distinct phases and slow transitions between them. This extends the existing correspondence between classical and quantum metastability. It enables the computation of committors for the quantum phases, and the mechanisms of rare transitions between them. For the two-qubit model, the decoherence-free subspace appears in the unravelled trajectories as a slow manifold on which the quantum state has a continuous slow evolution. This provides a classical (non-metastable) analogue of this quantum effect. We discuss the general implications of these results, and we highlight the useful role of quantum reset processes for analysis of quantum trajectories in metastable systems.

quant-ph↗

arXiv2023

Metastability and quantum coherence-assisted sensing in interacting parallel quantum dots

We study the transient dynamics subject to quantum coherence effects of two interacting parallel quantum dots weakly coupled to macroscopic leads. The stationary particle current of this quantum system is sensitive to perturbations much smaller than any other energy scale, specifically compared to the system-lead coupling and the temperature. We show that this is due to the presence of a parity-like symmetry in the dynamics, as a consequence of which, two distinct stationary states arise. In the presence of small perturbations breaking this symmetry, the system exhibits metastability with two metastable phases that can be approximated by a combination of states corresponding to stationary states in the unperturbed limit. Furthermore, the long-time dynamics can be described as classical dynamics between those phases, leading to a unique stationary state. In particular, the competition of those two metastable phases explains the sensitive behavior of the stationary current towards small perturbations. We show that this behavior bears the potential of utilizing the parallel dots as a charge sensor which makes use of quantum coherence effects to achieve a signal to noise ratio that is not limited by the temperature. As a consequence, the parallel dots outperform an analogous single-dot charge sensor for a wide range of temperatures.

cond-mat.mes-hall↗

arXiv2021

Theory of classical metastability in open quantum systems

We present a general theory of classical metastability in open quantum systems. Metastability is a consequence of a large separation in timescales in the dynamics, leading to the existence of a regime when states of the system appear stationary, before eventual relaxation toward a true stationary state at much larger times. In this work, we focus on the emergence of classical metastability, i.e., when metastable states of an open quantum system with separation of timescales can be approximated as probabilistic mixtures of a finite number of states. We find that a number of classical features follow from this approximation, for the manifold of metastable states, long-time dynamics between them, and symmetries of the dynamics. Namely, those states are approximately disjoint and thus play the role of metastable phases, the relaxation toward the stationary state is approximated by a classical stochastic dynamics between them, and weak symmetries correspond to their permutations. Importantly, the classical dynamics is observed not only on average, but also at the level of individual quantum trajectories: We show that time coarse-grained continuous measurement records can be viewed as noisy classical trajectories, while their statistics can be approximated by that of the classical dynamics. Among others, this explains how first-order dynamical phase transitions arise from metastability. Finally, to verify the presence of classical metastability in a given open quantum system, we develop an efficient numerical approach that delivers the set of metastable phases together with the effective classical dynamics. Since the proximity to a first-order dissipative phase transition manifests as metastability, the theory and tools introduced in this work can be used to investigate such transitions through the metastable behavior of many-body systems of moderate sizes accessible to numerics.

cond-mat.stat-mech↗

arXiv2021

Operational approach to metastability

In this work, we introduce an information-theoretic approach for considering changes in dynamics of finitely dimensional open quantum systems governed by master equations. This experimentally motivated approach arises from considering how the averages of system observables change with time and quantifies how non-stationary the system is during a given time regime. By drawing an analogy with the exponential decay, we are able to further investigate regimes when such changes are negligible according to the logarithmic scale of time, and thus the system is approximately stationary. While this is always the case within the initial and final regimes of the dynamics, with the system respectively approximated by its initial and asymptotic states, we show that a distinct regime of approximate stationarity may arise. In turn, we establish a quantitative description of the phenomenon of metastability in open quantum systems. The initial relaxation occurring before the corresponding metastable regime and of the long-time dynamics taking place afterwards are also characterised. Furthermore, we explain how metastability relates to the separation in the real part of the master equation spectrum and connect our approach to the spectral theory of metastability, clarifying when the latter follows. All of our general results directly translate to Markovian dynamics of classical stochastic systems.

