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A new class of distances on complex projective spaces

The complex projective space P(Cn) can be interpreted as the space of all quantum pure states of size n. A distance on this space, interesting from the perspective of quantum physics, can be induced from a classical distance defined on the n-point probability simplex by the ‘earth mover problem’. We...

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Bibliographic Details
Published in:Linear algebra and its applications 2024-10
Main Authors: Bistroń, Rafał, Eckstein, Michał, Friedland, Shmuel, Miller, Tomasz, Życzkowski, Karol
Format: Article
Language:English
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Summary:The complex projective space P(Cn) can be interpreted as the space of all quantum pure states of size n. A distance on this space, interesting from the perspective of quantum physics, can be induced from a classical distance defined on the n-point probability simplex by the ‘earth mover problem’. We show that this construction leads to a quantity satisfying the triangle inequality, which yields a true distance on complex projective space belonging to the family of quantum 2-Wasserstein distances.
ISSN:0024-3795
DOI:10.1016/j.laa.2024.10.017