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arXiv · 2312.02583

A new class of distances on complex projective spaces

Rafał Bistroń·Michał Eckstein·Shmuel Friedland·Tomasz Miller·Karol Życzkowski
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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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Rafał Bistroń, Michał Eckstein, Shmuel Friedland, Tomasz Miller, Karol Życzkowski. 2023-12-05. A new class of distances on complex projective spaces. https://arxiv.org/abs/2312.02583

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