Emergence of typical entanglement in two-party random processes

Abstract

We investigate the entanglement within a system undergoing a random, local process. We find that there is initially a phase of very fast generation and spread of entanglement. At the end of this phase the entanglement is typically maximal. In previous work we proved that the maximal entanglement is reached to a fixed arbitrary accuracy within $O(N^3)$ steps, where $N$ is the total number of qubits. Here we provide a detailed and more pedagogical proof. We demonstrate that one can use the so-called stabilizer gates to simulate this process efficiently on a classical computer. Furthermore, we discuss three ways of identifying the transition from the phase of rapid spread of entanglement to the stationary phase: (i) the time when saturation of the maximal entanglement is achieved, (ii) the cut-off moment, when the entanglement probability distribution is practically stationary, and (iii) the moment block entanglement scales exhibits volume scaling. We furthermore investigate the mixed state and multipartite setting. Numerically we find that classical and quantum correlations appear to behave similarly and that there is a well-behaved phase-space flow of entanglement properties towards an equilibrium, We describe how the emergence of typical entanglement can be used to create a much simpler tripartite entanglement description. The results form a bridge between certain abstract results concerning typical (also known as generic) entanglement relative to an unbiased distribution on pure states and the more physical picture of distributions emerging from random local interactions.

32 pages, 11 figures

References in corpus (38)

• A computable measure of entanglement
• Average Entropy of a Subsystem
• The logarithmic negativity: A full entanglement monotone that is not convex
• Multi-party entanglement in graph states
• The foundations of statistical mechanics from entanglement: Individual states vs. averages
• Stabilizer Codes and Quantum Error Correction
• Exact and Approximate Unitary 2-Designs: Constructions and Applications
• On the quantum, classical and total amount of correlations in a quantum state
• Scalable Noise Estimation with Random Unitary Operators
• Instantaneous non-local computation of low T-depth quantum circuits
• The Heisenberg Representation of Quantum Computers
• Exact and Asymptotic Measures of Multipartite Pure State Entanglement
• Entanglement Properties of the Harmonic Chain
• Entropy, entanglement, and area: analytical results for harmonic lattice systems
• Evenly distributed unitaries: on the structure of unitary designs
• Aspects of generic entanglement
• Quantum Data Hiding
• Entanglement in Quantum Information Theory
• Random Quantum Circuits and Pseudo-Random Operators: Theory and Applications
• An entanglement-area law for general bosonic harmonic lattice systems
• Superdense coding of quantum states
• Efficient Generation of Generic Entanglement
• Random Matrix Theory and Entanglement in Quantum Spin Chains
• Quantum Approach to a Derivation of the Second Law of Thermodynamics
• Convergence Conditions for Random Quantum Circuits
• Entanglement on mixed stabiliser states--I: Normal Forms and Reduction Procedures
• Entanglement in the stabilizer formalism
• Typical entanglement of stabilizer states
• Ground state approximation for strongly interacting systems in arbitrary dimension
• Bound entanglement provides convertibility of pure entangled states
• Multi-particle entanglement manipulation under positive partial transpose preserving operations
• Tripartite entanglement and quantum relative entropy
• Multipartite pure-state entanglement and the generalized GHZ states
• Optimal superdense coding of entangled states
• Canonical and micro-canonical typical entanglement of continuous variable systems
• Teleportation fidelities of squeezed states from thermodynamical state space measures
• Reversibility of local transformations of multiparticle entanglement
• Entanglement and decoherence in spin gases

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• Efficient classical simulation of random shallow 2D quantum circuits
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• Quantum chaos in the Brownian SYK model with large finite $N$: OTOCs and tripartite information
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• Minimal Model for Fast Scrambling
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• Noisy Coupled Qubits: Operator Spreading and the Fredrickson-Andersen Model
• Efficient Quantum Pseudorandomness
• Ensemble averaged entanglement of two-particle states in Fock space
• Entanglement Typicality
• Comment on the paper "Random Quantum Circuits are Approximate 2-designs"
• Generating a state $t$-design by diagonal quantum circuits
• Efficiency of Producing Random Unitary Matrices with Quantum Circuits
• Parameters of Pseudo-Random Quantum Circuits
• Fastest local entanglement scrambler, multistage thermalization, and a non-Hermitian phantom
• Diagonal quantum circuits: their computational power and applications
• Relaxation due to random collisions with a many-qudit environment
• Solvable non-Hermitian skin effect in many-body unitary dynamics
• Optimal Universal Quantum Error Correction via Bounded Reference Frames
• Canonical and micro-canonical typical entanglement of continuous variable systems
• Entanglement dynamics and relaxation in a few qubit system interacting with random collisions
• Unifying typical entanglement and coin tossing: on randomization in probabilistic theories
• Phase-random states: ensembles of states with fixed amplitudes and uniformly distributed phases in a fixed basis
• Ensembles of physical states and random quantum circuits on graphs
• Two-step phantom relaxation of out-of-time-ordered correlations in random circuits
• Quantum pseudo-randomness from cluster-state quantum computation
• Local random quantum circuits are approximate polynomial-designs - numerical results
• Real-time correlators in chaotic quantum many-body systems
• Random circuits by measurements on weighted graph states
• Diagonal-unitary 2-designs and their implementations by quantum circuits
• On the negativity of random pure states
• Decoupling with random diagonal unitaries
• Pseudo-randomness and Learning in Quantum Computation
• Superpolynomial speedups based on almost any quantum circuit
• Designs from Local Random Quantum Circuits with SU(d) Symmetry
• Inhibition of spread of typical bipartite and genuine multiparty entanglement in response to disorder
• Invariant measures on multimode quantum Gaussian states
• Purity decay rate in random circuits with different configurations of gates
• Entanglement entropy scaling of noisy random quantum circuits in two dimensions
• Quantum circuit for three-qubit random states
• Generation of Pseudo-Random Quantum States on Actual Quantum Processors
• Pseudo-Random Circuits from Clifford Plus T-Gates
• Generic Entanglement Entropy for Quantum States with Symmetry
• Efficient generation of random multipartite entangled states using time optimal unitary operations
• Estimating phase transition of perturbed J1-J2 Heisenberg quantum chain in mixtures of ground and first excited states
• Fidelity decay and error accumulation in random quantum circuits
• Quantum Cramer-Rao Precision Limit of Noisy Continuous Sensing
• Propagation of correlations in Local Random Quantum Circuits
• Simulating typical entanglement with many-body Hamiltonian dynamics