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Physical Review Letters

Quantum Calibration of Measurement Instrumentation

Giacomo Mauro D’Ariano, Lorenzo Maccone, Paoloplacido Lo Presti

Published Dec 16, 2004• 97 citations
Publisher

Abstract

By quantum calibration we name an experimental procedure apt to completely characterize an unknown measurement apparatus by comparing it with a few other calibrated apparatuses. Here we show how to achieve the calibration of an arbitrary measuring apparatus, by using it in combination with a tomographer in a correlation setup with an input bipartite system. The method is robust to imperfections of the tomographer, and works for practically any input state of the bipartite system.

DOI
10.1103/physrevlett.93.250407

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By quantum calibration we name an experimental procedure apt to completely characterize an unknown measurement apparatus by comparing it with a few other calibrated apparatuses. Here we show how to achieve the calibration of an arbitrary measuring apparatus, by using it in combination with a tomographer in a correlation setup with an input bipartite system. The method is robust to imperfections of the tomographer, and works for practically any input state of the bipartite system.
The calibration of quantum measurements is limited by the ability to accurately prepare quantum states under unknown device errors. We develop an accurate calibration protocol for the measurement apparatus of a quantum computer that is `blind' to the state preparation. Blind calibration quantifies and corrects measurement errors from simple tomographic data on a noisy quantum state. Importantly, it calibrates multiple error mechanisms in a single experiment, eliminating the need for bespoke, separate calibration experiments. Using a trapped-ion quantum computer, we systematically demonstrate the accuracy of the method. We use blind calibration to estimate the native calibration parameters of the experimental system. The recovered calibrations are consistent with directly measured values and perform similarly in predicting the state properties.
Measurement is the only part of a general quantum system that has yet to be characterised experimentally in a complete manner. Detector tomography provides a procedure for doing just this; an arbitrary measurement device can be fully characterised, and thus calibrated, in a systematic way without access to its components or its design. The result is a reconstructed POVM containing the measurement operators associated with each measurement outcome. We consider two detectors, a single-photon detector and a photon-number counter, and propose an easily realised experimental apparatus to perform detector tomography on them. We also present a method of visualising the resulting measurement operators.
Performance of quantum process estimation is naturally limited by fundamental, random, and systematic imperfections of preparations and measurements. These imperfections may lead to considerable errors in the process reconstruction because standard data-analysis techniques usually presume ideal devices. Here, by utilizing generic auxiliary quantum or classical correlations, we provide a framework for the estimation of quantum dynamics via a single measurement apparatus. By construction, this approach can be applied to quantum tomography schemes with calibrated faulty-state generators and analyzers. Specifically, we present a generalization of the work begun by M. Mohseni and D. A. Lidar [Phys. Rev. Lett. 97, 170501 (2006)] with an imperfect Bell-state analyzer. We demonstrate that for several physically relevant noisy preparations and measurements, classical correlations and a small data-processing overhead suffice to accomplish the full system identification. Furthermore, we provide the optimal input states whereby the error amplification due to inversion of the measurement data is minimal.
Recent efforts have applied quantum tomography techniques to the calibration and characterization of complex quantum detectors using minimal assumptions. In this work, we provide detail and insight concerning the formalism, the experimental and theoretical challenges and the scope of these tomographical tools. Our focus is on the detection of photons with avalanche photodiodes and photon-number resolving detectors and our approach is to fully characterize the quantum operators describing these detectors with a minimal set of well-specified assumptions. The formalism is completely general and can be applied to a wide range of detectors.