Tip of the Quantum Entropy Cone

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Tip of the Quantum Entropy Cone. / Christandl, Matthias; Durhuus, Bergfinnur; Wolff, Lasse Harboe.

In: Physical Review Letters, Vol. 131, No. 24, 240201, 2023, p. 1-6.

Research output: Contribution to journalJournal articleResearchpeer-review

Harvard

Christandl, M, Durhuus, B & Wolff, LH 2023, 'Tip of the Quantum Entropy Cone', Physical Review Letters, vol. 131, no. 24, 240201, pp. 1-6. https://doi.org/10.1103/PhysRevLett.131.240201

APA

Christandl, M., Durhuus, B., & Wolff, L. H. (2023). Tip of the Quantum Entropy Cone. Physical Review Letters, 131(24), 1-6. [240201]. https://doi.org/10.1103/PhysRevLett.131.240201

Vancouver

Christandl M, Durhuus B, Wolff LH. Tip of the Quantum Entropy Cone. Physical Review Letters. 2023;131(24):1-6. 240201. https://doi.org/10.1103/PhysRevLett.131.240201

Author

Christandl, Matthias ; Durhuus, Bergfinnur ; Wolff, Lasse Harboe. / Tip of the Quantum Entropy Cone. In: Physical Review Letters. 2023 ; Vol. 131, No. 24. pp. 1-6.

Bibtex

@article{7de37b4c566b481b857cb739bac42ac6,
title = "Tip of the Quantum Entropy Cone",
abstract = "Relations among von Neumann entropies of different parts of an N-partite quantum system have direct impact on our understanding of diverse situations ranging from spin systems to quantum coding theory and black holes. Best formulated in terms of the set Σ∗N of possible vectors comprising the entropies of the whole and its parts, the famous strong subaddivity inequality constrains its closure ¯Σ∗N, which is a convex cone. Further homogeneous constrained inequalities are also known. In this Letter we provide (nonhomogeneous) inequalities that constrain Σ∗N near the apex (the vector of zero entropies) of ¯Σ∗N, in particular showing that Σ∗N is not a cone for N≥3. Our inequalities apply to vectors with certain entropy constraints saturated and, in particular, they show that while it is always possible to upscale an entropy vector to arbitrary integer multiples it is not always possible to downscale it to arbitrarily small size, thus answering a question posed by Winter.",
author = "Matthias Christandl and Bergfinnur Durhuus and Wolff, {Lasse Harboe}",
year = "2023",
doi = "10.1103/PhysRevLett.131.240201",
language = "English",
volume = "131",
pages = "1--6",
journal = "Physical Review Letters",
issn = "0031-9007",
publisher = "American Physical Society",
number = "24",

}

RIS

TY - JOUR

T1 - Tip of the Quantum Entropy Cone

AU - Christandl, Matthias

AU - Durhuus, Bergfinnur

AU - Wolff, Lasse Harboe

PY - 2023

Y1 - 2023

N2 - Relations among von Neumann entropies of different parts of an N-partite quantum system have direct impact on our understanding of diverse situations ranging from spin systems to quantum coding theory and black holes. Best formulated in terms of the set Σ∗N of possible vectors comprising the entropies of the whole and its parts, the famous strong subaddivity inequality constrains its closure ¯Σ∗N, which is a convex cone. Further homogeneous constrained inequalities are also known. In this Letter we provide (nonhomogeneous) inequalities that constrain Σ∗N near the apex (the vector of zero entropies) of ¯Σ∗N, in particular showing that Σ∗N is not a cone for N≥3. Our inequalities apply to vectors with certain entropy constraints saturated and, in particular, they show that while it is always possible to upscale an entropy vector to arbitrary integer multiples it is not always possible to downscale it to arbitrarily small size, thus answering a question posed by Winter.

AB - Relations among von Neumann entropies of different parts of an N-partite quantum system have direct impact on our understanding of diverse situations ranging from spin systems to quantum coding theory and black holes. Best formulated in terms of the set Σ∗N of possible vectors comprising the entropies of the whole and its parts, the famous strong subaddivity inequality constrains its closure ¯Σ∗N, which is a convex cone. Further homogeneous constrained inequalities are also known. In this Letter we provide (nonhomogeneous) inequalities that constrain Σ∗N near the apex (the vector of zero entropies) of ¯Σ∗N, in particular showing that Σ∗N is not a cone for N≥3. Our inequalities apply to vectors with certain entropy constraints saturated and, in particular, they show that while it is always possible to upscale an entropy vector to arbitrary integer multiples it is not always possible to downscale it to arbitrarily small size, thus answering a question posed by Winter.

U2 - 10.1103/PhysRevLett.131.240201

DO - 10.1103/PhysRevLett.131.240201

M3 - Journal article

C2 - 38181127

VL - 131

SP - 1

EP - 6

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 24

M1 - 240201

ER -

ID: 375969621