Quantum tomography in position and momentum space

Abstract

We introduce a method of quantum tomography for a continuous variable system in position and momentum space. We consider a single two-level probe interacting with a quantum harmonic oscillator by means of a class of Hamiltonians, linear in position and momentum variables, during a tunable time span. We study two cases: the reconstruction of the wavefunctions of pure states and the direct measurement of the density matrix of mixed states. We show that our method can be applied to several physical systems where high quantum control can be experimentally achieved.

5 pages, 2 figures. To be published in EPJD

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• Classical shadow tomography for continuous variables quantum systems
• Pulsed Quantum-State Reconstruction of Dark Systems
• Uncertainty relations for characteristic functions
• Investigating the origin of time with trapped ions
• Pulsed characteristic-function measurement of a thermalizing harmonic oscillator