quant-ph↗

arXiv2021

Quantum jump Monte Carlo simplified: Abelian symmetries

We consider Markovian dynamics of a finitely dimensional open quantum system featuring a weak unitary symmetry, i.e., when the action of a unitary symmetry on the space of density matrices commutes with the master operator governing the dynamics. We show how to encode the weak symmetry in quantum stochastic dynamics of the system by constructing a weakly symmetric representation of the master operator: a symmetric Hamiltonian, and jump operators connecting only the symmetry eigenspaces with a fixed eigenvalue ratio. In turn, this representation simplifies both the construction of the master operator as well as quantum jump Monte Carlo simulations, where, for a symmetric initial state, stochastic trajectories of the system state are supported within a single symmetry eigenspace at a time, which is changed only by the action of an asymmetric jump operator. Our results generalize directly to the case of multiple Abelian weak symmetries.

quant-ph↗

arXiv2020

Hierarchical classical metastability in an open quantum East model

We study in detail an open quantum generalisation of a classical kinetically constrained model -- the East model -- known to exhibit slow glassy dynamics stemming from a complex hierarchy of metastable states with distinct lifetimes. Using the recently introduced theory of classical metastability for open quantum systems, we show that the driven open quantum East model features a hierarchy of classical metastabilities at low temperature and weak driving field. We find that the effective long-time description of its dynamics is not only classical, but shares many properties with the classical East model, such as obeying an effective detailed balance condition, and lacking static interactions between excitations, but with this occurring within a modified set of metastable phases which are coherent, and with an effective temperature that is dependent on the coherent drive.

cond-mat.stat-mech↗

arXiv2020

Dissipative quantum state preparation and metastability in two-photon micromasers

We study the preparation of coherent quantum states in a two-photon micromaser for applications in quantum metrology. While this setting can be in principle realized in a host of physical systems, we consider atoms interacting with the field of a cavity. We focus on the case of the interaction described by the Jaynes-Cummings Hamiltonian, which cannot be achieved by the conventional approach with three-level atoms coupled to the cavity field at two-photon resonance. We find that additional levels are required in order to cancel Stark shifts emerging in the leading order. Once this is accomplished, the dynamics of the cavity features a degenerate stationary state manifold of pure states. We derive the analytic form of these states and show that they include Schrödinger cat states with a tunable mean photon number. We also confirm these states can be useful in phase estimation protocols with their quantum Fisher information exceeding the standard limit. To account for realistic imperfections, we consider single-photon losses from the cavity, finite lifetime of atom levels, and higher order corrections in the far-detuned limit, which result in metastability of formerly stationary cavity states and long-time dynamics with a unique mixed stationary state. Despite being mixed, this stationary state can still feature quantum Fisher information above the standard limit. Our work delivers a comprehensive overview of the two-photon micromaser dynamics with particular focus on application in phase estimation and, while we consider the setup with atoms coupled to a cavity, the results can be directly translated to optomechanical systems.

quant-ph↗

arXiv2019

Coherence, entanglement and quantumness in closed and open systems with conserved charge, with an application to many-body localisation

While the scaling of entanglement in a quantum system can be used to distinguish many-body quantum phases, it is usually hard to quantify the amount of entanglement in mixed states of open quantum systems, while measuring entanglement experimentally, even for the closed systems, requires in general quantum state tomography. In this work we show how to remedy this situation in system with a fixed or conserved charge, e.g., density or magnetization, due to an emerging relation between quantum correlations and coherence. First, we show how, in these cases, the presence of multipartite entanglement or quantumness can be faithfully witnessed simply by detecting coherence in the quantum system, while bipartite entanglement or bipartite quantum discord are implied by asymmetry (block coherence) in the system. Second, we prove that the relation between quantum correlations and coherence is also quantitative. Namely, we establish upper and lower bounds on the amount of multipartite and bipartite entanglement in a many-body system with a fixed local charge, in terms of the amount of coherence and asymmetry present in the system. Importantly, both for pure and mixed quantum states, these bounds are expressed as closed formulas, and furthermore, for bipartite entanglement, are experimentally accessible by means of the multiple quantum coherence spectra. In particular, in one-dimensional systems, our bounds may detect breaking of the area law of entanglement entropy. We illustrate our results on the example of a many-body localized system, also in the presence of dephasing.

