Entanglement transition from variable-strength weak measurements (1903.05452v2)

Abstract: 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.

Entanglement Transition Induced by Variable-Strength Weak Measurements

The paper authored by M. Szyniszewski and collaborators explores the fascinating phenomenon of entanglement transition in many-body quantum systems. Using a quantum circuit model with variable-strength weak measurements, the authors systematically investigate the transition from an ergodic thermal phase characterized by high entropy to a localized non-ergodic phase exhibiting reduced entropy. This paper elucidates the conditions under which such a transition is feasible, emphasizing the role of measurement strength.

Core Findings

• Phase Transition: The authors demonstrate that weak measurements can indeed provoke a quantum phase transition when the measurement strength surpasses a critical threshold. Below this critical strength, the system remains ergodic, irrespective of the measurement probability, thus preserving the extensive volume-law scaling of entanglement entropy.
• Measurement Modeling: While projective measurements are a conventional method in quantum systems, this research employs positive operator-valued measurements (POVMs) modeled by continuous Gaussian probes. This approach provides a more comprehensive and realistic depiction of environments with a spectrum of measurement outcomes and stochastic back-action effects.
• Phase Boundary Mapping: Through data collapse and analysis of entropy fluctuations, the paper identifies a consistent phase boundary in the parameter space of measurement strength and probability. This establishes a critical measurement strength below which localization does not occur, marking a significant distinction from scenarios purely involving projective measurements.
• Finite-Size Scaling: Employing finite-size scaling techniques, the authors extract critical parameters and verify the sharpness of the transition in large systems, providing robust numerical evidence for the transition's specificity and predictability.

Methodology

The authors utilize a one-dimensional quantum circuit model with local interactions to track entanglement dynamics over discrete stochastic time steps. This model entails a chain of spins undergoing random unitary operations, interposed with weak measurements occurring probabilistically. The interaction with the environment is characterized by a Hamiltonian relating to spin measurement, allowing the derivation of a continuous Lindblad dynamics framework in the limit of rapid sequential measurements.

Implications

This paper presents implications for quantum engineering, particularly in controlling many-body systems through environmental manipulation. By accurately modulating measurement strength and probability, it is possible to influence the entanglement properties of quantum systems, offering potential avenues for the design of nonergodic states for quantum computation and information protocols. Moreover, the findings underscore the importance of nonprojective measurements in understanding quantum transitions, suggesting broader applicability to various open quantum systems.

Future Directions

Future research could explore these transition dynamics in higher dimensions or alternative measurement frameworks to ascertain the universality of these findings. The potential to extend these insights to practical quantum feedback and control mechanisms remains a promising domain. Additionally, investigations into non-stochastic unitary dynamics and different system interaction models may enrich the understanding of quantum phase transitions under weak measurement influence.

In summary, Szyniszewski et al. provide a comprehensive examination of entanglement phase transitions driven by weak measurements, with implications for both theoretical exploration and practical applications in quantum system control.