A new class of distances on complex projective spaces
| Autor: | Bistroń, Rafał, Eckstein, Michał, Friedland, Shmuel, Miller, Tomasz, Życzkowski, Karol |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | The complex projective space $\mathbb{P}(\mathbb{C}^n)$ 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. Comment: 31 pages |
| Databáze: | arXiv |
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