arXiv:2305.19326 · Quantum

Quantum Chaos and Coherence: Random Parametric Quantum Channels

Apollonas S. Matsoukas-Roubeas, Tomaž Prosen, Adolfo del Campo

Published Aug 27, 2024• 13 citations

Abstract

The survival probability of an initial Coherent Gibbs State (CGS) is a natural extension of the Spectral Form Factor (SFF) to open quantum systems. To quantify the interplay between quantum chaos and decoherence away from the semi-classical limit, we investigate the relation of this generalized SFF with the corresponding l1 -norm of coherence. As a working example, we introduce Parametric Quantum Channels (PQC), a discrete-time model of unitary evolution mixed with the effects of measurements or transient interactions with an environment. The Energy Dephasing (ED) dynamics arises as a specific case in the Markovian limit. We demonstrate our results in a series of random matrix models.

DOI: 10.22331/q-2024-08-27-1446

Related papers

Quantum coherence as a signature of chaos

Namit Anand, Georgios Styliaris, Meenu Kumari +1 more

We establish a rigorous connection between quantum coherence and quantum chaos by employing coherence measures originating from the resource theory framework as a diagnostic tool for quantum chaos.We quantify this connection at two different levels: quantum states and quantum channels.At the level of states, we show how several well-studied quantifiers of chaos are, in fact, quantum coherence measures in disguise (or closely related to them).We further this connection for all quantum coherence measures by using tools from majorization theory.Then we numerically study the coherence of chaotic-versus-integrable eigenstates and find excellent agreement with random matrix theory in the bulk of the spectrum.At the level of channels, we show that the coherence-generating power (CGP)-a measure of how much coherence a dynamical process generates on average-emerges as a subpart of the out-of-time-ordered correlator (OTOC), a measure of information scrambling in many-body systems.Via numerical simulations of the (nonintegrable) transverse-field Ising model, we show that the OTOC and CGP capture quantum recurrences in quantitatively the same way.Moreover, using random matrix theory, we analytically characterize the OTOC-CGP connection for the Haar and Gaussian ensembles.In closing, we remark on how our coherence-based signatures of chaos relate to other diagnostics, namely, the Loschmidt echo, OTOC, and the Spectral Form Factor.

arXiv:2009.02760Physical Review ResearchJun 17, 202149 citations

Tailoring Quantum Chaos With Continuous Quantum Measurements

Preethi Gopalakrishnan, András Grabarits, Adolfo del Campo

We investigate the role of quantum monitoring in the dynamical manifestations of Hamiltonian quantum chaos. Specifically, we analyze the generalized spectral form factor, defined as the survival probability of a coherent Gibbs state under continuous energy measurements. We show that quantum monitoring can tailor the signatures of quantum chaos in the dynamics, such as the extension of the ramp in the spectral form factor, by varying the measurement strength and detection efficiency. In particular, a typical quantum trajectory obtained by monitoring with unit efficiency exhibits enhanced quantum chaos relative to the average dynamics and to unitary evolution without measurements. Our results hold for systems across symmetry classes and for other diagnostics of quantum chaos, such as out-of-time-order correlators and Liouvillian spectral statistics.

quant-pharXiv:2602.02663Feb 4, 20260 citations

Boundary chaos: Spectral form factor

Felix Fritzsch, Tomaž Prosen

Random matrix spectral correlations is a defining feature of quantum chaos. Here, we study such correlations in a minimal model of chaotic many-body quantum dynamics where interactions are confined to the system’s boundary, dubbed , in terms of the spectral form factor and its fluctuations. We exactly calculate the latter in the limit of large local Hilbert space dimension q q for different classes of random boundary interactions and find it to coincide with random matrix theory, possibly after a non-zero Thouless time. The latter effect is due to a drastic enhancement of the spectral form factor, when integer time and system size fulfill a resonance condition. We compare our semiclassical (large q q ) results with numerics at small local Hilbert space dimension ( q=2,3 q = 2 , 3 ) and observe qualitatively similar features as in the semiclassical regime.

arXiv:2312.12452SciPost PhysicsNov 22, 20242 citations

Proposal for many-body quantum chaos detection

Adway Kumar Das, Cameron Cianci, Delmar G. A. Cabral +8 more

In this work, the term “quantum chaos” refers to spectral correlations similar to those found in the random matrix theory. Quantum chaos can be diagnosed through the analysis of level statistics using, e.g., the spectral form factor, which detects both short- and long-range level correlations. The spectral form factor corresponds to the Fourier transform of the two-point spectral correlation function and exhibits a typical slope-dip-ramp-plateau structure (aka correlation hole) when the system is chaotic. We discuss how this structure could be detected through the quench dynamics of two physical quantities accessible to experimental many-body quantum systems: the survival probability and the spin autocorrelation function. The survival probability is equivalent to the spectral form factor with an additional filter. When the system is small, the dip of the correlation hole reaches sufficiently large values at times which are short enough to be detected with current experimental platforms. As the system is pushed away from chaos, the correlation hole disappears, signaling integrability or localization. We also provide a relatively shallow circuit with which the correlation hole could be detected with commercially available quantum computers.

arXiv:2401.01401Physical Review ResearchFeb 19, 202522 citations

Universal spectral correlations in interacting chaotic few-body quantum systems

Felix Fritzsch, Maximilian F. I. Kieler

The emergence of random matrix spectral correlations in interacting quantum systems is a defining feature of quantum chaos. We study such correlations in terms of the spectral form factor in interacting chaotic few- and many-body systems, modeled by suitable random-matrix ensembles, and obtain exact results for large Hilbert space dimensions. The transition of the spectral form factor from the non-interacting to the strongly interacting case can be described as a simple combination of these two limiting cases, which we confirm by extensive numerical studies in few-body systems. This transition is universally governed by a single scaling parameter. Moreover, our approach accurately captures spectral correlations in actual physical system, which we demonstrate for coupled kicked rotors.

arXiv:2302.08983Feb 17, 20230 citations

Universal spectral correlations in interacting chaotic few-body quantum systems

Felix Fritzsch, Maximilian F. I. Kieler

The emergence of random matrix spectral correlations in interacting quantum systems is a defining feature of quantum chaos. We study such correlations in terms of the spectral form factor and its moments in interacting chaotic few- and many-body systems, modeled by suitable random-matrix ensembles. We obtain the spectral form factor exactly for large Hilbert space dimension. Extrapolating those results to finite Hilbert space dimension we find a universal transition from the non-interacting to the strongly interacting case, which can be described as a simple combination of these two limits. This transition is governed by a single scaling parameter. In the bipartite case we derive similar results also for all moments of the spectral form factor. We confirm our results by extensive numerical studies and demonstrate that they apply to more realistic systems given by a pair of quantized kicked rotors as well. Ultimately we complement our analysis by a perturbative approach covering the small coupling regime.

arXiv:2302.09955Feb 20, 20230 citations