PureMathematicsnØêÆ,2023,13(8),2231-2239PublishedOnlineAugust2023inHans.https://www.hanspub.org/journal/pmhttps://doi.org/10.12677/pm.2023.138229Bernoulli•¼þÄu;KjéÜ�þf�444ŽŽŽ)))Ü�“‰ŒÆêƆÚOÆ�§[‹=²ÂvFϵ2023c6�26F¶¹^Fϵ2023c7�27F¶uÙFϵ2023c8�3FÁ‡þfBernoulliD((QBNs)´Š^u²•ŒÈBernoulli•¼˜mþ��«ÚO)Žfx§÷v�ž;K‡�†'X(CAR)"�«†O)Žf�ÚŽf´Bernoulli•¼˜mþ�˜�gŠŽf§¡•Bernoulli•¼þ�;Kjéܧ�©ÄuBernoulli•¼˜m�f˜mþ�;Kjéܧ�E�˜a—ÝŽf§•Ä�T—ÝŽf�þf�±9þf��eZ5Ÿ"'…cþfBernoulliD(§jéܧþf�QuantumEntropyBasedonCanonicalUnitaryInvolutiononBernoulliFunctionalShengshengLiuCollegeofMathematicsandstatistics,NorthwestNormalUniversity,LanzhouGansuReceived:Jun.26th,2023;accepted:Jul.27th,2023;published:Aug.3rd,2023©ÙÚ^:4Ž).Bernoulli•¼þÄu;KjéÜ�þf�[J].nØêÆ,2023,13(8):2231-2239.DOI:10.12677/pm.2023.1382294Ž)AbstractQuantumBernoullinoises(QBNs)arethefamilyofannihilationandcreationoperatorsactingonthespaceofsquareintegrableBernoullifunctional,whichsatisfyacanonicalanti-commutationrelation(CAR)inequaltime.Thesumoperatorofannihilationandcreationoperatorisaseriesofself-adjointoperatoronBernoullifunctionalspace,whichiscalledcanonicalunitaryinvolutiononBernoullifunctional.Inthispaper,basedonthecanonicalunitaryinvolutiononthesubspaceoftheBernoullifunctionalspace,weconstructaclassofdensityoperators,andconsiderthequantumentropyofthedensityoperatorandsomepropertiesofthequantumentropy.KeywordsQuantumBernoulliNoises,UnitaryInvolution,QuantumEntropyCopyrightc⃝2023byauthor(s)andHansPublishersInc.ThisworkislicensedundertheCreativeCommonsAttributionInternationalLicense(CCBY4.0).http://creativecommons.org/licenses/by/4.0/1.Úóþf&EnØ´y“ÔnÆ�Ä:[1,2],þf�K´þf&EnØ¥�˜‡-‡óä,3êÆÚÔnþéþf��ïÄØ=äk›©-‡�nØdŠ,�…y²§kX2•�A^cµ.VonNeumann�Ò´Ù¥˜«-‡�þf�,Œ±^5Ýþ&EXÚ¥�Ø(½5.þfBernoulliD((QBNs)´Š^u²•ŒÈBernoulli•¼˜mþ��«ÚO)Žfx{...
