Generation of Volume-Law Entanglement by Local-Measurement-Only Quantum Dynamics

TL;DR

This work shows that volume-law entanglement can be generated purely by local, nonrandom measurement dynamics in a system without intrinsic unitary evolution, using a main fermionic chain coupled to an ancilla and measured via detector qubits. Two measurement schemes are explored: a one-body model that surprisingly yields volume-law entanglement between main-chain halves, and a three-body model with kinetic constraints that can suppress or modify entanglement generation. The authors analyze quantum trajectories, stationary distributions, and system-size scalings, revealing a rich phenomenology including non-Gaussian entanglement dynamics, discrete stationary states in the three-body case, and a form of limited ergodicity in the one-body model. The results highlight the potential of nonrandom measurement protocols for controlled entanglement generation and invite further study of measurement-only nonunitary many-body dynamics, including continuous-time limits and replica analyses.

Abstract

Repeated local measurements typically have adversarial effects on entangling unitary dynamics, as local measurements usually degrade entanglement. However, recent works on measurement-only dynamics have shown that strongly entangled states can be generated solely through non-commuting random multi-site and multi-spin projective measurements. In this work, we explore a generalized measurement setup in a system without intrinsic unitary dynamics and show that volume-law entangled states can be generated through local, non-random, yet non-commuting measurements. Specifically, we construct a one-dimensional model comprising a main fermionic chain and an auxiliary (ancilla) chain, where generalized measurements are performed by locally coupling the system to detector qubits. Our results demonstrate that long-time states with volume-law entanglement or mutual information are generated between different parts of the main chain purely through non-unitary measurement dynamics. Remarkably, we find that such large-entanglement generation can be achieved using only the measurements of one-body operators. Moreover, we show that measurements of non-local higher-body operators can be used to control and reduce entanglement generation by introducing kinetic constraints to the dynamics. We discuss the statistics of entanglement measures along the quantum trajectories, the approach to stationary distributions of entanglement or long-time steady states, and the associated notions of limited ergodicity in the measurement-only dynamics. Our findings highlight the potential of non-random measurement protocols for controlled entanglement generation and the study of non-unitary many-body dynamics.

Figures (29)

• Figure 1: The system-detector setup for measurement only dynamics. Each triangular structure comprises two consecutive sites from the main chain (blue, inner chain) and one from the ancilla or auxiliary chain (red, outer chain), forming a 'block'. Because of sharing a fermionic main-chain site, consecutive blocks do not commute. Triggered by the 'local' coupling (wavy lines) between a block (e.g., $i$-th block in shaded triangle) and the detector qubit (square) at the center, particles can hop between the main and ancilla chains (shown as double-headed arrows). There is no direct hopping among the main-chain sites. The subsystems $B$ and $B'$ (shaded half circle comprising half of main-chain sites) and their union $C = B \cup B'$ are used to compute entanglement after each measurement in the detector, which projects the qubit state, initialized in the ${|\!\uparrow\rangle}$ state, to ${|\!\uparrow\rangle}$ (no-click outcome) or ${|\!\downarrow\rangle}$ (click outcome) state.
• Figure 2: Entanglement entropy $S_B$ for the half of the main chain as a function of discrete measurement times $t_m$ for three different quantum trajectories, $\mathcal{C}_k$$(k=1, 2, 3)$, shown on a logarithmic scale along the $x$-axis. These trajectories are sampled for $\tilde{\alpha}=\pi/4$ and a system of size $L=12$, initialized in a product state, Eq. (\ref{['eq:Psi-p']}). The inset provides a closer view of $S_B$ over the last 20 measurement sweeps on linear scale, illustrating the persistent oscillations around a finite value of $S_B$. This indicates the absence of convergence to a stationary state.
• Figure 3: The trajectory-averaged entanglement entropy $S_B$ as a function of discrete measurement times $t_m$, shown for $\tilde{\alpha}=0.14,\, \pi/4,\, \pi/2, 3\pi/4$ on logarithmic scale along the $x$-axis. The data points are computed for the system size $L=12$, when the system is initialized in a product state [Eq. \ref{['eq:Psi-p']}]. The average $S_B$ shows convergence to stationary values in the long-time limit.
• Figure 4: The probability density function $p(S_B)$ of $S_B$ at different measurement steps $t_m$ for the product initial state $|\Psi_p\rangle$ with $\tilde{\alpha} = 3\pi/4$ and $L=12$. The histograms show the numerically obtained distributions, whereas the smooth curves are obtained with the kernel density estimation (KDE) for distributions. As $t_m$ increases, $p(S_B)$ broadens and converges to a stationary distribution.
• Figure 5: The metric distance or total variation distance (TVD) between the distribution at time $t_m$ and the long-time distribution at $t_m=5000$, plotted as a function of $t_m$ for different values of $\tilde{\alpha}$ and $L=12$. The results show a rapid decrease in TVD, indicating convergence to a stationary distribution. A much slower convergence is observed for small $\tilde{\alpha}=0.14$.