Nonconvex optimization strategy for computing convex-roof entanglement

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68378271%3A_____%2F25%3A00619000" target="_blank" >RIV/68378271:_____/25:00619000 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1103/PhysRevA.111.032435" target="_blank" >https://doi.org/10.1103/PhysRevA.111.032435</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1103/PhysRevA.111.032435" target="_blank" >10.1103/PhysRevA.111.032435</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Nonconvex optimization strategy for computing convex-roof entanglement

Popis výsledku v původním jazyce

We develop a numerical methodology for the computation of entanglement measures for mixed quantum states. Using the well-known Schr¨odinger-HJW theorem, the computation of convex roof entanglement measures is reframed as a search for unitary matrices, a nonconvex optimization problem. To address this non-convexity, we modify a genetic algorithm, known in the literature as differential evolution, constraining the search space to unitary matrices by using a QR factorization. We then refine results using a quasi-Newton method. We benchmark our method on simple test problems and, as an application, compute entanglement between a system and its environment over time for pure dephasing evolutions. We also study the temperature dependence of Gibbs state en- tanglement for a class of block-diagonal Hamiltonians to provide a complementary test scenario with a set of entangled states that are qualitatively different. We find that the method works well enough to reliably reproduce entanglement curves, even for comparatively large systems. To our knowledge, the modified genetic algorithm represents the first derivative-free and non-convex computational method that broadly applies to the computation of convex roof entanglement measures.

Název v anglickém jazyce

Nonconvex optimization strategy for computing convex-roof entanglement

Popis výsledku anglicky

We develop a numerical methodology for the computation of entanglement measures for mixed quantum states. Using the well-known Schr¨odinger-HJW theorem, the computation of convex roof entanglement measures is reframed as a search for unitary matrices, a nonconvex optimization problem. To address this non-convexity, we modify a genetic algorithm, known in the literature as differential evolution, constraining the search space to unitary matrices by using a QR factorization. We then refine results using a quasi-Newton method. We benchmark our method on simple test problems and, as an application, compute entanglement between a system and its environment over time for pure dephasing evolutions. We also study the temperature dependence of Gibbs state en- tanglement for a class of block-diagonal Hamiltonians to provide a complementary test scenario with a set of entangled states that are qualitatively different. We find that the method works well enough to reliably reproduce entanglement curves, even for comparatively large systems. To our knowledge, the modified genetic algorithm represents the first derivative-free and non-convex computational method that broadly applies to the computation of convex roof entanglement measures.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10306 - Optics (including laser optics and quantum optics)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Physical Review A

ISSN

2469-9926

e-ISSN

2469-9934

Svazek periodika

111

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

10

Strana od-do

032435

Kód UT WoS článku

001459100200005

EID výsledku v databázi Scopus

2-s2.0-105001681216