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Journal Articles Journal of Mathematical Physics Year : 2011

## Generating random density matrices

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Karol Zyczkowski
• Function : Author
Ion Nechita

#### Abstract

We study various methods to generate ensembles of quantum density matrices of a fixed size N and analyze the corresponding probability distributions P(x), where x denotes the rescaled eigenvalue, x=N\lambda. Taking a random pure state of a two-partite system and performing the partial trace over one subsystem one obtains a mixed state represented by a Wishart--like matrix W=GG^{\dagger}, distributed according to the induced measure and characterized asymptotically, as N -> \infty, by the Marchenko-Pastur distribution. Superposition of k random maximally entangled states leads to another family of explicitly derived distributions, describing singular values of the sum of k independent random unitaries. Taking a larger system composed of 2s particles, constructing $s$ random bi-partite states, performing the measurement into a product of s-1 maximally entangled states and performing the partial trace over the remaining subsystem we arrive at a random state characterized by the Fuss-Catalan distribution of order s. A more general class of ensembles of random states containing also Bures and arcsine ensembles is constructed.

### Dates and versions

hal-00559120 , version 1 (24-01-2011)

### Identifiers

• HAL Id : hal-00559120 , version 1
• ARXIV :
• DOI :

### Cite

Karol Zyczkowski, Karol A. Penson, Ion Nechita, Benoit Collins. Generating random density matrices. Journal of Mathematical Physics, 2011, 52 (6), pp.062201. ⟨10.1063/1.3595693⟩. ⟨hal-00559120⟩

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