Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum optimal transport with quantum channels   We propose a new generalization to quantum states of the Wasserstein
distance, which is a fundamental distance between probability distributions
given by the minimization of a transport cost. Our proposal is the first where
the transport plans between quantum states are in natural correspondence with
quantum channels, such that the transport can be interpreted as a physical
operation on the system. Our main result is the proof of a modified triangle
inequality for our transport distance. We also prove that the distance between
a quantum state and itself is intimately connected with the Wigner-Yanase
metric on the manifold of quantum states. We then specialize to quantum
Gaussian systems, which provide the mathematical model for the electromagnetic
radiation in the quantum regime. We prove that the noiseless quantum Gaussian
attenuators and amplifiers are the optimal transport plans between thermal
quantum Gaussian states, and that our distance recovers the classical
Wasserstein distance in the semiclassical limit.

8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin