Fully-quantum learning: Comparison of unknown unitary channels with multiple uses

IQC Colloquium - Mio Murao, University of Tokyo

Please note the start time of 3:00 PM. Snacks and coffee to follow the event

Efficiently learning properties of unknown quantum objects is a fundamental task in quantum mechanics and quantum information. When there are two unknown quantum objects, and if we want to learn just the relationship between the objects, a method to directly compare the two objects without identifying their descriptions is preferable, especially when the number of available copies of each target object is limited. In this work, we investigate the comparison of unknown unitary channels with multiple uses of the unitary channels based on the quantum tester formalism.  We obtain the optimal minimum-error strategy and the optimal unambiguous strategy of unitary comparison of two unknown d-dimensional unitary channels when the number of uses of the channels satisfies a certain condition. These optimal strategies are implemented by parallel uses of the unitary channels, even though all sequential and adaptive strategies implementable by the quantum circuit model are considered. When the number of the smaller uses of the unitary channels is fixed, the optimal averaged success probability is achieved by a certain number of uses of the other channel. This feature contrasts with the case of pure-state comparison, where adding more copies of the unknown pure states always improves the optimal averaged success probability. It highlights the difference between corresponding tasks for states and channels, which has been previously shown for quantum discrimination tasks.  

Reference: Y. Hashimoto, A. Soeda and M. Murao, Comparison of unknown unitary channels with multiple uses, arXiv:2208.12519