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 (13)

• Multi-party entanglement in graph states
• On the quantum, classical and total amount of correlations in a quantum state
• Evenly distributed unitaries: on the structure of unitary designs
• Aspects of generic entanglement
• Superdense coding of quantum states
• Entanglement in the stabilizer formalism
• 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
• 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
• Entanglement and decoherence in spin gases

Cited by in corpus (10)

• Exact convergence times for generation of random bipartite entanglement
• Ensemble averaged entanglement of two-particle states in Fock space
• Parameters of Pseudo-Random Quantum Circuits
• Relaxation due to random collisions with a many-qudit environment
• Entanglement dynamics and relaxation in a few qubit system interacting with random collisions
• Canonical and micro-canonical typical entanglement of continuous variable systems
• Quantum pseudo-randomness from cluster-state quantum computation
• Random circuits by measurements on weighted graph states
• Superpolynomial speedups based on almost any quantum circuit
• Efficient generation of random multipartite entangled states using time optimal unitary operations