Typicality of pure states randomly sampled according to the Gaussian adjusted projected measure

Reimann P (2008)
JOURNAL OF STATISTICAL PHYSICS 132(5): 921-935.

Journal Article | Published | English

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Abstract
Consider a mixed quantum mechanical state, describing a statistical ensemble in terms of an arbitrary density operator rho of low purity, tr rho(2) << 1, and yielding the ensemble averaged expectation value tr(rho A) for any observable A. Assuming that the given statistical ensemble rho is generated by randomly sampling pure states vertical bar psi > according to the corresponding so-called Gaussian adjusted projected measure (Goldstein et al. in J. Stat. Phys. 125:1197, 2006), the expectation value is shown to be extremely close to the ensemble average tr(rho A) for the overwhelming majority of pure states vertical bar psi > and any experimentally realistic observable A. In particular, such a 'typicality' property holds whenever the Hilbert space H of the system contains a high dimensional subspace H+ subset of H with the property that all vertical bar psi > epsilon H+ are realized with equal probability and all other vertical bar psi > epsilon H are excluded.
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Reimann P. Typicality of pure states randomly sampled according to the Gaussian adjusted projected measure. JOURNAL OF STATISTICAL PHYSICS. 2008;132(5):921-935.
Reimann, P. (2008). Typicality of pure states randomly sampled according to the Gaussian adjusted projected measure. JOURNAL OF STATISTICAL PHYSICS, 132(5), 921-935.
Reimann, P. (2008). Typicality of pure states randomly sampled according to the Gaussian adjusted projected measure. JOURNAL OF STATISTICAL PHYSICS 132, 921-935.
Reimann, P., 2008. Typicality of pure states randomly sampled according to the Gaussian adjusted projected measure. JOURNAL OF STATISTICAL PHYSICS, 132(5), p 921-935.
P. Reimann, “Typicality of pure states randomly sampled according to the Gaussian adjusted projected measure”, JOURNAL OF STATISTICAL PHYSICS, vol. 132, 2008, pp. 921-935.
Reimann, P.: Typicality of pure states randomly sampled according to the Gaussian adjusted projected measure. JOURNAL OF STATISTICAL PHYSICS. 132, 921-935 (2008).
Reimann, Peter. “Typicality of pure states randomly sampled according to the Gaussian adjusted projected measure”. JOURNAL OF STATISTICAL PHYSICS 132.5 (2008): 921-935.
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