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Lecture notes in physics

2 Quantum Tomographic Methods

Giacomo Mauro D’Ariano, Matteo G. A. Paris, Massimiliano Federico Sacchi

Published Aug 18, 2004• 28 citations
Publisher
DOI
10.1007/978-3-540-44481-7_2

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A new approach to detecting and diagnosing faults in quantum circuits is introduced. In order to account for the probabilistic nature of quantum circuits, collections of test experiments, called binary tomographic tests (BTTs), are generated. A BTT can identify a fault with respect to some user-defined confidence threshold τ. We present an algorithm to generate BTTs that either detect, or ensure the absence of, all modeled faults in a given circuit. We also present an adaptive diagnostic method to locate quantum faults. While classical circuits, even probabilistic ones, only handle ordinary probabilities, quantum circuits deal with quantum states, which have phase as an extra probabilistic parameter. The tomographic testing methods introduced previously for probabilistic circuits are unable to detect differences in phase, and therefore leave many quantum faults undetected. In contrast, we develop a design-for-test method which is specifically intended to detect faults that only affect the phase of a quantum state. We give experimental results for benchmark and random circuits which show high coverage of quantum faults by BTTs, and good resolution in the case of the adaptive diagnosis method.
Abstract At present, there is an increasing awareness of some three-orthogonal-basis quantum key distribution protocols, such as, the reference-frame-independent (RFI) protocol and the six-state protocol. For secure key rate estimations of these protocols, there are two methods: one is the conventional approach, and another is the tomographic approach. However, a comparison between these two methods has not been given yet. In this work, with the general model of rotation channel, we estimate the key rate using conventional and tomographic methods respectively. Results show that conventional estimation approach in RFI protocol is equivalent to tomographic approach only in the case of that one of three orthogonal bases is always aligned. In other cases, tomographic approach performs much better than the respective conventional approaches of the RFI protocol and the six-state protocol. Furthermore, based on the experimental data, we illustrate the deep connections between tomography and conventional RFI approach representations.