# 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…

## 5 Citations

Computable lower bounds on the entanglement cost of quantum channels

- Computer Science
- 2022

This work establishes a lower bound for the entanglement cost of any channel, whether finite or infinite dimensional, that is computable as a semidefinite program and that can outperform previously known lower bounds, including ones based on quantum relative entropy.

No second law of entanglement manipulation after all

- Physics
- 2021

We prove that the theory of entanglement manipulation is asymptotically irreversible under all non-entangling operations, showing from ﬁrst principles that reversible entanglement transformations…

Convergence conditions for the quantum relative entropy and other applications of the deneralized quantum Dini lemma

- Mathematics
- 2022

We describe a generalized version of the result called quantum Dini lemma that was used previously for analysis of local continuity of basic correlation and entanglement measures. The generalization…

Asymptotically consistent measures of general quantum resources: Discord, non-Markovianity, and non-Gaussianity

- PhysicsPhysical Review A
- 2021

Kohdai Kuroiwa ∗ and Hayata Yamasaki 3, † Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada, N2L…

Hierarchy of continuous-variable quantum resource theories

- Computer ScienceNew Journal of Physics
- 2021

It is shown that the maximal Gaussian coherence (where states and operations are required to be Gaussian) can be quantified analytically by the relative entropy, and it is proved that the equality of Gaussian non-uniformity and maximal Gaussia coherence is proved.

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