Asymptotic Majorization of Finite Probability Distributions

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Standard

Asymptotic Majorization of Finite Probability Distributions. / Jensen, Asger Kjaerulff.

I: IEEE Transactions on Information Theory, Bind 65, Nr. 12, 8735828, 2019, s. 8131-8139.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Jensen, AK 2019, 'Asymptotic Majorization of Finite Probability Distributions', IEEE Transactions on Information Theory, bind 65, nr. 12, 8735828, s. 8131-8139. https://doi.org/10.1109/TIT.2019.2922627

APA

Jensen, A. K. (2019). Asymptotic Majorization of Finite Probability Distributions. IEEE Transactions on Information Theory, 65(12), 8131-8139. [8735828]. https://doi.org/10.1109/TIT.2019.2922627

Vancouver

Jensen AK. Asymptotic Majorization of Finite Probability Distributions. IEEE Transactions on Information Theory. 2019;65(12):8131-8139. 8735828. https://doi.org/10.1109/TIT.2019.2922627

Author

Jensen, Asger Kjaerulff. / Asymptotic Majorization of Finite Probability Distributions. I: IEEE Transactions on Information Theory. 2019 ; Bind 65, Nr. 12. s. 8131-8139.

Bibtex

@article{5c5bfdbc6788490f905f9484c0e37605,
title = "Asymptotic Majorization of Finite Probability Distributions",
abstract = "This paper studies the majorization of high tensor powers of finitely supported probability distributions. Taking two probability distributions P and q to the n 'th and m 'th tensor power, respectively, in such a way that the power of q majorizes the power of P , we ask how large the ratio m/n can become. It is shown that the supremum of such ratios is equal to the minimal ratio of the α -R{\'e}nyi entropies of P and q for α \in [0,∞]. Consideration of this ratio of tensor powers is motivated, to the author, by the resource theory of quantum entanglement, where the supremum of these ratios corresponds to the asymptotic conversion rate of bipartite pure quantum states under exact, deterministic LOCC transformations.",
keywords = "asymptotic conversion rates, LOCC, majorization, Quantum entanglement, resource theory",
author = "Jensen, {Asger Kjaerulff}",
year = "2019",
doi = "10.1109/TIT.2019.2922627",
language = "English",
volume = "65",
pages = "8131--8139",
journal = "IEEE Transactions on Information Theory",
issn = "0018-9448",
publisher = "Institute of Electrical and Electronics Engineers",
number = "12",

}

RIS

TY - JOUR

T1 - Asymptotic Majorization of Finite Probability Distributions

AU - Jensen, Asger Kjaerulff

PY - 2019

Y1 - 2019

N2 - This paper studies the majorization of high tensor powers of finitely supported probability distributions. Taking two probability distributions P and q to the n 'th and m 'th tensor power, respectively, in such a way that the power of q majorizes the power of P , we ask how large the ratio m/n can become. It is shown that the supremum of such ratios is equal to the minimal ratio of the α -Rényi entropies of P and q for α \in [0,∞]. Consideration of this ratio of tensor powers is motivated, to the author, by the resource theory of quantum entanglement, where the supremum of these ratios corresponds to the asymptotic conversion rate of bipartite pure quantum states under exact, deterministic LOCC transformations.

AB - This paper studies the majorization of high tensor powers of finitely supported probability distributions. Taking two probability distributions P and q to the n 'th and m 'th tensor power, respectively, in such a way that the power of q majorizes the power of P , we ask how large the ratio m/n can become. It is shown that the supremum of such ratios is equal to the minimal ratio of the α -Rényi entropies of P and q for α \in [0,∞]. Consideration of this ratio of tensor powers is motivated, to the author, by the resource theory of quantum entanglement, where the supremum of these ratios corresponds to the asymptotic conversion rate of bipartite pure quantum states under exact, deterministic LOCC transformations.

KW - asymptotic conversion rates

KW - LOCC

KW - majorization

KW - Quantum entanglement

KW - resource theory

UR - http://www.scopus.com/inward/record.url?scp=85077391853&partnerID=8YFLogxK

U2 - 10.1109/TIT.2019.2922627

DO - 10.1109/TIT.2019.2922627

M3 - Journal article

AN - SCOPUS:85077391853

VL - 65

SP - 8131

EP - 8139

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

SN - 0018-9448

IS - 12

M1 - 8735828

ER -

ID: 238856055