• Corpus ID: 234763083

Attainability and lower semi-continuity of the relative entropy of entanglement, and variations on the theme

@inproceedings{Lami2021AttainabilityAL,
  title={Attainability and lower semi-continuity of the relative entropy of entanglement, and variations on the theme},
  author={Ludovico Lami and Maksim E. Shirokov},
  year={2021}
}
The relative entropy of entanglement ER is defined as the distance of a multi-partite quantum state from the set of separable states as measured by the quantum relative entropy. We show that this optimisation is always achieved, i.e. any state admits a (unique) closest separable state, even in infinite dimension; also, ER is everywhere lower semi-continuous. These results, which seem to have gone unnoticed so far, hold not only for the relative entropy of entanglement and its multi-partite… 
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References

SHOWING 1-10 OF 109 REFERENCES
Principles of Quantum Communication Theory: A Modern Approach
TLDR
This work adopts an information-theoretic perspective throughout and gives a comprehensive account of fundamental results in quantum communication theory from the past decade, with an emphasis on the modern one-shot-to-asymptotic approach that underlies much of today's state-of-the-art research in this field.
QUANTUM SYSTEMS
The damping of the harmonic oscillator is studied in the framework of the Lindblad theory for open quantum systems. A generalization of the fundamental constraints on quantum mechanical diffusion
Quantum Theory for Mathematicians
1 The Experimental Origins of Quantum Mechanics.- 2 A First Approach to Classical Mechanics.- 3 A First Approach to Quantum Mechanics.- 4 The Free Schrodinger Equation.- 5 A Particle in a Square
Intermediate Spectral Theory and Quantum Dynamics
Preface.- Selectec Notation.- A Glance at Quantum Mechanics.- 1 Linear Operators and Spectrum.- 1.1 Bounded Operators.- 1.2 Closed Operators.- 1.3 Compact Operators.- 1.4 Hilbert-Schmidt Operators.-
Probabilistic and Statistical Aspects of Quantum Theory
Foreword to 2nd English edition.- Foreword to 2nd Russian edition.- Preface.- Chapters: I. Statistical Models.- II. Mathematics of Quantum Theory.- III. Symmetry Groups in Quantum Mechanics.- IV.
Matrix analysis
TLDR
This new edition of the acclaimed text presents results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications.
Unbounded Self-adjoint Operators on Hilbert Space
I Basics onClosed Operators.- 1 Closed Operators and Adjoint Operators.- 2 Spectrum of Closed Operators.- 3 Some Classes of Unbounded Operators.- II Spectral Theory.- 4 Spectral Measures and Spectral
MATH
TLDR
It is still unknown whether there are families of tight knots whose lengths grow faster than linearly with crossing numbers, but the largest power has been reduced to 3/z, and some other physical models of knots as flattened ropes or strips which exhibit similar length versus complexity power laws are surveyed.
Classical Fourier Analysis
Preface.- 1. Lp Spaces and Interpolation.- 2. Maximal Functions, Fourier Transform, and Distributions.- 3. Fourier Series.- 4. Topics on Fourier Series.- 5. Singular Integrals of Convolution Type.-
An Introduction to Banach Space Theory
1 Basic Concepts.- 1.1 Preliminaries.- 1.2 Norms.- 1.3 First Properties of Normed Spaces.- 1.4 Linear Operators Between Normed Spaces.- 1.5 Baire Category.- 1.6 Three Fundamental Theorems.- 1.7
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