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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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Published in: | Linear algebra and its applications 2024-10 |
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Main Authors: | , , , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites |
Online Access: | Get full text |
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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. |
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ISSN: | 0024-3795 |
DOI: | 10.1016/j.laa.2024.10.017 |