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arXiv:2302.06477 · Physical review. B./Physical review. B

Multipartite entanglement in the measurement-induced phase transition of the quantum Ising chain

Alessio Paviglianiti, Alessandro Silva

Published Nov 6, 2023• 54 citations
arXivHTMLPDF

Abstract

Quantum systems subject to external monitoring manifest a rich phenomenology in their entanglement properties. Here, the authors use quantum Fisher information to uncover a multipartite entanglement phase transition in the monitored quantum Ising chain. By changing the measurement rate, they observe a shift from bounded to long-range multipartiteness of quantum correlations. They show that the quantum Fisher information displays distinct behavior from the entanglement entropy, and the two outline different phase boundaries.

DOI
10.1103/physrevb.108.184302

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Quantum systems subject to external monitoring manifest a rich phenomenology in their entanglement properties. Here, the authors use quantum Fisher information to uncover a multipartite entanglement phase transition in the monitored quantum Ising chain. By changing the measurement rate, they observe a shift from bounded to long-range multipartiteness of quantum correlations. They show that the quantum Fisher information displays distinct behavior from the entanglement entropy, and the two outline different phase boundaries.
Abstract The theory of multipartite entanglement provides a robust framework for understanding complex phenomena in quantum many-body systems, while multipartite entanglement also serves as a key resource in numerous quantum information processing tasks. Using density matrix renormalization group calculations, we study the multipartite entanglement in one-dimensional quantum long-range ferromagnetic and antiferromagnetic Ising chains with algebraically decaying interactions 1/ r α , respectively. To quantitatively probe the system’s multipartite entanglement structure, we employ the quantum Fisher information (QFI). Our results reveal two key behaviors: as the system size increases, the QFI rises, while the multipartite entanglement density decreases and converges toward a constant value. The latter trend points to a fundamental constraint on entanglement distribution in the thermodynamic limit. We further discuss the effects of the magnetic field and the exponent α on the QFI. We find that the peak values of the QFI increase with increasing α . Additionally, the discontinuity in the QFI can be regarded as a powerful tool for characterizing quantum phase transitions in the systems.
Measurement-induced phase transition arises from the competition between a deterministic quantum evolution and a repeated measurement process. We explore the measurement-induced phase transition through the Quantum Fisher Information in two different metrological scenarios. We demonstrate through the scaling behavior of the quantum Fisher information the transition of the multi-partite entanglement across the phases. In analogy with standard quantum phase transition, we reveal signature of a measurement-induced phase transition in the non-analytic behaviour of the quantum Fisher information as the measurement strength approaches the critical value. Our results offer novel insights into the features of a quantum systems undergoing measurement-induced phase transition and indicate potential avenues for further exploration in the field of quantum physics.
Recent years have witnessed major progress in the understanding of monitored quantum dynamics, an open quantum setting where the environment is a measurement apparatus that probes the system locally. For the resulting quantum trajectory, unitary evolution and local measurements have competing tendencies in the building of quantum correlations: while the coherent interactions in the former increase the entanglement, the resolving nature of the local measurement collapses the state of the system. Here, the authors study the interplay of monitoring and system dynamics by focusing on the monitored quantum Ising chain as the measurement strength is varied, going from the regime of weak detection, corresponding to the limit of infinite small jumps, to the case of post-selected no-jump case. A sharp transition is found between a logarithmic law phase to an area law phase for the entanglement entropy, which occurs at the same value of the measurement rate in the two limiting situations.
Non-equilibrium phase transitions of open quantum systems generically exhibit diverging classical but not quantum correlations. Still entanglement -- characterizing the latter correlations -- can be sensitive to the phase transition. Furthermore, mutual information, bounding the total correlations, should exhibit critical scaling at the transition. In this work, we study these quantities in the steady state of open quantum Ising chains with power-law interactions (with the exponent 0≤α≤30\le α\le 30≤α≤3) where spins are subject to spontaneous emission. The bulk of this paper is dedicated to a detailed analytical as well as numerical analysis of the infinite-range model (α=0α=0α=0), a model that is closely related to the paradigmatic open Dicke model. Our main findings are that the entanglement, while being finite, peaks, exhibits a kink and takes a universal value at the transition, while the mutual information exhibits critical scaling not only at the transition but well into the ordered phase, underscoring a hidden criticality that is not captured by (two-point) correlations. We consider three distinct entanglement measures: logarithmic negativity; quantum Fisher information; and, spin squeezing. Specifically, we show that the collective spin operator that maximizes the quantum Fisher information can be identified with the \textit{gapless} mode of the phase transition, while the squeezed direction is that of the \textit{gapped} mode. Finally, we investigate power-law interacting models using matrix product states where we find comparable bounds on squeezing even when no phase transition is expected (for larger ααα), thus the connection to the phase transition does not appear to hold for shorter-range interactions.
We study the competing effects of collective generalized measurements and interaction-induced scrambling in the dynamics of an ensemble of spin-1/2 particles at the level of quantum trajectories. This setup can be considered as analogous to the one leading to measurement-induced transitions in quantum circuits. We show that the interplay between collective unitary dynamics and measurements leads to three regimes of the average Quantum Fisher Information (QFI), which is a witness of multipartite entanglement, as a function of the monitoring strength. While both weak and strong measurements lead to extensive QFI density (i.e., individual quantum trajectories yield states displaying Heisenberg scaling), an intermediate regime of classical-like states emerges for all system sizes where the measurement effectively competes with the scrambling dynamics and precludes the development of quantum correlations, leading to sub-Heisenberg-limited states. We characterize these regimes and the crossovers between them using numerical and analytical tools, and discuss the connections between our findings, entanglement phases in monitored many-body systems, and the quantum-to-classical transition.
In this paper, we investigate Quantum Phase Transitions (QPTs) in the long-range XXZ spin chain using two information-theoretic probes: The half-chain entanglement entropy and a witness of genuine multipartite nonlocality. Both quantities effectively identify the phase boundary, but exhibit distinct scaling behaviors: the entanglement entropy grows linearly with system size N, while the multipartite nonlocality increases exponentially, with [Formula: see text]. By independently tuning the power-law decay exponents of the transverse ([Formula: see text]) and longitudinal ([Formula: see text]) couplings, we uncover contrasting trends in the critical point [Formula: see text]: Increasing [Formula: see text] shifts it to larger values, while increasing [Formula: see text] shifts it to smaller ones. These monotonic and saturating dependencies are captured by an empirical exponential model, offering a compact and physically transparent description of the critical behavior. Our results highlight the crucial role of interaction range in driving criticality, with implications for engineered quantum systems and long-range entanglement control.