Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Monotonicity of the quantum 2-Wasserstein distance   We study a quantum analogue of the 2-Wasserstein distance as a measure of
proximity on the set $\Omega_N$ of density matrices of dimension $N$. We show
that such (semi-)distances do not induce Riemannian metrics on the tangent
bundle of $\Omega_N$ and are typically not unitary invariant. Nevertheless, we
prove that for $N=2$ dimensional Hilbert space the quantum 2-Wasserstein
distance (unique up to rescaling) is monotonous with respect to any
single-qubit quantum operation. Furthermore, for any $N \geq 3$ and the quantum
cost matrix proportional to a projector we demonstrate the monotonicity under
arbitrary mixed unitary channels. Finally, we provide numerical evidence which
allows us to conjecture that the unitary invariant quantum 2-Wasserstein
semi-distance is monotonous with respect to all CPTP maps in any dimension $N$.

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The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: econ
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th