# Title:Detection of quantum correlations and typical properties of isospectral density matrices

Abstract: Given a class of pure states of an arbitrary quantum system we call a mixed state "non-correlated" if it can be expressed as a convex mixture of states from this class. We give a general sufficient criterion for deciding whether a given mixed state is correlated. Our criterion is given by a simple formula and is valid for an arbitrary dimension of the considered Hilbert space. We implement our method to particular classes of pure states: separable states, separable bosonic states, Slater determinants and fermionic Gaussian states. In each of these cases we study typical correlation properties of mixed states belonging the set of isospectral density matrices. Using our criterion and concentration of measure techniques we prove that for purity exceeding some critical value $P_{\mathrm{cr}}$ (depending upon the considered problem) measure of correlated states on a given set of isospectral density matrices is bounded from below by $1-\Delta$ where $\Delta$ tends to zero exponentially fast with the dimension of the relevant Hilbert space.
 Comments: 7 pages, 1 figure, one reference added, We corrected the results concerning the application of our method to fermionic gaussian states. Our results are still valid but the accurate threshold, below which the exemplary state $ρ_{a_8}(p)$ is not gaussian, is smaller Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph) Cite as: arXiv:1312.7359 [quant-ph] (or arXiv:1312.7359v2 [quant-ph] for this version)

## Submission history

From: Michał Oszmaniec [view email]
[v1] Fri, 27 Dec 2013 21:59:14 UTC (20 KB)
[v2] Mon, 20 Jan 2014 07:55:07 UTC (20 KB)
[v3] Fri, 20 Jun 2014 14:19:09 UTC (24 KB)
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