Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Optimal Transport for Tensor Field Processing   This article introduces a new notion of optimal transport (OT) between tensor
fields, which are measures whose values are positive semidefinite (PSD)
matrices. This "quantum" formulation of OT (Q-OT) corresponds to a relaxed
version of the classical Kantorovich transport problem, where the fidelity
between the input PSD-valued measures is captured using the geometry of the
Von-Neumann quantum entropy. We propose a quantum-entropic regularization of
the resulting convex optimization problem, which can be solved efficiently
using an iterative scaling algorithm. This method is a generalization of the
celebrated Sinkhorn algorithm to the quantum setting of PSD matrices. We extend
this formulation and the quantum Sinkhorn algorithm to compute barycenters
within a collection of input tensor fields. We illustrate the usefulness of the
proposed approach on applications to procedural noise generation, anisotropic
meshing, diffusion tensor imaging and spectral texture synthesis.

11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
2
The categories of this paper are: math
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin