Measurement-Induced Phase Transitions in the Dynamics of Entanglement

By B. Skinner, J. Ruhman, A. Nahum. Physical Review X, 2018

827 citations recorded by the source corpus.

We define dynamical universality classes for many-body systems whose unitary evolution is punctuated by projective measurements. In cases where such measurements occur randomly at a finite rate $p$ for each degree of freedom, we show that the system has two dynamical phases: `entangling' and `disentangling'. The former occurs for $p$ smaller than a critical rate $p_c$, and is characterized by volume-law entanglement in the steady-state and `ballistic' entanglement growth after a quench. By contrast, for $p > p_c$ the system can sustain only area-law entanglement. At $p = p_c$ the steady state is scale-invariant and, in 1+1D, the entanglement grows logarithmically after a quench. To obtain a simple heuristic picture for the entangling-disentangling transition, we first construct a toy model that describes the zeroth Renyi entropy in discrete time. We solve this model exactly by mapping it to an optimization problem in classical percolation. The generic entangling-disentangling transition can be diagnosed using the von Neumann entropy and higher Renyi entropies, and it shares many qualitative features with the toy problem. We study the generic transition numerically in quantum spin chains, and show that the phenomenology of the two phases is similar to that of the toy model, but with distinct `quantum' critical exponents, which we calculate numerically in $1+1$D. We examine two different cases for the unitary dynamics: Floquet dynamics for a nonintegrable Ising model, and random circuit dynamics. We obtain compatible universal properties in each case, indicating that the entangling-disentangling phase transition is generic for projectively measured many-body systems. We discuss the significance of this transition for numerical calculations of quantum observables in many-body systems.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/7e0264d91926a3016018026bb956cce2949d19d1

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Citations in the corpus

Entanglement Membrane in Chaotic Many-Body Systems (2019, background): “[83] Brian Skinner, Jonathan Ruhman, and Adam Nahum.”
Measurement-induced entanglement phase transition on a superconducting quantum processor with mid-circuit readout (2022, methodology): “A complication is that the scaling function F , which sets the curve onto which the data collapses, is unknown, and the procedure must depend only on the experiment dataset [17, 57, 58].”
Entanglement and Charge-Sharpening Transitions in U(1) Symmetric Monitored Quantum Circuits (2021, methodology): “In fact, `DW undergoes a percolation transition at pc = 1/2, where `DW is extensive in |A| for p < 1/2, and becomes O(1) for p > 1/2 [14].”
Measurement-induced topological entanglement transitions in symmetric random quantum circuits (2020, methodology): “In each updating step, we either: (1) apply a random three-qubit Clifford unitary between qubits i − 1, i and i + 1 with probability pu, for a random i drawn from 2, ⋯ , N − 1; (2) measure the single-qubit operator Zi with probability ps for a random i drawn from 1, ⋯ , N; or (3) measure the stabili”
Measurement and Entanglement Phase Transitions in All-To-All Quantum Circuits, on Quantum Trees, and in Landau-Ginsburg Theory (2020, background): “The surface tension of this membrane/domain wall is positive in the entangling phase [6].”
Statistical mechanics of quantum error correcting codes (2020, methodology): “5 In the case of a pure initial state [13, 15] where this transition was first found, p < pc corresponds to a “volume law entangled phase”, where one should be thinking in terms of the reduced (mixed) density matrix of a subsystem which holds a finite entropy density as T →∞.”
Random Quantum Circuits (2022, background): “Numerical evidence for this transition has by now been found in a wide range of microscopic models (52, 53, 58, 68, 65, 66, 61, 62, 54, 63, 64, 77, 67).”
Entanglement transition from variable-strength weak measurements (2019, methodology): “Alternative entanglement measures used in the literature include Rényi entropies [18, 20, 21] and mutual information [20, 21, 38].”