Query: measurement driven  entanglement transitions

title: Measurement Induced Phase Transitions in the Dynamics of Entanglement
abstract: 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.

title: Quantum Zeno effect and the many body entanglement transition
abstract: We introduce and explore a one dimensional `hybrid' quantum circuit model consisting of both unitary gates and projective measurements. While the unitary gates are drawn from a random distribution and act uniformly in the circuit, the measurements are made at random positions and times throughout the system. By varying the measurement rate we can tune between the volume law entangled phase for the random unitary circuit model (no measurements) and a `quantum Zeno phase' where strong measurements suppress the entanglement growth to saturate in an area law. Extensive numerical simulations of the quantum trajectories of the many particle wave functions (exploiting Clifford circuitry to access systems up to 512 qubits) provide evidence for a stable `weak measurement phase' that exhibits volume law entanglement entropy, with a coefficient decreasing with increasing measurement rate. We also present evidence for a continuous quantum dynamical phase transition between the `weak measurement phase' and the `quantum Zeno phase, driven by a competition between the entangling tendencies of unitary evolution and the disentangling tendencies of projective measurements. Detailed steady state and dynamic critical properties of this quantum entanglement transition are accessed.

title: Measurement driven entanglement transition in hybrid quantum circuits
abstract: Quantum information tends to spread out in interacting systems, leading to thermalization as characterized by the volume law entropy of entanglement, while local measurements that extract classical information of the state tend to interrupt the propagation of information and reduce the entanglement entropy. Can entanglement sustain repeated measurements? The authors address this question in a toy hybrid circuit model, where qubits undergo both unitary time evolution and sporadic local measurements. The phase diagram features a stable volume law phase of entanglement for weak measurements and an area law phase for strong measurements. The two domains in the diagram are separated by a single second order phase transition. Characterization of both phases as well as of the critical point are presented.

title: Unitary projective entanglement dynamics
abstract: Starting from a state of low quantum entanglement, local unitary time evolution increases the entanglement of a quantum many body system. In contrast, local projective measurements disentangle degrees of freedom and decrease entanglement. We study the interplay of these competing tendencies by considering time evolution combining both unitary and projective dynamics. We begin by constructing a toy model of Bell pair dynamics which demonstrates that measurements can keep a system in a state of low (i.e. area law) entanglement, in contrast with the volume law entanglement produced by generic pure unitary time evolution. While the simplest Bell pair model has area law entanglement for any measurement rate, as seen in certain non interacting systems, we show that more generic models of entanglement can feature an area to volume law transition at a critical value of the measurement rate, in agreement with recent numerical investigations. As a concrete example of these ideas, we analytically investigate Clifford evolution in qubit systems which can exhibit an entanglement transition. We are able to identify stabilizer size distributions characterizing the area law, volume law and critical 'fixed points. We also discuss Floquet random circuits, where the answers depend on the order of limits one order of limits yields area law entanglement for any non zero measurement rate, whereas a different order of limits allows for an area law volume law transition. Finally, we provide a rigorous argument that a system subjected to projective measurements can only exhibit a volume law entanglement entropy if it also features a subleading correction term, which provides a universal signature of projective dynamics in the high entanglement phase.  The results presented here supersede those of all previous versions of this manuscript, which contained some erroneous claims.

title: Measurement induced criticality in random quantum circuits
abstract: We investigate the critical behavior of the entanglement transition induced by projective measurements in (Haar) random unitary quantum circuits. Using a replica approach, we map the calculation of the entanglement entropies in such circuits onto a two dimensional statistical mechanics model. In this language, the area to volume law entanglement transition can be interpreted as an ordering transition in the statistical mechanics model. We derive the general scaling properties of the entanglement entropies and mutual information near the transition using conformal invariance. We analyze in detail the limit of infinite on site Hilbert space dimension in which the statistical mechanics model maps onto percolation. In particular, we compute the exact value of the universal coefficient of the logarithm of subsystem size in the $n$th R\'enyi entropies for $n \geq 1$ in this limit using relatively recent results for conformal field theory describing the critical theory of 2D percolation, and we discuss how to access the generic transition at finite on site Hilbert space dimension from this limit, which is in a universality class different from 2D percolation. We also comment on the relation to the entanglement transition in Random Tensor Networks, studied previously in Ref. 1.

title: Deterministic entanglement generation from driving through quantum phase transitions
abstract: Transitional approach to entanglement In an entangled many particle system, changing the state of one constituent affects the rest of the system. This property can be used as a resource in quantum information processing, but getting many particles to participate in entanglement is tricky. Luo et al. used another collective phenomenon, a quantum phase transition, to entangle more than 900 atoms in a Bose Einstein condensate. The size of the entangled ensemble remained stable, making the approach practical for precision measurements. Science, this issue p. 620 A large entangled 87Rb atom ensemble robust to number fluctuations was created. Many body entanglement is often created through the system evolution, aided by nonlinear interactions between the constituting particles. These very dynamics, however, can also lead to fluctuations and degradation of the entanglement if the interactions cannot be controlled. Here, we demonstrate near deterministic generation of an entangled twin Fock condensate of ~11,000 atoms by driving a rubidium 87 Bose Einstein condensate undergoing spin mixing through two consecutive quantum phase transitions (QPTs) We directly observe number squeezing of 10.7 0.6 decibels and normalized collective spin length of 0.99 0.01. Together, these observations allow us to infer an entanglement enhanced phase sensitivity of ~6 decibels beyond the standard quantum limit and an entanglement breadth of ~910 atoms. Our work highlights the power of generating large scale useful entanglement by taking advantage of the different entanglement landscapes separated by QPTs.

