Coexistence of effects from an algebra of two projections

Journal of Physics A: Mathematical and Theoretical

Volumn , Issue 22, 2014, Pages

  Heinosaari, Teiko ^a   Kiukas, Jukka ^b   Reitzner, Daniel ^c,d  

^a UNIVERSITY OF TURKU   (Finland)

^b UNIVERSITY OF NOTTINGHAM   (United Kingdom)

^c TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^d INSTITUTE OF CHEMISTRY   (Slovakia)

Author keywords

coexistence; quantum effect; two projections; von Neumann algebra

Indexed keywords

EID: 84937046248     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/47/22/225301     Document Type: Article

References (25)

1. Ludwig G 1985 An Axiomatic Basis for Quantum Mechanics vol 1 (Berlin: Springer) (Translated from the German manuscript by Leo F Boroń)
2. Kraus K 1983 States, Effects, and Operations (Berlin: Springer)
3. Busch P 1986 Unsharp reality and joint measurements for spin observables Phys. Rev. D 33 2253-61
4. Stano P, Reitzner D and Heinosaari T 2008 Coexistence of qubit effects Phys. Rev. A 78 012315
5. Yu S, Liu N-L, Li L and Oh C H 2010 Joint measurement of two unsharp observables of a qubit Phys. Rev. A 81 062116
6. Busch P and Schmidt H-J 2010 Coexistence of qubit effects Quantum Inform. Process. 9 143-69
7. Holevo A S 1982 Probabilistic and Statistical Aspects of Quantum Theory (Amsterdam: North-Holland)
8. Busch P, Grabowski M and Lahti P J 1997 Operational Quantum Physics (Berlin: Springer) (Second corrected printing)
9. Heinosaari T and Ziman M 2012 The Mathematical Language of Quantum Theory (Cambridge: Cambridge University Press)
10. Reeb D, Reitzner D and Wolf M M 2013 Coexistence does not imply joint measurability J. Phys. A: Math. Theor. 46 462002
11. Heinosaari T 2013 A simple sufficient condition for the coexistence of quantum effects J. Phys. A: Math. Theor. 46 152002
12. Kato T 1966 Perturbation Theory for Linear Operators (Berlin: Springer)
13. Pedersen G K 1968 Measure theory for C∗ algebras: II Math. Scand. 22 63-74
14. Halmos P R 1969 Two subspaces Trans. Am. Math. Soc. 144 381-9
15. Davis C and Kahan W M 1970 The rotation of eigenvectors by a perturbation: III SIAM J. Numer. Anal. 7 1-46
16. Giles R and Kummer H 1971 A matrix representation of a pair of projections in a Hilbert space Can. Math. Bull. 14 35-44
17. Raeburn I and Sinclair A M 1989 The C∗-algebra generated by two projections Math. Scand. 65 278-90
18. Avron J, Seiler R and Simon B 1994 The index of a pair of projections J. Funct. Anal. 120 220-37
19. Borac S 1995 On the algebra generated by two projections J. Math. Phys. 36 863-74
20. Vasilevski N L 1998 C∗-algebras generated by orthogonal projections and their applications Integ. Eqns Oper. Theory 31 113-32 (Pubitemid 128341725)
21. Kiukas J and Werner R F 2010 Maximal violation of Bell inequalities by position measurements J. Math. Phys. 51 072105
22. Busch P and Lahti P J 1986 To what extent do position and momentum commute? Phys. Lett. A 115 259-64
23. Reed M and Simon B 1980 Methods of Modern Mathematical Physics: Functional Analysis vol 1 (London: Academic) (revised and enlarged edition)
24. Kadison R V and Ringrose J R 1986 Fundamentals of the Theory of Operator Algebras: Advanced Theory vol 2 (Orlando, FL: Academic)
25. Davis C 1955 Generators of the ring of bounded operators Proc. Am. Math. Soc. 6 907-72