We show that weak measurements can induce a quantum phase transition of interacting many-body systems from an ergodic thermal phase with a large entropy to a nonergodic localized phase with a small entropy, but only if the measurement strength exceeds a critical value. We demonstrate this effect for a one-dimensional quantum circuit evolving under random unitary transformations and generic positive operator-valued measurements of variable strength. As opposed to projective measurements describing a restricted class of open systems, the measuring device is modeled as a continuous Gaussian probe, capturing a large class of environments. By employing data collapse and studying the enhanced fluctuations at the transition, we obtain a consistent phase boundary in the space of the measurement strength and the measurement probability, clearly demonstrating a critical value of the measurement strength below which the system is always ergodic, irrespective of the measurement probability. These findings provide guidance for quantum engineering of many-body systems by controlling their environment.
Random quantum circuits provide a framework for probing universal dynamical phenomena in chaotic quantum many-body systems, by circumventing the microscopic details of Hamiltonian evolution. Bipartite entanglement measures can be used to characterize the dynamical phases that emerge in these systems. Typically, under random unitary evolution, bipartite entanglement entropies exhibit a linear growth, and attain steady-state values that scale extensively with the system volume. However, when local projective measurements are introduced, a suppression of steady-state bipartite entropies occurs, leading to a sub-extensive scaling with the system volume. This class of entanglement scaling transitions, from an extensive to a sub-extensive scaling regime, has sparked interest in a broader class of measurement-induced phase transitions, with a potential to further our understanding of fault-tolerance in quantum computing, and in realizing synthetic quantum phases on digital quantum simulators. In this work, we characterize entanglement scaling transitions in one-dimensional random quantum circuits composed of q-level systems, with the local Hilbert space dimension q ≥ 2. This predominantly numerical study employs generalizations of the stabilizer formalism and the Clifford group to higher-dimensional Hilbert spaces to simulate the measurement-induced transitions. We find that the nature of the entanglement scaling transition remains invariant under changes in the local Hilbert space dimension. However, the critical measurement rate inducing the transition increases with q, asymptotically approaching 1/2 in the limit q → ∞. To further explore this classical limit, we develop a minimal dynamical model that captures entanglement structures under unitary evolution. We analyze the entanglement structures in thermal stabilizer states using this model, and propose an approach for incorporating measurements within this framework.
We introduce and explore a one-dimensional ``hybrid'' quantum circuit model consisting of both unitary gates and projective measurements. While the unitary gates are drawn from a random distribution and act uniformly in the circuit, the measurements are made at random positions and times throughout the system. By varying the measurement rate we can tune between the volume law entangled phase for the random unitary circuit model (no measurements) and a ``quantum Zeno phase'' where strong measurements suppress the entanglement growth to saturate in an area law. Extensive numerical simulations of the quantum trajectories of the many-particle wave functions (exploiting Clifford circuitry to access systems up to 512 qubits) provide evidence for a stable ``weak measurement phase'' that exhibits volume-law entanglement entropy, with a coefficient decreasing with increasing measurement rate. We also present evidence for a continuous quantum dynamical phase transition between the ``weak measurement phase'' and the ``quantum Zeno phase,'' driven by a competition between the entangling tendencies of unitary evolution and the disentangling tendencies of projective measurements. Detailed steady-state and dynamic critical properties of this quantum entanglement transition are accessed.
Generic many-body systems coupled to an environment lose their quantum entanglement due to decoherence and evolve to a mixed state with only classical correlations. Here, we show that measurements can stabilize quantum entanglement within open quantum systems. Specifically, in random unitary circuits with dephasing at the boundary, we find both numerically and analytically that projective measurements performed at a small nonvanishing rate result in a steady state with an L^{1/3} power-law scaling entanglement negativity within the system. Using an analytical mapping to a statistical mechanics model of directed polymers in a random environment, we show that the power-law negativity scaling can be understood as Kardar-Parisi-Zhang fluctuations due to the random measurement locations. Further increasing the measurement rate leads to a phase transition into an area-law negativity phase, which is of the same universality as the entanglement transition in monitored random circuits without decoherence.
We utilize the concept of a measurement-induced entanglement transition to analyze the interplay and competition of processes that generate and destroy entanglement in a one-dimensional quantum spin chain evolving under a locally noisy and disordered Hamiltonian. We employ continuous measurements of variable strength to induce a transition from volume to area-law scaling of the steady-state entanglement entropy. While static background disorder systematically reduces the critical measurement strength, this critical value depends nonmonotonically on the strength of nonstatic noise. According to the extracted finite-size scaling exponents, the universality class of the transition is independent of the noise and disorder strength. We interpret the results in terms of the effect of static and nonstatic disorder on the intricate dynamics of the entanglement generation rate due to the Hamiltonian in the absence of measurement, which is fully reflected in the behavior of the critical measurement strength. Our results establish a firm connection between this entanglement growth and the steady-state behavior of the measurement-controlled systems, which therefore can serve as a tool to quantify and investigate features of transient entanglement dynamics in complex many-body systems via a steady-state phase transition.
We investigate entanglement phase transitions from volume-law to area-law entanglement in a quantum many-body state under continuous position measurement on the basis of the quantum trajectory approach. We find the signatures of the transitions as peak structures in the mutual information as a function of measurement strength, as previously reported for random unitary circuits with projective measurements. At the transition points, the entanglement entropy scales logarithmically and various physical quantities scale algebraically, implying emergent conformal criticality, for both integrable and nonintegrable one-dimensional interacting Hamiltonians; however, such transitions have been argued to be absent in noninteracting regimes in some previous studies. With the aid of
U(1) symmetry in our model, the measurement-induced criticality exhibits a spectral signature resembling a Tomonaga-Luttinger liquid theory from symmetry-resolved entanglement. These intriguing critical phenomena are unique to steady-state regimes of the conditional dynamics at the single-trajectory level and are absent in the unconditional dynamics obeying the Lindblad master equation, in which the system ends up with the featureless, infinite-temperature mixed state. We also propose a possible experimental setup to test the predicted entanglement transition based on the subsystem particle-number fluctuations. This quantity should readily be measured by the current techniques of quantum gas microscopy and is in practice easier to obtain than the entanglement entropy itself.
In this work, we numerically study the effect of weak measurement on deconfined quantum critical point(DQCP). Particularly, we consider the ground state of an one-dimensional spin
1/2 system with next-nearest-neighbour exchange interactions(
K), which shows analogues phase transition to DQCP in the thermodynamic limit. This system is in the ferromagnetic phase below the critical exchange interaction
Kc and in the valance bond solid phase above
Kc. The weak measurement is carried out by coupling a secondary ancilla system to the critical system via unitary interactions and later measuring the ancilla spins projectively. We numerically calculate entanglement entropy,correlation length, and order parameters of leading post-measurement states using uniform matrix product state representation of the quantum many-body state in the thermodynamic limit. We report asymmetric restructuring of entanglement of the post measurement states across the phase boundary under weak measurements. Especially, the trajectory
(↓↓) describing a uniform measurement outcome given the all ancilla spins initiated in the same
(↓) state, shows anomalous entanglement when increasing the strength of weak measurement. The bipartite entanglement entropy strongly increases when
K<Kc whereas it weakly decreases when
K>Kc. We argue with numerical evidences that observed asymmetry in entanglement would lead to a weak first order phase boundary in the thermodynamic limit. We also discuss important aspects in experimental observation of measurement induced effects linked to the strength of weak measurement and probability of post-measurement states.