Generating random density matrices
arXiv:1010.3570 · doi:10.1063/1.3595693
Abstract
We study various methods to generate ensembles of random density matrices of a fixed size N, obtained by partial trace of pure states on composite systems. Structured ensembles of random pure states, invariant with respect to local unitary transformations are introduced. To analyze statistical properties of quantum entanglement in bi-partite systems we analyze the distribution of Schmidt coefficients of random pure states. Such a distribution is derived in the case of a superposition of k random maximally entangled states. For another ensemble, obtained by performing selective measurements in a maximally entangled basis on a multi--partite system, we show that this distribution is given by the Fuss-Catalan law and find the average entanglement entropy. A more general class of structured ensembles proposed, containing also the case of Bures, forms an extension of the standard ensemble of structureless random pure states, described asymptotically, as N \to \infty, by the Marchenko-Pastur distribution.
13 pages in latex with 8 figures included
References in corpus (10)
- Classifying quantum phases using Matrix Product States and PEPS
- Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
- On a class of free Levy laws related to a regression problem
- Product of Ginibre matrices: Fuss-Catalan and Raney distributions
- Random Quantum Operations
- Eigenvalues and Singular Values of Products of Rectangular Gaussian Random Matrices
- Generating and using truly random quantum states in Mathematica
- Universality of spectra for interacting quantum chaotic systems
- Subnormalized states and trace-nonincreasing maps
- On Explicit Probability Densities Associated with Fuss-Catalan Numbers
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