Nonconvex optimization strategy for computing convex-roof entanglement
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Nonconvex optimization strategy for computing convex-roof entanglement
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10306 - Optics (including laser optics and quantum optics)
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Physical Review A
ISSN
2469-9926
e-ISSN
2469-9934
Volume of the periodical
111
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
10
Pages from-to
032435
UT code for WoS article
001459100200005
EID of the result in the Scopus database
2-s2.0-105001681216