State tomography with photon counting after a beam splitter

Presenting Author: Arik Avagyan, National Institute of Standards and Technology, Boulder
Contributing Author(s): Hilma Vasconcelos, Scott Glancy, Emanuel Knill

Quantum optics offers several proposed ways of achieving a scalable quantum computer. In order to characterize such a computer one needs to be able to perform state tomography on quantum states of light. A popular tomographic procedure, called homodyne detection, uses a strong coherent state, called the local oscillator (LO), which interferes on a beam splitter with the unknown state. The output beams are measured by photodiodes whose signals are subtracted and normalized. By changing the LO phase, it is possible to infer the optical state in the mode matching the LO. In this work we determine what can also be learned about the contents of the modes not matching the LO by counting photons in one or both outgoing paths after the beam splitter, keeping the local oscillator mode fixed but choosing its phase and amplitude. We prove that given the probabilities of photon counts of just one of the counters as a function of LO amplitude, it is possible to determine the content of the unknown optical state in the mode matching the LO mode conditional on each number of photons in orthogonal modes on the same path. If the unknown optical state has at most n photons, we determine finite sets of LO amplitudes sufficient for inferring the state. Such a setup thus allows a more extensive characterization of the quantum state of light as compared to the standard homodyne tomography.

(Session 9a : Sunday from 5:45pm - 6:15pm)


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