Fermionic systems for quantum information people
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61388955%3A_____%2F21%3A00559766" target="_blank" >RIV/61388955:_____/21:00559766 - isvavai.cz</a>
Result on the web
<a href="https://hdl.handle.net/11104/0332967" target="_blank" >https://hdl.handle.net/11104/0332967</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1088/1751-8121/ac0646" target="_blank" >10.1088/1751-8121/ac0646</a>
Alternative languages
Result language
angličtina
Original language name
Fermionic systems for quantum information people
Original language description
The operator algebra of fermionic modes is isomorphic to that of qubits, the difference between them is twofold: the embedding of subalgebras corresponding to mode subsets and multiqubit subsystems on the one hand, and the parity superselection in the fermionic case on the other. We discuss these two fundamental differences extensively, and illustrate these through the Jordan-Wigner representation in a coherent, self-contained, pedagogical way, from the point of view of quantum information theory. Our perspective leads us to develop useful new tools for the treatment of fermionic systems, such as the fermionic (quasi-)tensor product, fermionic canonical embedding, fermionic partial trace, fermionic products of maps and fermionic embeddings of maps. We formulate these by direct, easily applicable formulas, without mode permutations, for arbitrary partitionings of the modes. It is also shown that fermionic reduced states can be calculated by the fermionic partial trace, containing the proper phase factors. We also consider variants of the notions of fermionic mode correlation and entanglement, which can be endowed with the usual, local operation based motivation, if the parity superselection rule is imposed. We also elucidate some other fundamental points, related to joint map extensions, which make the parity superselection inevitable in the description of fermionic systems.
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
10403 - Physical chemistry
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Physics A-Mathematical and Theoretical
ISSN
1751-8113
e-ISSN
1751-8121
Volume of the periodical
54
Issue of the periodical within the volume
39
Country of publishing house
GB - UNITED KINGDOM
Number of pages
70
Pages from-to
393001
UT code for WoS article
000712604300001
EID of the result in the Scopus database
2-s2.0-85111483316