Phase transitions of bipartite entanglement.

We analyze the statistical properties of the entanglement of a large bipartite quantum system. By framing the problem in terms of random matrices and a fictitious temperature, we unveil the existence of two phase transitions, characterized by different spectra of the reduced density matrices.

• Publication year

  2007

• Venue

  Physical Review Letters

• Publication date

  2007-11-30

• Fields of study

  Medicine, Physics

• Identifiers
  DOI 10.1103/PhysRevLett.101.050502arXiv 0712.0015PMID 18764381
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

• Entanglement in many-body systems

  2007cited by this paper
• Quantum phase transitions and bipartite entanglement.

  2004cited by this paper
• Scaling of entanglement close to a quantum phase transition

  2002cited by this paper
• Average entropy of a subsystem.

  1993cited by this paper
• Spin Glass Theory and Beyond

  1987cited by this paper

• Atomic Quantum Technologies for Quantum Matter and Fundamental Physics Applications

  2024cites this paper
• Condensation of vanishing photon emission rates in random atomic clouds

  2024cites this paper
• Generating entanglement by quantum resetting

  2023cites this paper
• Probabilities of moderately atypical fluctuations of the size of a swarm of Brownian bees.

  2022cites this paper
• Relations between the average bipartite entanglement and N-partite correlation functions

  2022cites this paper
• An exact formula for the variance of linear statistics in the one-dimensional jellium model

  2022cites this paper
• Fluctuations and first-passage properties of systems of Brownian particles with reset.

  2022cites this paper
• Visualizing quantum phase transitions in the XXZ model via the quantum steering ellipsoid

  2021cites this paper
• Fastest Local Entanglement Scrambler, Multistage Thermalization, and a Non-Hermitian Phantom

  2021cites this paper
• Edge fluctuations and third-order phase transition in harmonically confined long-range systems

  2021cites this paper
• General truncated linear statistics for the top eigenvalues of random matrices

  2021cites this paper
• Demonstrate Absolutely Maximally Entangled of Four- and Eight-qubit States Inexistence via Simple Constraint Condition

  2021cites this paper
• Critical exponents for higher order phase transitions: Landau theory and RG flow

  2021cites this paper
• Generation of Bures-Hall mixed states using coupled kicked tops

  2021cites this paper
• Entanglement distribution in the quantum symmetric simple exclusion process.

  2021cites this paper
• Generic aspects of the resource theory of quantum coherence

  2020cites this paper
• Holographic Pseudo Entropy

  2020cites this paper
• Multipartite Entanglement Generation in a Structured Environment

  2020cites this paper
• Entanglement Dynamics of Random GUE Hamiltonians

  2020cites this paper
• Constructing five qutrit absolutely maximally entangled state via recurrence relation

  2020cites this paper
• Typical entanglement for Gaussian states

  2019cites this paper
• Bures–Hall ensemble: spectral densities and average entropies

  2019cites this paper
• Entanglement statistics in Markovian open quantum systems: A matter of mutation and selection.

  2019cites this paper
• Volume of the set of LOCC-convertible quantum states

  2019cites this paper
• Phase diagram of bipartite entanglement

  2019cites this paper
• Entanglement dynamics of n-qubit states in a hierarchical environment

  2018cites this paper
• Two forms for 3-uniform states of eight-qubits

  2018cites this paper
• Théorie des matrices aléatoires en physique statistique : théorie quantique de la diffusion et systèmes désordonnés

  2018influential citation
• Third-Order Phase Transition: Random Matrices and Screened Coulomb Gas with Hard Walls

  2018cites this paper
• New form Simple Structure of Maximally Eight-qubit Entanglement State

  2018cites this paper
• Truncated Linear Statistics Associated with the Top Eigenvalues of Random Matrices

  2017cites this paper
• Smallest eigenvalue density for regular or fixed-trace complex Wishart–Laguerre ensemble and entanglement in coupled kicked tops

  2017cites this paper
• Feynman graphs and the large dimensional limit of multipartite entanglement

  2017cites this paper
• Universality of the weak pushed-to-pulled transition in systems with repulsive interactions

  2017cites this paper
• Universality of the third-order phase transition in the constrained Coulomb gas

  2017cites this paper
• Entanglement entropy of a three-spin-interacting spin chain with a time-reversal-breaking impurity at one boundary.

