We demonstrate a surprising connection between pure steady-state entanglement and relaxation time scales in an extremely broad class of Markovian open systems, where two (possibly many-body) systems, A and B , interact locally with a common dissipative environment. This setup also encompasses a broad class of adaptive quantum dynamics based on continuous measurement and feedback. As steady-state entanglement increases, there is generically an emergent strong symmetry that leads to a dynamical slow-down. Using this, we can prove rigorous bounds on relaxation times set by steady-state entanglement. We also find that this time must necessarily diverge for maximal entanglement. To test our bound, we consider the dynamics of a random ensemble of local Lindbladians that support pure steady states, finding that the bound does an excellent job of predicting how the dissipative gap varies with the amount of entanglement. Our work provides general insights into how dynamics and entanglement are connected in open systems and has specific relevance to quantum reservoir engineering. Published by the American Physical Society 2024
We demonstrate a surprising connection between pure steady-state entanglement and relaxation time scales in an extremely broad class of Markovian open systems, where two (possibly many-body) systems, A and B , interact locally with a common dissipative environment. This setup also encompasses a broad class of adaptive quantum dynamics based on continuous measurement and feedback. As steady-state entanglement increases, there is generically an emergent strong symmetry that leads to a dynamical slow-down. Using this, we can prove rigorous bounds on relaxation times set by steady-state entanglement. We also find that this time must necessarily diverge for maximal entanglement. To test our bound, we consider the dynamics of a random ensemble of local Lindbladians that support pure steady states, finding that the bound does an excellent job of predicting how the dissipative gap varies with the amount of entanglement. Our work provides general insights into how dynamics and entanglement are connected in open systems and has specific relevance to quantum reservoir engineering. Published by the American Physical Society 2024
The generation of entanglement in mixed states is relevant to quantum systems coupled to an environment. The dissipative and mixing properties of the environment are unavoidable in physical platforms for quantum simulation and information processing, where entanglement can be a vital resource. In this work, we explore entanglement and heterogeneity in random Lindbladian dynamics describing open quantum systems. We propose a model of a one-dimensional chain of noninteracting, spinless fermions coupled to a local ensemble of baths. The jump operator mediating the interaction with the bath linked to each site has a power-law tail with an exponent p . We show that the system undergoes volume-to-area law entanglement phase transition in the mixed steady state by tuning p which remains stable in the presence of coherent hopping. Unlike the entanglement transition in the pure-state quantum trajectories of open systems, this transition is exhibited by the averaged steady-state density matrix of the Lindbladian. The steady state in the area-law phase is characterized by a spatial heterogeneity in local population imbalance, while the jump operators exhibit a constant participation ratio of the sites they affect. Our work provides a theoretical description of an entanglement transition realized in long-ranged open quantum systems and provides an avenue to stabilize quantum correlations in mixed states. Published by the American Physical Society 2024
Recent studies have revealed a deep connection between the asymmetry of cross-correlations and thermodynamic quantities in the short-time limit. In this study, we address the finite-time domain of the asymmetry for both open classical and quantum systems. Focusing on Markovian dynamics, we show that the asymmetry observed in finite-time cross-correlations is upper bounded by dissipation. We prove that, for classical systems in a steady state with arbitrary operational durations, the asymmetry exhibits, at most, linear growth over time, with the growth speed determined by the rates of entropy production and dynamical activity. In the long-time regime, the asymmetry exhibits exponential decay, with the decay rate determined by the spectral gap of the transition matrix. Remarkably, for quantum cases, quantum coherence is equally important as dissipation in constraining the asymmetry of correlations. We demonstrate an example where only quantum coherence bounds the asymmetry while the entropy production rate vanishes. Furthermore, we generalize the short-time bounds on correlation asymmetry, as reported by Shiraishi [] and Ohga [], to encompass finite-time scenarios. These findings offer insights into the thermodynamic aspects of correlation asymmetry. Published by the American Physical Society 2024
