We study the emergence of complexity in finite-size quantum systems as their dynamics transition from closed and coherent evolution to interacting and effectively open behavior. Using a state-based geometric framework, we represent mixed quantum states as probability measures on complex projective Hilbert space. This representation allows us to track how interactions reshape the underlying pure-state geometry. We introduce two complementary diagnostics: a distinguishability measure, based on the Wasserstein distance between probability-measure representations of mixed states, that quantifies sensitivity to initial states, and a state-space coverage index that measures long-time exploration of the subsystem state space. These diagnostics provide a geometric perspective on the emergence and evolution of quantum dynamical complexity. When applied to the quantum kicked top, both diagnostics generally increase with interaction strength. Their dependence on environment size is structured by parity symmetry, with integer-spin systems often exhibiting greater sensitivity and state-space coverage than half-integer-spin systems. These results highlight finite-size quantum effects and provide a geometric approach to quantifying dynamical complexity deep in the quantum regime
Quantum-state complexity diagnostics provide valuable insight into many-body dynamics, information scrambling, and quantum computation. Here, we investigate the real-time dynamics of quantum complexity in $1+1$-dimensional Abelian U(1) and non-Abelian SU(2) lattice gauge theories (LGTs), focusing on the disorder-free localization (DFL) regime. Using stabilizer R\'enyi entropy, participation R\'enyi entropy, and fermionic non-Gaussianity as measures of complexity, we observe, for both theories, two main behaviors as a function of the gauge coupling: at intermediate values, a power-law relaxation towards saturation, consistent with observations in many-body localization, and, at sufficiently large values, an ultraslow double-logarithmic growth, which we substantiate with a configuration-space bound verified by exact counting. Our results not only provide deeper insight into the dynamics of DFL but also highlight the role of gauge invariance in constraining quantum resources and are relevant to recent quantum simulations of LGTs.
D. S. Bhakuni, Giovanni Cataldi, Jad C. Halimeh et al.· 2 citations
Quantum resource theories characterize distinct forms of nonclassicality in many-body quantum states, raising the question of whether these resources evolve independently under generic ergodic dynamics. Considering diagnostics quadratic in the state, we show that the dynamics of different resource measures become mutually interdependent and are governed by a few common degrees of freedom. For Haar-random circuits, the purity together with a single resource witness suffices to reconstruct the remaining resource measures, as we demonstrate for coherence, various asymmetries, and number entropies. The same relations hold, to a good approximation, under chaotic Floquet and continuous-time Hamiltonian dynamics, establishing that this dynamical resource equivalence extends beyond random circuits. We further derive an exact coherence--imaginarity relation, remarkably accurate also beyond Haar-random circuits. Our results reveal an emergent simplification of many-body dynamics, in which sufficiently strong scrambling reduces seemingly distinct quantum resources to a few common dynamical degrees of freedom.
Sreemayee Aditya, X. Turkeshi, P. Sierant· 1 citation
Quantum complexity has emerged as a natural probe of chaos, thermalization, and the black hole interior on timescales long after local observables have equilibrated. However, its time evolution has been studied almost exclusively in subsystems confined to a single connected region. We show, using complementary tools from holography and random quantum circuits, that noncontiguous subsystems composed of multiple disjoint regions give rise to qualitatively new physics compared to the contiguous case. First, at finite temperature, a subsystem occupying less than half of the total system can carry high complexity at late times, even as the complexity of its larger complement remains low. This inversion of the usual hierarchy is intrinsically thermal: it vanishes in the infinite-temperature limit, which is the regime modeled by random quantum circuits. Second, if a subsystem's complexity equilibrates at an early time, then fragmenting it into $m$ disjoint components can further reduce this timescale by a factor of $m$, a phenomenon we exhibit in both holography and random quantum circuits. These results not only sharpen the correspondence between geometric and computational notions of complexity, but also motivate the search for novel complexity phenomena in quantum dynamics.
Yale Fan, Nicholas Hunter-Jones, A. Karch et al.· 0 citations
Quantum Fisher Information (QFI) is a powerful spectroscopic tool to witness many-body quantum entanglement in solid state materials, but it is not always obvious how to relate it to other characteristics of condensed matter systems. In this study we elaborate on the meaning and interpretation of QFI in condensed matter by examining simple theoretical spin systems. We use finite sized spin systems to illustrate that QFI quantifies the momentum- dependent degree of quantum entanglement (that is the entanglement depth at a given wave vector) within a wave function. We subsequently use semiclassical frustrated spin models to show that, in the context of linear spin wave theory (LSWT), QFI quantifies the momentum-dependent degree of magnon squeezing in the ground state. In antiferromagnets with a zero-energy Goldstone mode, LSWT breaks down and QFI (and entanglement depth) diverges at the magnetic ordering wave vector. We also show examples of emergent quantum phases in frustrated spin systems that do not appear in classical phase diagrams. When these emergent phases are approached, QFI diverges across multiple wave vectors in momentum space. Taken together, QFI is not only helpful as a lower bound for entanglement depth, but serves as a momentum-resolved probe of entanglement that offers a novel perspective on quantum critical phenomena.
W. Simeth, P. Laurell, Allen O. Scheie· 1 citation
The quantum first-passage problem involves stochastic trajectories conditioned on measurement outcomes. The timing statistics of such trajectories remain largely unexplored in open quantum systems. Here, we investigate the first-passage time to an energy threshold for a ubiquitous model: a harmonic oscillator driven by classical additive noise. We find that projective measurements and energy quantization lead to substantial differences between the quantum and classical first-passage-time distributions at low thresholds, while these differences gradually diminish as the threshold energy increases. We treat the problem using both ensemble-averaged conditioned density-matrix dynamics and trajectory-resolved stochastic pure-state dynamics. The two descriptions yield indistinguishable timing statistics. Quantization effects appear in the ensemble-level phase-space distributions of the surviving states and vanish at larger threshold energies. Individual trajectories reveal emergent quantum signatures from the repeated measurements, such as persistent Wigner negativity. Our results provide a framework for using first-passage processes to create measurement-induced nonclassical resource states and to study the quantum-classical crossover of monitored systems.
Joseph M. Ryan, Simon Gorbaty, S. Teitsworth et al.· 0 citations
We find that the measurement-induced phase transition generated by deterministic global measurements, previously observed in the integrable transverse-field Ising model (TFIM), persists in non-integrable variants of the same. To address this question, we consider the TFIM with longitudinal field and the axial next-nearest-neighbor Ising (ANNNI) model. We show that both the survival probability and the bipartite entanglement entropy consistently capture a transition between area-law and volume-law entangled phases for two distinct initial states: a product state with all spins polarized along the transverse direction and a Greenberger-Horne-Zeilinger (GHZ) state. Finite-size scaling reveals a pronounced initial state dependence: for the polarized product state, the transition point follows an inverse-square-root scaling with system size in both non-integrable models, consistent with the integrable TFIM, whereas for the GHZ initial state, it deviates from this scaling and approaches zero considerably more slowly in the non-integrable models than in the integrable TFIM. These results establish the robustness of measurement-induced transitions under deterministic measurements against integrability breaking while highlighting the crucial role of the initial state in governing their scaling behavior.
Paranjoy Chaki, P. Nandi, S. Dasgupta et al.· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
