Taming multiparty entanglement at measurement-induced phase transitions

TL;DR

This paper investigates measurement-induced phase transitions in quantum systems, using large-scale simulations to analyze critical behavior and multiparty entanglement decay, revealing new universal properties and bounds.

Contribution

It provides the first large-scale numerical analysis of a trapped-ion MIPT, identifying critical exponents and algebraic decay of multiparty entanglement, and establishes bounds for these quantities.

Findings

Critical measurement rate and correlation length exponent near percolation values.

Robust algebraic decay of genuine multiparty entanglement with separation.

Lower bounds for multiparty entanglement and mutual information.

Abstract

Measurement-induced phase transitions (MIPT) give rise to novel dynamical states of quantum matter realized by balancing unitary evolution and measurements. We present large-scale numerical simulations of a trapped-ion native MIPT, argued to belong to the universality class described by the Haar non-unitary conformal field theory. First, through a finite-size analysis we obtained the critical measurement rate, and correlation length exponent, which falls close to the percolation value. Second, by leveraging a monotone computable via semi-definite programming, we uncover robust algebraic decay of genuine multiparty entanglement (GME) versus separation for 2, 3, and 4 parties. The corresponding critical exponents are lower-bounded by those of the multiparty mutual information, which we determine up to 4 parties, and conjecture to be (k+2) for k parties. Additionally, we derive lower bounds for both GME and multiparty mutual information.