Séminaire du LPTMS: Fabio Deelan Cunden


11:00 - 12:00

LPTMS, salle 201, 2ème étage, Bât 100, Campus d'Orsay
15 Rue Georges Clemenceau, Orsay, 91405
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Polarized ensembles of random pure states


Fabio  Deelan Cunden, Dipartimento di Matematica, Università di Bari

In the last years many researchers  have been investigating  the typical properties of random pure states, i.e. unit vectors drawn at « random » from the Hilbert space associated to a quantum system. This subject has attracted the attention in several directions, and some important results have been achieved. The standard ensemble which has been intensively investigated is that of random pure states  with measure induced by the Haar measure on the unitary group. This ensemble, being the maximally symmetric one, implements in a natural way the  case of minimal knowledge on a quantum state.
We recently presented a new family of polarized ensembles of random pure quantum states. Our idea is to move beyond the unbiased ensemble by using a natural operation at hand in the Hilbert space, namely  superposition of vector states. These ensembles are quite manageable and manifestly show that the unitarily invariant measures interact nicely with the operation of linear superposition of states. Our approach has been oriented to the study of  typical bipartite entanglement between subsystems, as measured by the local purity. This strategy yields an efficient and simple sampling of random pure states with fixed value of purity, and paves the way to further explorations and a deeper characterization of the geometry of isopurity manifolds.

Cunden F D, Facchi P, Florio G (2013) J. Phys. A: Math. Theor. 46, 315306.

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