  2017cites this paper
• Entanglement critical length at the many-body localization transition

  2016cites this paper
• Title Random matrix techniques in quantum information theory

  2016cites this paper
• Random pure states: Quantifying bipartite entanglement beyond the linear statistics.

  2016cites this paper
• Truncated Linear Statistics Associated with the Top Eigenvalues of Random Matrices

  2016cites this paper
• Number statistics for β-ensembles of random matrices: Applications to trapped fermions at zero temperature.

  2016cites this paper
• Number statistics in random matrices and applications to quantum systems

  2015cites this paper
• Total correlations of the diagonal ensemble herald the many-body localization transition

  2015cites this paper
• Fluctuations in the two-dimensional one-component plasma and associated fourth-order phase transition.

  2015cites this paper
• Quantum typicality and initial conditions

  2015cites this paper
• 3-Uniform states and orthogonal arrays

  2015cites this paper
• A shortcut through the Coulomb gas method for spectral linear statistics on random matrices

  2015cites this paper
• Random matrix techniques in quantum information theory

  2015cites this paper
• Generic Entanglement Entropy for Quantum States with Symmetry

  2014cites this paper
• Phase transitions and edge scaling of number variance in Gaussian random matrices.

  2014cites this paper
• Large deviations of the shifted index number in the Gaussian ensemble

  2014cites this paper
• Spectral order statistics of Gaussian random matrices: large deviations for trapped fermions and associated phase transitions.

  2014cites this paper
• Large deviations of spread measures for Gaussian matrices

  2014cites this paper
• Diagonal quantum circuits: Their computational power and applications

  2014cites this paper
• Random density matrices versus random evolution of open system

  2014cites this paper
• Quantum Random State Generation with Predefined Entanglement Constraint

  2014cites this paper
• Top eigenvalue of a random matrix: large deviations and third order phase transition

  2013cites this paper
• Polarized ensembles of random pure states

  2013cites this paper
• Wigner time-delay distribution in chaotic cavities and freezing transition.

  2013cites this paper
• Index distribution of Cauchy random matrices

  2013cites this paper
• Entropy-driven phase transitions of entanglement

  2013cites this paper
• Invariant measures on multimode quantum Gaussian states

  2012cites this paper
• Generalized criterion for a maximally multi-qubit entangled state

  2012cites this paper
• Purity distribution for generalized random Bures mixed states

  2011cites this paper
• Statistical distribution of the local purity in a large quantum system

  2011cites this paper
• How many eigenvalues of a Gaussian random matrix are positive?

  2010cites this paper
• Largest Schmidt eigenvalue of random pure states and conductance distribution in chaotic cavities

  2010cites this paper
• Entangled random pure states with orthogonal symmetry: exact results

  2010cites this paper
• Classical statistical mechanics approach to multipartite entanglement

  2010cites this paper
• Statistical Distribution of Quantum Entanglement for a Random Bipartite State

  2010cites this paper
• Index distribution of gaussian random matrices.

  2009cites this paper
• Entanglement and Localization of Wavefunctions

  2009cites this paper
• Berry phase in superconducting charge qubits interacting with a cavity field

  2009cites this paper
• Probability distributions of linear statistics in chaotic cavities and associated phase transitions

  2009cites this paper
• Phase transitions and metastability in the distribution of the bipartite entanglement of a large quantum system

  2009cites this paper
• Nonintersecting Brownian interfaces and Wishart random matrices.

  2009cites this paper
• Phase transitions in the distribution of bipartite entanglement of a random pure state.

  2009cites this paper
• Distributions of conductance and shot noise and associated phase transitions.

  2008cites this paper
• Statistical mechanics of multipartite entanglement

  2008cites this paper