Probing a quantum system disrupts its state in a phenomenon known as backaction. In this work we investigate the conditions for this disruption to result in a phase transition in the information dynamics of a monitored system. We introduce a framework that captures a wide range of experiments encompassing probes comprised of projective measurements and probes which more generally transfer quantum information from the system to a quantum computer. The latter case is relevant to the recently introduced quantum-enhanced experiments in which quantum postprocessing is performed on a quantum computer and which can offer an exponential sampling advantage over projective measurements and classical postprocessing. Our framework explicitly considers the effects of an environment using a model of unitary evolution which couples the system, apparatus, and environment. Information dynamics is investigated using the R\'enyi and von Neumann entropies of the evolving state, and we construct a replica theory for studying these quantities. We identify the possible replica symmetries an experiment can possess and discuss the meaning of their spontaneous symmetry breaking. In particular, we identify a minimum subgroup whose spontaneous symmetry breaking results in an entanglement transition. This symmetry is only possible when the information in the apparatus is as informative about the dynamics of the system as the information transferred to the environment. We call this requirement the information exchange symmetry and quantify it by a relationship between the entropies. We then introduce a generalized notion of spontaneous symmetry breaking such that the entanglement transition can be understood as the spontaneous breaking of the information exchange symmetry and without referring to the replica theory. Information exchange symmetry breaking is then shown to generalize the phenomenology of the measurement-induced phase transition (MIPT). We apply this theory to a quantum-enhanced experiment probing the unitary dynamics of a Haar brickwork quantum circuit, and we determine that the universality class of the critical point is distinct from that for the MIPT. This notion of information exchange symmetry breaking generalizes the MIPT and provides a framework for understanding the dynamics of quantum information in quantum-enhanced experiments.
Probing a quantum system disrupts its state in a phenomenon known as backaction. In this work we investigate the conditions for this disruption to result in a phase transition in the information dynamics of a monitored system. We introduce a framework that captures a wide range of experiments encompassing probes comprised of projective measurements and probes which more generally transfer quantum information from the system to a quantum computer. The latter case is relevant to the recently introduced quantum-enhanced experiments in which quantum postprocessing is performed on a quantum computer and which can offer an exponential sampling advantage over projective measurements and classical postprocessing. Our framework explicitly considers the effects of an environment using a model of unitary evolution which couples the system, apparatus, and environment. Information dynamics is investigated using the R'enyi and von Neumann entropies of the evolving state, and we construct a replica theory for studying these quantities. We identify the possible replica symmetries an experiment can possess and discuss the meaning of their spontaneous symmetry breaking. In particular, we identify a minimum subgroup whose spontaneous symmetry breaking results in an entanglement transition. This symmetry is only possible when the information in the apparatus is as informative about the dynamics of the system as the information transferred to the environment. We call this requirement the information exchange symmetry and quantify it by a relationship between the entropies. We then introduce a generalized notion of spontaneous symmetry breaking such that the entanglement transition can be understood as the spontaneous breaking of the information exchange symmetry and without referring to the replica theory. Information exchange symmetry breaking is then shown to generalize the phenomenology of the measurement-induced phase transition (MIPT). We apply this theory to a quantum-enhanced experiment probing the unitary dynamics of a Haar brickwork quantum circuit, and we determine that the universality class of the critical point is distinct from that for the MIPT. This notion of information exchange symmetry breaking generalizes the MIPT and provides a framework for understanding the dynamics of quantum information in quantum-enhanced experiments.
We study the critical properties of random quantum circuits with a U(1) symmetry subject to local projective measurements that explicitly break this symmetry. We find that, at the measurement-induced phase transition, symmetry-breaking measurements act as a relevant perturbation at large scales, leading to the same universal critical properties as the corresponding monitored random circuit with non-symmetric unitary dynamics. In particular, we consider monitored U(1)-symmetric Haar-random circuits in the limit of large local Hilbert-space dimension, where the trajectory-averaged entanglement entropy can be exactly obtained in terms of a classical statistical mechanics model. In this model, the charge associated with the conservation law follows a symmetric simple exclusion process, in which symmetry-breaking measurements correspond to disordered defects that create and destroy charges. We prove that the charge correlation length remains finite for any measurement rate, ruling out a charge-sharpening transition, in contrast to the case of symmetry-preserving measurements. We further support our predictions at finite local Hilbert-space dimension through numerical finite-size scaling analyses of the entanglement transition in monitored U(1)-symmetric Haar and stabilizer random circuits.
We study the critical properties of random quantum circuits with a U(1) symmetry subject to local projective measurements that explicitly break this symmetry. We find that, at the measurement-induced phase transition, symmetry-breaking measurements act as a relevant perturbation at large scales, leading to the same universal critical properties as the corresponding monitored random circuit with non-symmetric unitary dynamics. In particular, we consider monitored U(1)-symmetric Haar-random circuits in the limit of large local Hilbert-space dimension, where the trajectory-averaged entanglement entropy can be exactly obtained in terms of a classical statistical mechanics model. In this model, the charge associated with the conservation law follows a symmetric simple exclusion process, in which symmetry-breaking measurements correspond to disordered defects that create and destroy charges. We prove that the charge correlation length remains finite for any measurement rate, ruling out a charge-sharpening transition, in contrast to the case of symmetry-preserving measurements. We further support our predictions at finite local Hilbert-space dimension through numerical finite-size scaling analyses of the entanglement transition in monitored U(1)-symmetric Haar and stabilizer random circuits.
