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arXiv:2507.22151 · Physical Review A

Efficient detection of localization transitions using predictability

Tiago Pernambuco, Jonas Maziero, Rafael Chaves

Published Nov 6, 2025• 1 citation
arXivHTMLPDF

Abstract

Identifying phase transition points is a fundamental challenge in condensed-matter physics, particularly for transitions driven by quantum interference effects such as Anderson and many-body localization. Recent studies have demonstrated that quantum coherence provides an effective means of detecting localization transitions, offering a practical alternative to full quantum state tomography and related approaches. Building on this idea, we investigate localization transitions through complementarity relations that connect local predictability, local coherence, and entanglement in bipartite pure states. Our results show that predictability serves as a robust and efficient marker for localization transitions. Crucially, its experimental determination requires exponentially fewer measurements than coherence or entanglement, making it a powerful tool for probing localization phase transitions.

DOI
10.1103/ss38-wgzf

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Identifying phase transition points is a fundamental challenge in condensed-matter physics, particularly for transitions driven by quantum interference effects such as Anderson and many-body localization. Recent studies have demonstrated that quantum coherence provides an effective means of detecting localization transitions, offering a practical alternative to full quantum state tomography and related approaches. Building on this idea, we investigate localization transitions through complementarity relations that connect local predictability, local coherence, and entanglement in bipartite pure states. Our results show that predictability serves as a robust and efficient marker for localization transitions. Crucially, its experimental determination requires exponentially fewer measurements than coherence or entanglement, making it a powerful tool for probing localization phase transitions.
A dynamical signature of localization in quantum systems is the absence of transport which is governed by the amount of coherence that configuration space states possess with respect to the Hamiltonian eigenbasis. To make this observation precise, we study the localization transition via quantum coherence measures arising from the resource theory of coherence. We show that the escape probability, which is known to show distinct behavior in the ergodic and localized phases, arises naturally as the average of a coherence measure. Moreover, using the theory of majorization, we argue that broad families of coherence measures can detect the uniformity of the transition matrix (between the Hamiltonian and configuration bases) and hence act as probes to localization. We provide supporting numerical evidence for Anderson and many-body localization (MBL). For infinitesimal perturbations of the Hamiltonian, the differential coherence defines an associated Riemannian metric. We show that the latter is exactly given by the dynamical conductivity, a quantity of experimental relevance which is known to have a distinctively different behavior in the ergodic and in the many-body localized phases.
Quantum coherence, a fundamental resource in quantum computing and quantum information, often competes with localization effects that affect quantum states in disordered systems. In this work, we prove exact trade-off relations between quantum coherence and a measure of localization and many-body localization, namely, the inverse participation ratio (IPR). We prove that for a pure quantum state, the l1{l}_{1}l1​ norm of quantum coherence and the relative entropy of coherence satisfy complementarity relations with IPR. For a mixed state, IPR and the l2{l}_{2}l2​ norm of quantum coherence as well as relative entropy of coherence satisfy trade-off inequalities. We further explore the applicability of these general relations between quantum coherence and measure of localization in the context of delocalization to many-body localization transition in a disordered interacting quantum many-body system and demonstrate that quantum coherence is also an ideal characterization of the delocalization to many-body localization transition. Our numerical analysis shows that though the full system loses coherence in the many-body localization phase, coherence of a subsystem can increase with the combined effect of disorder and interactions. We believe that these trade-off relations can help in better understanding of how coherence can be preserved or lost in realistic many-body quantum systems, which is vital for developing robust quantum technologies and uncovering new phases of quantum matter.
We introduce bipartite projected ensembles (BPEs) for quantum many-body wave functions, which consist of pure states supported on two local subsystems, with each state associated with the outcome of a projective measurement of the complementary subsystem in a fixed local basis. We demonstrate that the corresponding ensemble-averaged entanglements (EAEs) between two subsystems can effectively identify entanglement phases. In volume-law entangled states, EAE converges to a nonzero value with increasing distance between subsystems. For critical systems, EAE exhibits power-law decay, and it decays exponentially for area-law systems. Thus, entanglement phase transitions can be viewed as a disordered-ordered phase transition. We also apply BPE and EAE to measured random Clifford circuits to probe measurement-induced phase transitions. We show that EAE not only serves as a witness to phase transitions, but also unveils additional critical phenomena properties, including dynamical scaling and surface critical exponents. Our findings provide an alternative approach to diagnosing entanglement laws, thus enhancing the understanding of entanglement phase transitions. Moreover, given the accessibility of measuring EAE in quantum simulators, our results hold promise for impacting quantum simulations.
As strength of disorder enhances beyond a threshold value in many-body systems, a fundamental transformation happens through which the entire spectrum localizes, a phenomenon known as many-body localization. This has profound implications as it breaks down fundamental principles of statistical mechanics, such as thermalization and ergodicity. Due to the complexity of the problem, the investigation of the many-body localization transition has remained a big challenge. The experimental exploration of the transition point is even more challenging as most of the proposed quantities for studying such an effect are practically infeasible. Here, we experimentally implement a scalable protocol for detecting the many-body localization transition point, using the dynamics of an N=12N=12N=12 superconducting qubit array. We show that the sensitivity of the dynamics to random samples becomes maximum at the transition point, which leaves its fingerprints in all spatial scales. By exploiting three quantities, each with a different spatial resolution, we identify the transition point with an excellent match between simulation and experiment. In addition, one can detect the evidence of a mobility edge through slight variation of the transition point as the initial state varies. The protocol is easily scalable and can be performed across various physical platforms.
We demonstrate that the dynamics of quantum coherence serves as an effective probe for identifying dephasing, which is a distinctive signature of many-body localization (MBL). Quantum coherence can be utilized to measure both the local coherence of specific subsystems and the total coherence of the whole system in a consistent manner. Our results reveal that the local coherence of small subsystems decays over time following a power law in the MBL phase, while it reaches a stable value within the same time window in the Anderson-localized (AL) phase. In contrast, the total coherence of the whole system exhibits logarithmic growth during the MBL phase and reaches a stable value in the AL phase. Notably, this dynamic characteristic of quantum coherence remains robust even with weak interactions and displays unbounded behavior in infinite systems. Our results provide insights into understanding many-body dephasing phenomena in MBL systems and reveal a feasible method for identifying and characterizing MBL phases in experiments.
In quantum many-body systems, characterizing topological phase transitions typically requires complex many-body topological invariants, which are costly to compute and measure. Inspired by quantum reservoir computing, we propose an unsupervised quantum phase detection method based on a many-body localized evolution, enabling efficient identification of phase transitions in the extended SSH model. The evolved quantum states produce feature distributions under local measurements, which, after simple post-processing and dimensionality reduction, naturally cluster according to different Hamiltonian parameters. Numerical simulations show that the evolution combined with local measurements can significantly amplify distinctions between quantum states, providing an efficient means to detect topological phase transitions. Our approach requires neither complex measurements nor full density matrix reconstruction, making it practical and feasible for noisy intermediate-scale quantum devices.