A new class of distances on complex projective spaces

• URL: http://arxiv.org/abs/2312.02583v1
• Date: Tue, 5 Dec 2023 08:55:57 GMT
• Title: A new class of distances on complex projective spaces
• Abstract summary: The complex projective space $mathbbP(mathbbCn)$ can be interpreted as the space of all quantum pure states of size $n$. A distance on this space 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.
• Score: 0.873811641236639
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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