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Quantum Calibration
The first experimental demonstration of detector tomography
How would you calibrate a detector? A first approach might be to send many known states, record the outcomes, and label the detector accordingly: “this state generates this outcome”.
However, moving into the kingdom of Quantum Physics life becomes more complex. When detecting photon number, polarization or spin of a given state there is no guarantee of a given result. This uncertainty is of course encoded in the quantum formalism as both detectors and states are described by similar operators and only probabilities can be extracted from them.
We could still imagine a calibrating experiment as follows: Send one photon, then two, three and any other desired number and record the probabilities. But unfortunately pure photon number states are very hard to produce, and generating a dozen is still a pipe dream. To overcome these challenges one needs a full quantum description of the detector, the state, and the calibrating experiment. In addition, reasonable probe or calibrating states are also required. Good ideas have been put forward to overcome this challenge. For example the use of entangled states together with maximum likelihood techniques [2,3]. However, up to now, partial calibrations have left the possibility of errors in state preparation and characterization open.
Our paper presents the first experimental demonstration of detector tomography. This calibrating technique has proven to be fast and reliable while using a black-box approach with minimal assumptions [1]. To this end we use techniques from state tomography [2], a readily available laser and efficient optimization tools to deal with statistical uncertainty.
The detectors were an avalanche photo-diode and a detector which sends the photons in a pulse to 8 different time-bins counting up to 9 photon numbers. Among the striking results we observed how different a “one click” looks for an avalanche photo diode (fig 2.a) and for the number resolving detector (fig 2.b). The reconstruction still showed a 98% agreement with the model of the detector.
This accurate knowledge of the detectors paves the way for detectors whose operators are engineered to accomplish specific quantum information tasks. It also provides a tool to benchmark different technologies aimed at measuring the same observables. Finally we hope it will become the standard tool for calibrating the ever more complex and refined quantum detectors that we need to analyze quantum information processors.
[1] J.S. Lundeen, A. Feito, H. B. Coldenstrodt-Ronge, T. Ralph, K.L. Pregnell, Ch. Silberhorn, J. Eisert, M.B. Plenio, I.A. Walmsley. “Tomography of Quantum Detectors.” Nature Physics 5, 27 (2009) and E-print arXiv:0807.2444 [quant-ph]
[2] A. Luis and L.L. Sanchez-Soto, Phys. Rev. Lett. 83, 3573 (1999).
[3] J. Fiurasek, Phys. Rev. A 64, 024102 (2001);G.M. D'Ariano, L. Maccone, and P.L. Presti, Phys. Rev. Lett. 93 250407 (2004).
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