Open quantum systems undergo decoherence, which is responsible for the transition from quantum to classical behavior. The time scale in which decoherence takes place can be analyzed using upper limits to its rate. We examine the dynamics of open chaotic quantum systems governed by random Lindblad operators sourced from Gaussian and Ginibre ensembles with Wigner-Dyson symmetry classes. In these systems, the ensemble-averaged purity decays monotonically as a function of time. This decay is governed by the decoherence rate, which is upper-bounded by the dimension of their Hilbert space and is independent of the ensemble symmetry. These findings hold upon mixing different ensembles, indicating the universal character of the decoherence rate limit. Moreover, our findings reveal that open chaotic quantum systems governed by random Lindbladians tend to exhibit the most rapid decoherence, regardless of the initial state. This phenomenon is associated with the concentration of the decoherence rate near its upper bound. Our work identifies primary features of decoherence in dissipative quantum chaos, with applications ranging from quantum foundations to high-energy physics and quantum technologies. Published by the American Physical Society 2024
A wide variety of dissipative state preparation schemes suffer from a basic time-entanglement tradeoff: the more entangled the steady state, the slower the relaxation to the steady state. Here, we show how a minimal kind of adaptive dynamics can be used to completely circumvent this tradeoff, and allow the dissipative stabilization of maximally entangled states with a finite timescale. Our approach takes inspiration from simple fermionic stabilization schemes, which surprisingly are immune to entanglement-induced slowdown. We describe schemes for accelerated stabilization of many-body entangled qubit states (including spin squeezed states), both in the form of discretized Floquet circuits, as well as continuous time dissipative dynamics. Our ideas are compatible with a number of experimental platforms.
Understanding the fate of many-body quantum physics in the presence of noise is of both practical and fundamental interest. Practically, all quantum systems (especially near-term experiments) are interacting with their environment, and so understanding the role that noise plays is crucial to making predictions of observations. Fundamentally, one can find novel physical phenomena in open systems that exists only out of equilibrium. This motivates trying to get a basic understanding of mixed state phases of matter. This dissertation will be in two parts, linked by the common theme of understanding the dynamics and steady states of open, many-body quantum systems. We will first ask about dissipative state preparation, or thinking about how one can use openness in a quantum system to engineer interesting quantum states. We will present a number of exact solutions for spins, free bosons, and free fermions that have unique properties in the steady state, be they highly entangled or topological in nature. Then, we will discuss their dynamics, and present fundamental limits on the time it takes to prepare highly entangled states under local Markovian channels, and also ways that one can use additional ingredients to evade these bounds. The second part will focus on a novel technique to simulate the dynamics of open spin-1/2 systems whose coupling to the environment will formally make them interacting. This technique relies on encoding the many-body density matrix into a stochastic covariance matrix of the Jordan-Wigner fermions which we show can be sampled from efficiently. We use this technique to uncover rich phenomena outlined in a number of many-body systems, as well as provide certain situations in which the stochastic observables can be analytically re-averaged to get closed form solutions for the entire interacting system.
We show that steady-state entanglement in open quantum systems is controlled by the phase reference of a phase-sensitive reservoir. Using a covariance-matrix approach for Gaussian-preserving dynamics, we demonstrate that purely local, phase-sensitive dissipation can generate entanglement when combined with coherent coupling. The steady state exhibits a finite entangled region with an optimal squeezing strength that maximizes both the magnitude and thermal robustness of entanglement. We find that coherent coupling does not enhance entanglement monotonically, but instead regulates the conversion of local squeezing into nonlocal correlations. Importantly, the coupling dependence is controlled by the phase reference of the squeezed reservoir: phase-locked (rotating-frame) and laboratory-frame implementations yield qualitatively distinct steady states and entanglement structure. These results establish phase-sensitive reservoir engineering as a controllable route to steady-state entanglement in continuous-variable systems. Steady-state entanglement in phase-sensitive open systems depends explicitly on the reservoir phase reference and is not invariant under changes of that reference.}