This is a conference proceeding in the framework of workshop “OpenQMBP2023” * at Institute Pascal (Orsay, France) and associated with the lecture given by Prof. Ehud Altman. We provide a comprehensive analysis of recent results in the context of measurement-induced phase transitions (MIPT) in quantum systems, with a particular focus on hybrid quantum circuits as a model system in one-dimension. Recent resutls, demonstrate how varying the rate of projective measurements can induce phase transitions, resulting in abrupt changes in the properties of the entanglement. The interplay between unitary evolution and measurement processes can be investigated, through mappings to classical statistical models and the application of replica field theory techniques. Starting from a low-entangled state, there can be three regimes characterized by different dynamics of bipartite entanglement entropies for a portion of the system: high-rate measurements leading to rapid entanglement saturation (area law), low-rate measurements allowing linear entanglement growth (up to volume law), and a critical rate at which entanglement grows logarithmically. Finally, we present results on the non-local effects of local measurements by ex-amining the field theory of critical ground states in Tomonaga-Luttinger liquids.
Out-of-equilibrium quantum many-body systems stand at the forefront of modern theoretical physics, addressing fundamental questions on thermalization, transport, and universal phenomena. These fields, already well established in condensed matter, statistical physics, quantum optics, and quantum information theory, are progressively gaining even greater relevance with the rapid development of quantum technologies and simulation, which inherently operate in dynamical regimes. In recent years, the traditional paradigm of unitary quantum evolution has been expanded to include measurements, opening new directions in out-of-equilibrium physics. At the core of these advances lie measurement-induced phase transitions (MIPTs), which have emerged as a new class of dynamical critical phenomena characterizing the general behavior of monitored quantum dynamics. When external monitoring intertwines with unitary evolution, many-body quantum correlations change their structure, giving rise to distinct entanglement phases of matter. This discovery has sparked enormous interest in MIPTs, leading to significant advances in open quantum systems, entanglement theory, and more broadly quantum complexity. Despite much progress, a full understanding of monitored many-body dynamics is far from complete, leaving several open questions on the nature of MIPTs, their experimental observability, and the possibilities offered by measurements to enhance control over synthetic quantum matter. These issues persist due to the intrinsic complexity of the problem and the lack of efficient tools to study it, mainly caused by the stochastic character of monitored evolution. This thesis addresses these challenges by expanding the investigation of measurement-induced phenomena in new settings and introducing innovative probes of entanglement and many-body quantum complexity for MIPTs. A core question we investigate is the role of symmetries, non-ergodicity, and especially integrability in measurement-induced criticality, which dramatically affect the non-equilibrium phases. We further explore how these phenomena extend beyond bipartite quantum correlations to multipartite entanglement and quantum non-stabilizerness, highlighting the non-trivial interplay between measurements and complexity notions rooted in quantum information theory. Finally, we focus on the compelling problem of decoherence, modeling how noise spoils entanglement structures. These findings, supported by advanced numerical simulations and theoretical analysis, deepen the current understanding of entanglement, complexity, and integrability in monitored quantum many-body systems, offering new perspectives on their rich behavior. In parallel, we address the experimental problem of dissipation in MIPTs, which is of key relevance for practical implementations. We anticipate the present investigation to foster future research on the nature of monitored dynamical critical phenomena and, more broadly, the applications of measurements in quantum state evolution.
FINDING: Measurement-induced phase transitions (MIPT) in quantum systems reveal a sharp entanglement phase boundary driven by the competition between unitary evolution and projective measurements, with critical points often characterized by universal exponents and effective central charges. | MATH: The MIPT is typically studied via the entanglement entropy S=−Tr(ρAlnρA) scaling as S∼6clnL at criticality (for 1+1D conformal field theory), where c is the effective central charge. The critical measurement rate pc separates volume-law (S∝L) from area-law (S∝const) phases. For Clifford circuits, the transition is in the percolation universality class with c=0 (or c=ln2 for Haar random circuits). The "1/(2π)" appears in the context of the quantum Zeno effect: for a system measured at rate γ, the effective Hamiltonian is \(H_{\text{eff}} = H - i \frac{\gamma}{2} \sum_m |m\rangle\langle Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Scrambling dynamics induced by random unitary gates can protect information from low-rate measurements, which underpins the phenomenon known as the measurement-induced phase transition (MIPT). However, typical decoherence noise disrupts the volume-law phase, complicating the observation of the MIPT on noisy intermediate-scale quantum devices. Here, we demonstrate that incorporating quantum-enhanced operations can effectively protect the MIPT from environmental noise, thereby enabling its detection in experiment. The transition is characterized by conditional entanglement entropy, which is associated with a statistical mechanics model wherein noise and quantum-enhanced operations act as competing external random fields. When the net external field is zero, a ferromagnetic-paramagnetic phase transition is expected, resulting in the MIPT. This zero-field condition also ensures an average apparatus-environment symmetry, making conditional entanglement entropy a valid probe of entanglement and establishing the transition as a genuine entanglement phase transition. Additionally, we provide numerical results that demonstrate the MIPT in a (2+1)-dimensional quantum circuit under dephasing noise. We also propose a method to estimate the noise rate, enabling the zero-field condition to be achieved experimentally and ensuring the feasibility of our protocol. Our result serves as a concrete example of the power of quantum enhancement in combating noise.