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Quantum Relative Lorenz Curves
Quantum Physics · Submitted 19 Jul 2016
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Here we formulate the framework of quantum relative Lorenz curves, and show how it is able to unify majorization, thermomajorization, and their noncommutative analogues.
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The abstract, sentence by sentence
The theory of majorization and its variants, including thermomajorization, have been found to play a central role in the formulation of many physical resource theories, ranging from entanglement theory to quantum thermodynamics. Here we formulate the framework of quantum relative Lorenz curves, and show how it is able to unify majorization, thermomajorization, and their noncommutative analogues. In doing so, we define the family of Hilbert $\alpha$-divergences and show how it relates with other divergences used in quantum information theory. We then apply these tools to the problem of deciding the existence of a suitable transformation from an initial pair of quantum states to a final one, focusing in particular on applications to the resource theory of athermality, a precursor of quantum thermodynamics.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The theory of majorization and its variants, including thermomajorization, have been found to play a central role in the formulation of many physical resource theories, ranging from entanglement theory to quantum thermodynamics. | background 1.00 | 0.08 | 0.03 | asserted 1.00 |
| s1 | Here we formulate the framework of quantum relative Lorenz curves, and show how it is able to unify majorization, thermomajorization, and their noncommutative analogues. | contribution 1.00 | 0.96 | 0.57 | asserted 1.00 |
| s2 | In doing so, we define the family of Hilbert $\alpha$-divergences and show how it relates with other divergences used in quantum information theory. | contribution 0.93 | 0.94 | 0.09 | asserted 1.00 |
| s3 | We then apply these tools to the problem of deciding the existence of a suitable transformation from an initial pair of quantum states to a final one, focusing in particular on applications to the resource theory of athermality, a precursor of quantum thermodynamics. | contribution 0.94 | 0.93 | 0.17 | asserted 0.97 |
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The paper
Original abstract
The theory of majorization and its variants, including thermomajorization, have been found to play a central role in the formulation of many physical resource theories, ranging from entanglement theory to quantum thermodynamics. Here we formulate the framework of quantum relative Lorenz curves, and show how it is able to unify majorization, thermomajorization, and their noncommutative analogues. In doing so, we define the family of Hilbert $\alpha$-divergences and show how it relates with other divergences used in quantum information theory. We then apply these tools to the problem of deciding the existence of a suitable transformation from an initial pair of quantum states to a final one, focusing in particular on applications to the resource theory of athermality, a precursor of quantum thermodynamics.
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References
How the literature uses it
10 arXiv papers cite this in 20 sentences
Papers citing it · 13 sentences without a confident label
Cites it as background 6 papers
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Quantum relative majorization was defined recently in [ref] as an intended generalization of classical relative majorization concept in [ref], in which we write $(ρ,σ) ≻(ρ',σ')$, where $ρ$, $σ$, $ρ'$, and $σ'$ are quantum states, to indicate that the hypothesis testing region for $(ρ',σ')$ lies inside that of $(ρ,σ)$.
Relative Entropy and Catalytic Relative Majorization · Related work · 0.91
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There are several interesting approaches to formulate full quantum d-majorization on the basis of, e.g., a generalized Lorenz curve [ref] and matrix majorization [ref] .
Entropy, Divergence, and Majorization in Classical and Quantum Thermodynamics · Quantum d-majorization · 0.93
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The problem of identifying such functions has been studied intensively in the last years for different classes of free operations, providing families of valid measures that are regarded as generalizations of the free energy [ref] .
Axiomatic characterization of the quantum relative entropy and free energy · Introduction · 0.89
What it cites · 6 sentences without a confident label
Cites as background 1 paper
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This is one of the topics lying at the core of theories like quantum thermodynamics and, more generally, quantum resource theories [ref] .
A mathematical theory of resources · Introduction · 0.94
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