Statistical properties of random density matrices

Abstract

Statistical properties of ensembles of random density matrices are investigated. We compute traces and von Neumann entropies averaged over ensembles of random density matrices distributed according to the Bures measure. The eigenvalues of the random density matrices are analyzed: we derive the eigenvalue distribution for the Bures ensemble which is shown to be broader then the quarter--circle distribution characteristic of the Hilbert--Schmidt ensemble. For measures induced by partial tracing over the environment we compute exactly the two-point eigenvalue correlation function.

8 revtex pages with one eps file included, ver. 2 - minor misprints corrected

References in corpus (9)

• Average Entropy of a Subsystem
• Induced measures in the space of mixed quantum states
• Average Entropy of a Subsystem
• Bures volume of the set of mixed quantum states
• Random quantum correlations and density operator distributions
• Hilbert--Schmidt volume of the set of mixed quantum states
• Hall Normalization Constants for the Bures Volumes of the n-State Quantum Systems
• Average Entropy of a Subsystem from its Average Tsallis Entropy
• Quantum states on supersymmetric minisuperspace with a cosmological constant

Cited by in corpus (103)

• The foundations of statistical mechanics from entanglement: Individual states vs. averages
• Aspects of generic entanglement
• Generating random density matrices
• Extremal properties of the variance and the quantum Fisher information
• Average fidelity between random quantum states
• Statistical distribution of quantum entanglement for a random bipartite state
• Random matrix techniques in quantum information theory
• Random Quantum Operations
• Optimal full estimation of qubit mixed states
• Random Bures mixed states and the distribution of their purity
• Random pure states: quantifying bipartite entanglement beyond the linear statistics
• Entanglement of random vectors
• Almost Certain Escape from Black Holes
• Asymptotics of random density matrices
• Spectral and Steady-State Properties of Random Liouvillians
• Generating random quantum channels
• Distribution of bipartite entanglement for random pure states
• Quantum State Tomography of a Single Qubit: Comparison of Methods
• Random graph states, maximal flow and Fuss-Catalan distributions
• Restricted numerical range: a versatile tool in the theory of quantum information
• Relating the Bures measure to the Cauchy two-matrix model
• Spectral transitions and universal steady states in random Kraus maps and circuits
• Statistical properties of random matrix product states
• Energy correlations for a random matrix model of disordered bosons
• Monitoring of the process of system information broadcasting in time
• Gaussianization and eigenvalue statistics for random quantum channels (III)
• Activating hidden metrological usefulness
• Distribution of G-concurrence of random pure states
• Raney distributions and random matrix theory
• Entanglement between two subsystems, the Wigner semicircle and extreme value statistics
• Quantum state transfer in a XX chain with impurities
• Distinguishing Random and Black Hole Microstates
• Generic appearance of objective results in quantum measurements
• Diagonal unitary entangling gates and contradiagonal quantum states
• Almost all quantum channels are equidistant
• Purity estimation with separable measurements
• Measuring the purity of a qubit state: entanglement estimation with fully separable measurements
• Qubit-Qutrit Separability-Probability Ratios
• How often is a random quantum state k-entangled?
• Entanglement of localized states
• Bures-Hall Ensemble: Spectral Densities and Average Entropies
• Smallest eigenvalue distribution of the fixed trace Laguerre beta-ensemble
• Entanglement and localization transitions in eigenstates of interacting chaotic systems
• Distribution of the ratio of two consecutive level spacings in orthogonal to unitary crossover ensembles
• Compact smallest eigenvalue expressions in Wishart-Laguerre ensembles with or without fixed-trace
• The difference between two random mixed quantum states: exact and asymptotic spectral analysis
• Exact variance of von Neumann entanglement entropy over the Bures-Hall measure
• Eigenstate entanglement between quantum chaotic subsystems: universal transitions and power laws in the entanglement spectrum
• Non-crossing Brownian paths and Dyson Brownian motion under a moving boundary
• QuantumInformation.jl---a Julia package for numerical computation in quantum information theory
• Capacity of entanglement in random pure state
• System information propagation for spin structures
• Smallest eigenvalue density for regular or fixed-trace complex Wishart-Laguerre ensemble and entanglement in coupled kicked tops
• Wishart and random density matrices: Analytical results for the mean-square Hilbert-Schmidt distance
• Purity distribution for generalized random Bures mixed states
• Spectral density of generalized Wishart matrices and free multiplicative convolution
• Proof of Sarkar-Kumar's Conjectures on Average Entanglement Entropies over the Bures-Hall Ensemble
• Entanglement in coupled kicked tops with chaotic dynamics
• Trace distance from the viewpoint of quantum operation techniques
• Entangled random pure states with orthogonal symmetry: exact results
• Improving application performance with biased distributions of quantum states
• Entanglement of formation of mixed many-body quantum states via Tree Tensor Operators
• Entropy of entanglement and multifractal exponents for random states
• The PPT square conjecture holds generically for some classes of independent states
• Second-order statistics of fermionic Gaussian states
• Automated Machine Learning can Classify Bound Entangled States with Tomograms
• Average capacity of quantum entanglement
• Entanglement production by interaction quenches of quantum chaotic subsystems
• Largest Schmidt eigenvalue of entangled random pure states and conductance distribution in chaotic cavities
• Summing free unitary random matrices
• Two-Qubit Separability Probabilities and Beta Functions
• Statistically preferred basis of an open quantum system: Its relation to the eigenbasis of a renormalized self-Hamiltonian
• Continuous variable private quantum channel
• Low entropy output states for products of random unitary channels
• On the convergence of output sets of quantum channels
• Random density matrices: Analytical results for mean root fidelity and mean square Bures distance
• Spectral statistics for the difference of two Wishart matrices
• Polarized ensembles of random pure states
• On the comparison of volumes of quantum states
• Violations of Bell inequalities from random pure states
• On the joint distribution of the marginals of multipartite random quantum states
• Projections of Orbital Measures and Quantum Marginal Problems
• Convex set of quantum states with positive partial transpose analysed by hit and run algorithm
• Quantum interpolating ensemble: Biorthogonal polynomials and average entropies
• Random density matrices: Analytical results for mean fidelity and variance of squared Bures distance
• Spectral density of the non-central correlated Wishart ensembles
• Investigating bound entangled two-qutrit states via the best separable approximation
• Uniform Probability Distribution Over All Density Matrices
• Probability measure generated by the superfidelity
• Distribution of Schmidt-like eigenvalues for Gaussian Ensembles of the Random Matrix Theory
• Partial projected ensembles and spatiotemporal structure of information scrambling
• Generating random Gaussian states
• Exact eigenvalue order statistics for the reduced density matrix of a bipartite system
• Entanglement capacity of fermionic Gaussian states
• Onset of universality in the dynamical mixing of a pure state
• Fox H-kernel and $\theta$-deformation of the Cauchy two-matrix model and Bures ensemble
• Average mutual information for random fermionic Gaussian quantum states
• Volume-law entanglement entropy of typical pure quantum states
• Entanglement criteria for the bosonic and fermionic induced ensembles
• Entanglement and localization of wavefunctions
• Entanglement transitions induced by large deviations
• Moments of quantum purity and biorthogonal polynomial recurrence
• Entanglement Trajectory and its Boundary