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arXiv:2403.19364 · Physical Review Letters

Quantum Liang Information Flow Probe of Causality across Critical Points

Roopayan Ghosh, Bin Yi, Sougato Bose

Published Apr 18, 2025• 2 citations
arXivHTMLPDF

Abstract

Investigating causation in the quantum domain is crucial. Despite numerous studies of correlations in quantum many-body systems, causation, which is very distinct from correlations, has hardly been studied. We address this by demonstrating the efficacy of the newly established causation measure, quantum Liang information flow, in quantifying causality across phase diagrams of quantum many-body systems. We focus on quantum criticality, which are highly nonclassical points. We extract causation behavior across a spectrum-wide critical point and a ground state second-order phase transition in both integrable and nonintegrable systems. Across criticality, each case exhibits distinct hallmarks, different from correlation measures. We also deduce that quantum causation qualitatively follows the quasiparticle picture of information propagation in integrable systems but exhibits enhanced quantum nonlocality near criticality. At times significantly larger than the spatial separation, it extracts additional features from the equilibrium wave function, leading to a peak just before the critical point for near boundary sites.

DOI
10.1103/physrevlett.134.150202

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Investigating causation in the quantum domain is crucial. Despite numerous studies of correlations in quantum many-body systems, causation, which is very distinct from correlations, has hardly been studied. We address this by demonstrating the efficacy of the newly established causation measure, quantum Liang information flow, in quantifying causality across phase diagrams of quantum many-body systems. We focus on quantum criticality, which are highly nonclassical points. We extract causation behavior across a spectrum-wide critical point and a ground state second-order phase transition in both integrable and nonintegrable systems. Across criticality, each case exhibits distinct hallmarks, different from correlation measures. We also deduce that quantum causation qualitatively follows the quasiparticle picture of information propagation in integrable systems but exhibits enhanced quantum nonlocality near criticality. At times significantly larger than the spatial separation, it extracts additional features from the equilibrium wave function, leading to a peak just before the critical point for near boundary sites.
Liang information flow is widely used in classical systems and network theory for causality quantification and has been applied widely, for example, to finance, neuroscience, and climate studies. The key part of the theory is to freeze a node of a network to ascertain its causal influence on other nodes. Such a theory is yet to be applied to quantum network dynamics. Here, we generalize the Liang information flow to the quantum domain with respect to von Neumann entropy and exemplify its usage by applying it to a variety of small quantum networks.
We systematically compare Quantum Liang Information Flow (QLIF) a recently proposed causal information measure with the out-of-time-order correlator (OTOC) as diagnostics of quantum chaos in the one-dimensional mixed-field Ising chain. Using exact diagonalization and MPS-TEBD, we show that the early-time power-law growth and wavefront propagation velocity of QLIF are identical for integrable and chaotic parameters, being controlled solely by the local Hamiltonian structure. The QLIF signal strength depends sensitively on the initial state, spanning four orders of magnitude across product states, ground state eigenstate evolution, and quantum quench protocols. We identify the time-integrated QLIF as a late-time chaos diagnostic: it grows linearly (monotonically) in chaotic systems, reflecting irreversible thermalization, while saturating or oscillating in integrable systems, reflecting reversible quasiparticle dynamics. These findings establish QLIF as a complementary probe to OTOC, with distinct optimal operating regimes.
Information integration measures quantify coordination in complex systems, but conflate correlation with causation. High mutual information can arise from genuine causal influence, common inputs, or independent dynamics with shared constraints. We introduce a theoretical framework distinguishing these mechanisms through causal efficiency ρ=TE/MI\rho = \text{TE}/\text{MI}ρ=TE/MI, the fraction of correlation reflecting genuine information flow rather than self-prediction. We prove that this framework is mathematically equivalent to standard integration measures under bounded distortion, with distortion constants revealing three distinct regimes: (I) high causality where correlation accurately reflects integration, (II) heterogeneous coupling where structure matters, and (III) low causal efficiency where correlation masquerades as coordination. Applied to quantum measurement, we show that the triadic coordination capacity framework (duration, frequency, agency) provides natural context for detecting regime transitions. The formalism makes testable predictions: coordination events should exhibit ρ>0.7\rho > 0.7ρ>0.7 during genuine integration, while decoherence shows ρ<0.3\rho < 0.3ρ<0.3 despite persistent correlation. This establishes rigorous causal foundations for integration theory and characterizes when correlation-based measures succeed or systematically fail.
Based on transfer matrix theory and the multipartite nonlocality spectrum [Formula: see text], we systematically investigate ground-state nonlocal correlations across three canonical infinite, translation-invariant one-dimensional spin models, including the XXZ model, the three-body coupled Cluster–Ising model, and the Kitaev ladder model, which cover both conventional and topological Quantum Phase Transitions (QPTs). We show that the emergence of multipartite nonlocal correlations can be quantitatively determined via the leading eigenvalue criterion [Formula: see text], offering a concise and reliable indicator for diagnosing nonlocal quantum features. Further numerical comparisons reveal that the leading eigenvalue [Formula: see text] is strongly model-dependent and lacks universal applicability for identifying quantum critical behaviors across different QPT types. In contrast, the nonlocality spectral gap [Formula: see text] exhibits prominent robustness against variations in system symmetry, coupling strength, and intrinsic transition mechanisms. It characterizes quantum criticality through three distinct response modes, thereby enabling a unified description of both conventional and topological QPTs. This work establishes the nonlocality spectrum as a versatile and powerful framework for the joint characterization of multipartite nonlocality and quantum criticality in one-dimensional many-body quantum systems.
Quantum phase transitions are highly remarkable phenomena manifesting in quantum many-body systems. However, their precise identifications in equilibrium systems pose significant theoretical and experimental challenges. Thus far, dynamical detection protocols employing global quantum quenches have been proposed, wherein transitions are discerned via global nonequilibrium excitations. In this work, we demonstrate that quantum phase transitions can be detected through localized out-of-equilibrium excitations induced by local quantum quenches. While the resulting dynamics after the quench is influenced by both the local quench operation and the intrinsic dynamics of the quantum system, the effects of the former are exclusively extracted using the cutting-edge framework called quantum reservoir probing (QRP). Through the QRP, we find that the impacts of the local quenches vary across different quantum phases and are significantly suppressed by quantum fluctuations amplified near quantum critical points; consequently, phase boundaries are precisely delineated. We demonstrate that the QRP can detect quantum phase transitions in the paradigmatic integrable and nonintegrable quantum spin systems, and even topological quantum phase transitions, all within the identical framework employing local quantum quenches and single-site observables. Quantum phase transitions, traditionally examined for divergent fluctuations in space and time at equilibrium, are now revealing local, nonequilibrium signatures. Kobayashi and Motome explore nonequilibrium quantum dynamics triggered by local quantum quenches utilizing a new approach of quantum reservoir probing.
We study how the information flows in many-body dynamics governed by random quantum circuits and discover a rich set of dynamical phase transitions in this information flow.The phase-transition points and their critical exponents are established across Clifford and Haar random circuits through finite-size scaling.The flow of both classical and quantum information, measured respectively by Holevo and coherent information, shows similar dynamical phase transition behaviors.We investigate how the phase transitions depend on the initial location of the information and the final probe region, and find ubiquitous behaviors in these transitions, revealing interesting properties about the information propagation and scrambling in this quantum many-body model.Our paper underscores rich behaviors of the information flow in large systems with numerous phase transitions, thereby sheds light on the understanding of quantum many-body dynamics.