Quantum Zeno Effect and the Many-body Entanglement Transition (1808.06134v2)

Abstract: 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 wavefunctions (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 novel 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 novel quantum entanglement transition are accessed.

• The paper demonstrates that a hybrid quantum circuit model exhibits a measurement-driven entanglement phase transition between volume-law and area-law regimes.
• The study employs extensive numerical simulations using Clifford circuits on systems with up to 512 qubits to reveal critical measurement rates and universal scaling exponents.
• The results highlight the coexistence of long-range entanglement and measurement-induced decoherence, offering new perspectives for quantum information processing and experimental design.

Quantum Zeno Effect and the Many-body Entanglement Transition: An Overview

This paper presents a paper of quantum dynamical behavior in a one-dimensional "hybrid" quantum circuit model that combines unitary dynamics and projective measurements. The model is analyzed primarily through the lens of entanglement entropy, providing insights into the interplay between coherent evolution and measurement-induced decoherence in many-body systems. The authors notably investigate the emergence of distinct entangled phases and a novel quantum phase transition driven by measurements.

Circuit Model and Methodology

The hybrid circuit model comprises unitary gates and projective measurements, both chosen from random distributions. Unitary gates are applied uniformly across the circuit, while projective measurements occur at random locations, introducing a measurement rate parameter, $p$. This setup allows the tuning between distinct phases: a volume-law entangled phase reminiscent of pure unitary dynamics and an area-law "quantum Zeno phase" where frequent measurements dominate.

Numerical simulations, predominantly utilizing Clifford circuitry, enable exploration of systems up to 512 qubits. This approach is central to the paper, providing efficient access to the long-time quantum dynamics of large systems, thereby allowing detailed investigation of both steady-state and dynamic properties of the entanglement transition.

Key Findings and Numerical Results

The paper discovers a stable "weak measurement phase" characterized by volume-law entanglement entropy that persists even in the presence of weak measurements. Here, the entanglement entropy coefficient decreases with an increasing measurement rate while retaining volume-law scaling.

Crucially, the research identifies a continuous quantum entanglement phase transition at a critical measurement rate, $p_c$, demarcating the weak measurement phase from the "quantum Zeno phase." At $p_c$, the entanglement exhibits sub-linear power-law scaling with system size, suggesting persistent long-range entanglement even under conditions that generally suppress such behavior.

To substantiate these claims, finite-size scaling analyses are performed, yielding critical exponents for the transition. The findings suggest universal scaling behavior, with measured exponents indicating conventional dynamic scaling—contrasting with phenomena like the many-body localization transition.

Implications and Future Directions

This research contributes significantly to understanding the role of measurements in quantum many-body systems, particularly the counterintuitive persistence of volume-law entanglement in a hybrid circuit context. The identified phase transition offers a novel perspective on entanglement dynamics, with implications for quantum information processing where entanglement control is crucial.

Future research could extend these findings across different dimensional systems, exploring whether similar entanglement transition phenomena manifest universally. Additionally, analytical approaches to understand the critical behavior and potential experimental realizations in engineered quantum systems, such as ultracold atoms or superconducting qubits, could further elucidate the practical implications of the quantum Zeno effect and entanglement transitions.

In conclusion, this work provides a robust framework for exploring the boundaries between quantum coherence and measurement within complex systems, paving the way for further breakthroughs in quantum dynamics and information science.