You're viewing papers too quickly. Please wait a moment.<br>This helps keep the archive available for everyone.

Quick Navigation

Overview Topics Abstract Importance Paper Tools References Reactions Discussion Publication Related

Topics

Entanglement Theory Quantum Correlations Open Quantum Systems Decoherence Quantum Simulation

Logarithmic inequalities under an elementary symmetric polynomial dominance order

arXiv
Authors: Suvrit Sra

Year

2015

Paper ID

27146

Status

Preprint

Abstract Read

~2 min

Abstract Words

120

Citations

N/A

Abstract

We consider a dominance order on positive vectors induced by the elementary symmetric polynomials. Under this dominance order we provide conditions that yield simple proofs of several monotonicity questions. Notably, our approach yields a quick (4 line) proof of the so-called "sum-of-squared-logarithms" inequality conjectured in P. Neff, B. Eidel, F. Osterbrink, and R. Martin, emph{Applied Math. \& Mechanics., 2013}; P. Neff, Y. Nakatsukasa, and A. Fischle; emph{SIMAX, 35, 2014}. This inequality has been the subject of several recent articles, and only recently it received a full proof, albeit via a more elaborate complex-analytic approach. We provide an elementary proof, which moreover extends to yield simple proofs of both old and new inequalities for Rényi entropy, subentropy, and quantum Rényi entropy.

Why This Paper Matters

  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
  • It adds a 2015 reference point for readers tracking recent quantum research.
  • We consider a dominance order on positive vectors induced by the elementary symmetric polynomials.

Paper Tools

Become a member to use research tools

Sign in to open papers, visit source links, share, cite, compare, copy DOI links, request category corrections, and build your reading list.

Become a member Sign in
Show Paper arXiv Publisher Share Cite This Paper Copy URL Compare Copy DOI Add to Reading List Category Correction Request

References & Citation Signals

[1] DOI https://doi.org/arXiv:1509.05902 [2] arXiv https://arxiv.org/abs/1509.05902 [3] Publisher https://arxiv.org/abs/1509.05902

Local Citation Graph (Related-Paper Links)

Current Paper #27146 #69593 Local correlations in long-rang... #69591 Compact graphs and quantum auto... #69577 Real-time pseudo entropy and mo... #69569 Spin disorder competing with po...

External citation index: OpenAlex citation signal

Community Reactions

Quick sentiment from readers on this paper.

Score: 0
Likes: 0 Dislikes: 0

Sign in to react to this paper.

Discussion & Reviews (Moderated)

Average Rating: 0.0 / 5 (0 ratings)

No written reviews yet.