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Comparison of unitary transforms using Franson interferometry

Andersson, Anna and Bergou, J. and Jex, I. (2005) Comparison of unitary transforms using Franson interferometry. Journal of Modern Optics, 52 (10). pp. 1485-1494. ISSN 0950-0340

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Unknown unitary transforms may be compared to each other in a way which makes it possible to obtain an unambiguous answer, indicating that the transforms are different, already after a single application of each transform. Quantum comparison strategies may be useful for example if we want to test the performance of individual gates in a quantum information or quantum computing network. It is then possible to check for errors by comparing the elements to a master copy of the gate, instead of performing a complete tomography of the gate. In this paper we propose a versatile linear optical implementation based on the Franson interferometer with short and long arms. A click in the wrong output port unambiguously determines that the tested gate is faulty. This set-up can also be used for a variety of other tasks, such as confirming that the two transforms do not commute or do not anticommute.