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Quantum State Reconstruction and Random Evolution

Carlos Riofrio, University of New Mexico

(Session : Thursday from )

Abstract. In order to perform quantum state reconstruction, the set of measured observables must be informationally complete. In this poster, we explore the performance of the reconstruction algorithm developed by Silberfarb et al. (PRL 95, 030402 (2005)) under the asumption that the quantum system undergoes random evolution. We show that in that case, although the measurements do not span the space of all density matrices, we are able to reconstruct the set of all pure states and almost-all mixed states with very high fidelities. We find that this is only possible after the inclusion of the physical constraint of positivity. Using as an example the quantum states stored in the ground-electronic hyperfine manifold (F=3) of an ensemble of $^{133}$Cs atoms controlled by radio-frequency magnetic fields, we give a possible physical realization of this protocol provided that the dynamics exhibits a classically chaotic phase space. For this purpose, we chose the well studied quantum kicked top dynamics.

Quantum State Reconstruction and Random Evolution

Carlos Riofrio, University of New Mexico

(Session 5 : Friday from 5:00-7:00)

Abstract. In order to perform quantum state reconstruction, the set of measured observables must be informationally complete. In this poster, we explore the performance of the reconstruction algorithm developed by Silberfarb et al. (PRL 95, 030402 (2005)) under the asumption that the quantum system undergoes random evolution. We show that in that case, although the measurements do not span the space of all density matrices, we are able to reconstruct the set of all pure states and almost-all mixed states with very high fidelities. We find that this is only possible after the inclusion of the physical constraint of positivity. Using as an example the quantum states stored in the ground-electronic hyperfine manifold (F=3) of an ensemble of Cs 133 atoms controlled by radio-frequency magnetic fields, we give a possible physical realization of this protocol provided that the dynamics exhibits a classically chaotic phase space. For this purpose, we chose the well studied quantum kicked top dynamics.