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Prof. Cristina Butucea

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Quantum statistical models and inference

Was
  • FDM-Seminar
Wann 04.01.2017
von 10:35 bis 10:35
Wo Eckerstraße 1, Raum 404, 4. OG
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Quantum statistics is concerned with the inference for systems
described by quantum mechanics. After an introduction to the
main mathematical notions of quantum statistics: quantum states,
measurements, channels, we describe nonparametric quantum models.
We prove the local asymptotic equivalence (LAE) in the sense of
Le Cam theory of i.i.d. quantum pure states and a quantum Gaussian
state. We show nonparametric rates for the estimation of the quantum
states, of some quadratic functionals and for the testing of pure
states. The LAE allows to transfer proofs to a different model.
Surprisingly, a sharp testing rate of order n^{-1/2} is
obtained in a nonparametric quantum setup.
This is joint work with M. Guta and M. Nussbaum.

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