January 8, 2024 to March 22, 2024
Institut Henri Poincaré
Europe/Paris timezone
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Bures geodesics and quantum metrology

Feb 2, 2024, 11:00 AM
1h 30m
Institut Henri Poincaré

Institut Henri Poincaré

11, Rue Pierre et Marie Curie 75005 Paris


Dominique Spehner (Universidad de Concepcion, Chili)


We study the geodesics on the manifold of mixed quantum states for the Bures metric. It is shown that these geodesics correspond to physical non-Markovian evolutions of the system coupled to an ancilla. Furthermore, we argue that geodesic evolutions are of interest in quantum metrology. In fact, if the unknown parameter is a phase shift proportional to the time parametrizing the geodesic, the estimation error obtained by processing the data of measurements on the system is equal to the smallest error that can be achieved from joint detections on the system and ancilla. This means that the ancilla does not carry any information on the parameter. The estimation error can saturate the Heisenberg bound. In addition, the measurement on the system bringing most information on the parameter is parameter-independent and can be determined in terms of the intersections of the geodesic with the boundary of quantum states.

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