Entanglement Typicality

Abstract

We provide a summary of both seminal and recent results on typical entanglement. By typical values of entanglement, we refer here to values of entanglement quantifiers that (given a reasonable measure on the manifold of states) appear with arbitrarily high probability for quantum systems of sufficiently high dimensionality. We work within the Haar measure framework for discrete quantum variables, where we report on results concerning the average von Neumann and linear entropies as well as arguments implying the typicality of such values in the asymptotic limit. We then proceed to discuss the generation of typical quantum states with random circuitry. Different phases of entanglement, and the connection between typical entanglement and thermodynamics are discussed. We also cover approaches to measures on the non-compact set of Gaussian states of continuous variable quantum systems.

Review paper with two quotes and minimalist figures

References in corpus (8)

• Black holes as mirrors: quantum information in random subsystems
• Aspects of generic entanglement
• Statistical distribution of quantum entanglement for a random bipartite state
• Emergence of typical entanglement in two-party random processes
• Canonical and micro-canonical typical entanglement of continuous variable systems
• Teleportation fidelities of squeezed states from thermodynamical state space measures
• Random circuits by measurements on weighted graph states
• Invariant measures on multimode quantum Gaussian states