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 (40)

• Quantum entanglement
• Quantum information with continuous variables
• Gaussian Quantum Information
• Average Entropy of a Subsystem
• Entanglement in a simple quantum phase transition
• Black Holes: Complementarity or Firewalls?
• On the volume of the set of mixed entangled states
• Black holes as mirrors: quantum information in random subsystems
• 2D Gravity and Random Matrices
• Information in Black Hole Radiation
• The foundations of statistical mechanics from entanglement: Individual states vs. averages
• Exact and Approximate Unitary 2-Designs: Constructions and Applications
• Squeezing as an irreducible resource
• Better Late than Never: Information Retrieval from Black Holes
• Induced measures in the space of mixed quantum states
• Aspects of generic entanglement
• Random Quantum Circuits are Approximate 2-designs
• Average Entropy of a Subsystem
• Generating random density matrices
• A decoupling approach to the quantum capacity
• Statistical distribution of quantum entanglement for a random bipartite state
• Phase Transitions in the Distribution of Bipartite Entanglement of a Random Pure State
• Quantum Approach to a Derivation of the Second Law of Thermodynamics
• Phase transitions of bipartite entanglement
• Emergence of typical entanglement in two-party random processes
• Typical entanglement of stabilizer states
• Phase transitions and metastability in the distribution of the bipartite entanglement of a large quantum system
• Entanglement in random pure states: Spectral density and average von Neumann entropy
• Phase transitions for random states and a semi-circle law for the partial transpose
• Phase-random states: ensembles of states with fixed amplitudes and uniformly distributed phases in a fixed basis
• Canonical and micro-canonical typical entanglement of continuous variable systems
• Unifying typical entanglement and coin tossing: on randomization in probabilistic theories
• Entropy-Driven Phase Transitions of Entanglement
• Statistical mechanics of multipartite entanglement
• Teleportation fidelities of squeezed states from thermodynamical state space measures
• Non-local Correlations are Generic in Infinite-Dimensional Bipartite Systems
• Diagonal-unitary 2-designs and their implementations by quantum circuits
• Random circuits by measurements on weighted graph states
• Invariant measures on multimode quantum Gaussian states
• Typical Entanglement

Cited by in corpus (29)

• Universality in volume law entanglement of pure quantum states
• Random pure states: quantifying bipartite entanglement beyond the linear statistics
• Average coherence and its typicality for random pure states
• Minimal energy cost of entanglement extraction
• Average subentropy, coherence and entanglement of random mixed quantum states
• Large Block Properties of the Entanglement Entropy of Disordered Fermions
• Entanglement Growth and Minimal Membranes in $(d+1)$ Random Unitary Circuits
• Universal feedback control of two-qubit entanglement
• Wishart and random density matrices: Analytical results for the mean-square Hilbert-Schmidt distance
• How much entanglement can be created in a closed system?
• The volume of Gaussian states by information geometry
• Average skew information-based coherence and its typicality for random quantum states
• Page curves and typical entanglement in linear optics
• The absence of the selfaveraging property of the entanglement entropy of disordered free fermions in one dimension
• Inhibition of spread of typical bipartite and genuine multiparty entanglement in response to disorder
• The Volume of Two-Qubit States by Information Geometry
• Geometry on the manifold of Gaussian quantum channels
• Generation of Pseudo-Random Quantum States on Actual Quantum Processors
• All possible permutational symmetries of a quantum system
• Spread and asymmetry of typical quantum coherence and their inhibition in response to glassy disorder
• Quantum walks as thermalizations, with application to fullerene graphs
• Average Rényi Entanglement Entropy in Gaussian Boson Sampling
• Generalized Cross-Entropy Benchmarking for Random Circuits with Ergodicity
• Fidelity and Entanglement of Random Bipartite Pure States: Insights and Applications
• Quantum estimation through a bottleneck
• Statistics of Entanglement Transformation with Hierarchies among Catalysts
• Entanglement signatures of a percolating quantum system
• Entanglement Entropy of Free Fermions with a Random Matrix as a One-Body Hamiltonian
• Page Curve of average subsystem entropy