title: Quantum Error Correction in Scrambling Dynamics and Measurement Induced Phase Transition.
abstract: We analyze the dynamics of entanglement entropy in a generic quantum many body open system from the perspective of quantum information and error corrections. We introduce a random unitary circuit model with intermittent projective measurements, in which the degree of information scrambling by the unitary and the rate of projective measurements are independently controlled. This model displays two stable phases, characterized by the volume law and area law scaling entanglement entropy in steady states. The transition between the two phases is understood from the point of view of quantum error correction: the chaotic unitary evolution protects quantum information from projective measurements that act as errors. A phase transition occurs when the rate of errors exceeds a threshold that depends on the degree of information scrambling. We confirm these results using numerical simulations and obtain the phase diagram of our model. Our work shows that information scrambling plays a crucial role in understanding the dynamics of entanglement in an open quantum system and relates the entanglement phase transition to changes in quantum channel capacity.

title: Surfactant driven flow transitions in evaporating droplets.
abstract: An evaporating droplet is a dynamic system in which flow is spontaneously generated to minimize the surface energy, dragging particles to the borders and ultimately resulting in the so called "coffee stain effect" The situation becomes more complex at the droplet's surface, where surface tension gradients of different natures can compete with each other yielding different scenarios. With careful experiments and with the aid of 3D particle tracking techniques, we are able to show that different types of surfactants turn the droplet's surface either rigid or elastic, which alters the evaporating fluid flow, either enhancing the classical coffee stain effect or leading to a total flow inversion. Our measurements lead to unprecedented and detailed measurements of the surface tension difference along the evaporating droplet's surface with good temporal and spatial resolution.

title: In situ X ray diffraction measurement of shock wave driven twinning and lattice dynamics
abstract: Pressure driven shock waves in solid materials can cause extreme damage and deformation. Understanding this deformation and the associated defects that are created in the material is crucial in the study of a wide range of phenomena, including planetary formation and asteroid impact sites, the formation of interstellar dust clouds, ballistic penetrators, spacecraft shielding and ductility in high performance ceramics. At the lattice level, the basic mechanisms of plastic deformation are twinning (whereby crystallites with a mirror image lattice form) and slip (whereby lattice dislocations are generated and move) but determining which of these mechanisms is active during deformation is challenging. Experiments that characterized lattice defects have typically examined the microstructure of samples after deformation, and so are complicated by post shock annealing and reverberations. In addition, measurements have been limited to relatively modest pressures (less than 100 gigapascals) In situ X ray diffraction experiments can provide insights into the dynamic behaviour of materials, but have only recently been applied to plasticity during shock compression and have yet to provide detailed insight into competing deformation mechanisms. Here we present X ray diffraction experiments with femtosecond resolution that capture in situ, lattice level information on the microstructural processes that drive shock wave driven deformation. To demonstrate this method we shock compress the body centred cubic material tantalum an important material for high energy density physics owing to its high shock impedance and high X ray opacity. Tantalum is also a material for which previous shock compression simulations and experiments have provided conflicting information about the dominant deformation mechanism. Our experiments reveal twinning and related lattice rotation occurring on the timescale of tens of picoseconds. In addition, despite the common association between twinning and strong shocks, we find a transition from twinning to dislocation slip dominated plasticity at high pressure (more than 150 gigapascals) a regime that recovery experiments cannot accurately access. The techniques demonstrated here will be useful for studying shock waves and other high strain rate phenomena, as well as a broad range of processes induced by plasticity.

title: Critical properties of the measurement induced transition in random quantum circuits
abstract: We numerically study the measurement driven quantum phase transition of Haar random quantum circuits in $1+1$ dimensions. By analyzing the tripartite mutual information we are able to make a precise estimate of the critical measurement rate $p_c 0.17(1) We extract estimates for the associated bulk critical exponents that are consistent with the values for percolation, as well as those for stabilizer circuits, but differ from previous estimates for the Haar random case. Our estimates of the surface order parameter exponent appear different from that for stabilizer circuits or percolation, but we are unable to definitively rule out the scenario where all exponents in the three cases match. Moreover, in the Haar case the prefactor for the entanglement entropies $S_n$ depends strongly on the R\'enyi index $n$ for stabilizer circuits and percolation this dependence is absent. Results on stabilizer circuits are used to guide our study and identify measures with weak finite size effects. We discuss how our numerical estimates constrain theories of the transition.