cond-mat.stat-mech↗

arXiv2018

Unified thermodynamic uncertainty relations in linear response

Thermodynamic uncertainty relations (TURs) are recently established relations between the relative uncertainty of time-integrated currents and entropy production in nonequilibrium systems. For small perturbations away from equilibrium, linear response (LR) theory provides the natural framework to study generic nonequilibrium processes. Here we use LR to derive TURs in a straightforward and unified way. Our approach allows us to generalize TURs to systems without local time reversal symmetry, including, for example, ballistic transport, and periodically driven classical and quantum systems. We find that for broken time reversal, the bounds on the relative uncertainty are controlled both by dissipation and by a parameter encoding the asymmetry of the Onsager matrix. We illustrate our results with an example from mesoscopic physics. We also extend our approach beyond linear response: for Markovian dynamics it reveals a connection between the TUR and current fluctuation theorems.

cond-mat.stat-mech↗

arXiv2018

Non-equilibrium absorbing state phase transitions in discrete-time quantum dynamics

We introduce a discrete-time quantum dynamics on a two-dimensional lattice that describes the evolution of a $1+1$-dimensional spin system. The underlying quantum map is constructed such that the reduced state at each time step is separable. We show that for long times this state becomes stationary and displays a continuous phase transition in the density of excited spins. This phenomenon can be understood through a connection to the so-called Domany-Kinzel automaton, which implements a classical non-equilibrium process that features a transition to an absorbing state. Near the transition density-density correlations become long-ranged, but interestingly the same is the case for quantum correlations despite the separability of the stationary state. We quantify quantum correlations through the local quantum uncertainty and show that in some cases they may be determined experimentally solely by measuring expectation values of classical observables. This work is inspired by recent experimental progress in the realization of Rydberg lattice quantum simulators, which - in a rather natural way - permit the realization of conditional quantum gates underlying the discrete-time dynamics discussed here.

quant-ph↗

arXiv2017

Metastable decoherence-free subspaces and electromagnetically induced transparency in interacting many-body systems

We investigate the dynamics of a generic interacting many-body system under conditions of electromagnetically induced transparency (EIT). This problem is of current relevance due to its connection to non-linear optical media realized by Rydberg atoms. In an interacting system the structure of the dynamics and the approach to the stationary state becomes far more complex than in the case of conventional EIT. In particular, we discuss the emergence of a metastable decoherence free subspace, whose dimension for a single Rydberg excitation grows linearly in the number of atoms. On approach to stationarity this leads to a slow dynamics which renders the typical assumption of fast relaxation invalid. We derive analytically the effective non-equilibrium dynamics in the decoherence free subspace which features coherent and dissipative two-body interactions. We discuss the use of this scenario for the preparation of collective entangled dark states and the realization of general unitary dynamics within the spin-wave subspace.

cond-mat.quant-gas↗

arXiv2016

Metastability in an open quantum Ising model

We apply a recently developed theory for metastability in open quantum systems to a one-dimensional dissipative quantum Ising model. Earlier results suggest this model features either a non-equilibrium phase transition or a smooth but sharp crossover, where the stationary state changes from paramagnetic to ferromagnetic, accompanied by strongly intermittent emission dynamics characteristic of first-order coexistence between dynamical phases. We show that for a range of parameters close to this transition/crossover point the dynamics of the finite system displays pronounced metastability, i.e., the system relaxes first to long-lived metastable states, before eventual relaxation to the true stationary state. From the spectral properties of the quantum master operator we characterise the low-dimensional manifold of metastable states, which are shown to be probability mixtures of two, paramagnetic and ferromagnetic, metastable phases. We also show that for long times the dynamics can be approximated by a classical stochastic dynamics between the metastable phases that is directly related to the intermittent dynamics observed in quantum trajectories and thus the dynamical phases.

cond-mat.stat-mech↗

arXiv2016

Towards a theory of metastability in open quantum dynamics

By generalising concepts from classical stochastic dynamics, we establish the basis for a theory of metastability in Markovian open quantum systems. Partial relaxation into long-lived metastable states - distinct from the asymptotic stationary state - is a manifestation of a separation of timescales due to a splitting in the spectrum of the generator of the dynamics. We show here how to exploit this spectral structure to obtain a low dimensional approximation to the dynamics in terms of motion in a manifold of metastable states constructed from the low-lying eigenmatrices of the generator. We argue that the metastable manifold is in general composed of disjoint states, noiseless subsystems and decoherence-free subspaces.

cond-mat.stat-mech↗