Correlations in typicality and an affirmative solution to the exact catalytic entropy conjecture

Article Physics, Multidisciplinary

Transcendental Properties of Entropy-Constrained Sets

Vjosa Blakaj et al.

Summary: In this work, a criterion based on the analytic continuation of the Gauss map is provided to disprove the semialgebraic property of a set. Applied to the case of von Neumann entropy, it is shown that the level sets are nowhere semialgebraic in dimension d >= 3, ruling out the possibility of algebraic single-shot characterizations with finite ancilla. Similar results are also shown for related quantities, including relative entropy, and a discussion is provided on the transcendental, algebraic, or rational nature of entropy values.

ANNALES HENRI POINCARE (2023)

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Article Physics, Multidisciplinary

Fundamental Limits on Correlated Catalytic State Transformations

Roberto Rubboli et al.

Summary: This article studies the problem of catalytic transformations in resource theory, proving that a smaller residual correlation requires a higher amount of resources for the catalyst. It also demonstrates that in imperfect catalysis, a small error results in a highly important embezzling catalyst.

PHYSICAL REVIEW LETTERS (2022)

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Article Quantum Science & Technology

Variance of Relative Surprisal as Single-Shot Quantifier

Paul Boes et al.

Summary: The study comprehensively explores the application of variance of surprisal in (quantum) information theory and finds that it can be used to derive genuine approximate state transition conditions in the single-shot setting. It also clarifies its relation to entropy and proposes a monotone for resource theories. Certain properties of the variance of surprisal are determined, which are useful for further investigations.

PRX QUANTUM (2022)

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Article Physics, Multidisciplinary

Entropy and Reversible Catalysis

H. Wilming

Summary: Nondecreasing entropy serves as a necessary and sufficient condition for transforming the state of a physical system by a reversible transformation. This applies to both finite-dimensional quantum mechanics and systems described by probability distributions. The results provide a complete single-shot characterization of von Neumann entropy and Shannon entropy without external randomness.

PHYSICAL REVIEW LETTERS (2021)

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Article Physics, Multidisciplinary

Catalytic Transformations of Pure Entangled States

Tulja Varun Kondra et al.

Summary: This study explores the quantification of quantum entanglement and its relationship with entanglement distillation. It is shown that entanglement entropy completely characterizes state transformations in the presence of entangled catalysts, giving operational significance to asymptotic results in the single-copy setting.

PHYSICAL REVIEW LETTERS (2021)

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Article Physics, Multidisciplinary

Quantum Thermodynamics of Correlated-Catalytic State Conversion at Small Scale

Naoto Shiraishi et al.

Summary: By introducing a catalyst and allowing infinitesimal correlations, this study uncovers the complete characterization of catalytic state conversion in quantum and single-shot thermodynamics, resolving related conjectures and establishing resource theories.

PHYSICAL REVIEW LETTERS (2021)

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Article Physics, Multidisciplinary

Catalytic Quantum Teleportation

Patryk Lipka-Bartosik et al.

Summary: This study introduces a new teleportation protocol based on catalytic entanglement to overcome fundamental limitations of quantum teleportation. It demonstrates that catalytic entanglement can simulate a noiseless quantum channel with superior quality compared to using only shared entanglement, showing genuine advantages in quantum-information processing tasks. Additionally, the idea of entanglement catalysis can be applied to study more general problems in quantum mechanics.

PHYSICAL REVIEW LETTERS (2021)

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Article Physics, Multidisciplinary