Strong subadditivity of quantum mechanical entropy for semifinite von Neumann algebras

被引：1

作者：

Podsedkowska, Hanna ^{[1
]}

机构：

[1] Univ Lodz, Fac Math & Comp Sci, Banacha 22, PL-90238 Lodz, Poland

来源：

STUDIA MATHEMATICA | 2021年 / 257卷 / 01期

关键词：

entropy; relative information; strong subadditivity; states; semi-finite von Neumann algebra; measurable operators;

D O I：

10.4064/sm190929-7-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that for Segal entropy defined for states on an arbitrary von Neumann algebra with normal faithful semifinite trace, strong subadditivity holds. We also prove some other related properties of this generalized entropy, in particular the concavity of S(rho(12)) - S(rho(2)), the subadditivity of entropy, and a generalization of the Araki-Lieb inequality.

引用

页码：71 / 85

页数：15

共 18 条

[1]

Araki H., 1977, Publ. RIMS, Kyoto Univ., V13, P173, DOI [10.2977/prims/1195190105, DOI 10.2977/PRIMS/1195190105]

[2] REMARKS ON 2 THEOREMS OF E LIEB [J].

EPSTEIN, H .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1973, 31 (04) :317-325

[3] GENERALIZED S-NUMBERS OF TAU-MEASURABLE OPERATORS [J].

FACK, T ;

KOSAKI, H .

PACIFIC JOURNAL OF MATHEMATICS, 1986, 123 (02) :269-300

[4] MEAN ENTROPY OF STATES IN QUANTUM-STATISTICAL MECHANICS [J].

LANFORD, OE ;

ROBINSON, DW .

JOURNAL OF MATHEMATICAL PHYSICS, 1968, 9 (07) :1120-&

[5] PROOF OF STRONG SUBADDITIVITY OF QUANTUM-MECHANICAL ENTROPY [J].

LIEB, EH ;

RUSKAI, MB .

JOURNAL OF MATHEMATICAL PHYSICS, 1973, 14 (12) :1938-1941

[6] FUNDAMENTAL PROPERTY OF QUANTUM-MECHANICAL ENTROPY [J].

LIEB, EH ;

RUSKAI, MB .

PHYSICAL REVIEW LETTERS, 1973, 30 (10) :434-436

[7] CONVEX TRACE FUNCTIONS AND WIGNER-YANASE-DYSON CONJECTURE [J].

LIEB, EH .

ADVANCES IN MATHEMATICS, 1973, 11 (03) :267-288

[8]

Luczak A., 2019, ARXIV191209633

[9]

Neshveyev S., 2006, Dynamical entropy in operator algebras

[10]

Ochs W., 1978, Reports on Mathematical Physics, V14, P75, DOI 10.1016/0034-4877(78)90034-4

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