The quantum effects for a physical system can be described by the set of positive operators on a complex Hilbert space that are bounded above by the identity operator . For , , the operation of sequential product was proposed as a model for sequential quantum measurements. A nice investigation of properties of the sequential product has been carried over [Gudder, S. and Nagy, G., “Sequential quantum measurements,” J. Math. Phys. 42, 5212 (2001)]. In this note, we extend some results of this reference. In particular, a gap in the proof of Theorem 3.2 in this reference is overcome. In addition, some properties of generalized infimum are studied.
REFERENCES
1.
Ando
, T.
, “Problem of infimum in the positive cone; Analytic and geometric inequalities and applications
,” Math. Appl.
478
, 1
(1999
).2.
Busch
, P.
, and Singh
, J.
, “Luders theorem for unsharp quantum measurements
,” Phys. Lett. A
249
, 10
(1998
).3.
Du
, H. K.
, Deng
, C. Y.
, and Li
, Q. H.
, “On the infimum problem of Hilbert space effects
,” Sci. China, Ser. A: Math., Phys., Astron.
51
, 320
(2006
).4.
Dvurečenskij
, A.
, and Pulmannová
, S.
, “New trends in quantum structures, mathematics and Its applications
,” J. Math. Phys.
46
, 062102
(2005
).5.
Gheondea
, A.
, and Gudder
, S.
, “Sequential product of quantum effect
,” Proc. Am. Math. Soc.
132
, 503
(2004
).6.
Gheondea
, A.
, Gudder
, S.
, and Jonas
, P.
, “On the infimum of quantum effects
,” J. Math. Phys.
46
, 062102
(2005
).7.
Gudder
, S.
, “Examples, problems, and results in effect algebras
,” Int. J. Theor. Phys.
35
, 2365
(1996
).8.
Gudder
, S.
, “Lattice properties of quantum effects
,” J. Math. Phys.
37
, 2637
(1996
).9.
Gudder
, S.
, and Greechie
, R.
, “Sequential products on effect algebras
,” Rep. Math. Phys.
49
, 87
(2002
).10.
Gudder
, S.
, and Nagy
, G.
, “Sequential quantum measurements
,” J. Math. Phys.
42
, 5212
(2001
).11.
Gudder
, S.
, and Nagy
, G.
, “Sequentially independent effects
,” Proc. Am. Math. Soc.
130
, 1125
(2002
).12.
Jian
, Y.
, and Du
, H. K.
, “A note on commutativity up to a factor of bounded operators
,” Proc. Am. Math. Soc.
132
, 1713
(2004
).13.
Kadison
, R.
, “Order properties of bounded self-adjoint operators
,” Proc. Am. Math. Soc.
34
, 505
(1951
).14.
Kadison
, R.
, and Ringrose
, J.
, Fundamentals of the Theory of Operator Algebras (I)
(American Mathematical Society
, New York
, 1997
).15.
Lahti
, P.
, and Maczynski
, M.
, “Partial order of quantum effects
,” J. Math. Phys.
36
, 1673
(1995
).16.
Li
, Y.
, and Du
, H. K.
, “A note on the infimum problem of Hilbert space effects
,” J. Math. Phys.
47
, 102103
(2006
).17.
Moreland
, T.
, and Gudder
, S.
, “Infima of Hilbert space effects
,” Linear Algebr. Appl.
286
, 1
(1999
).18.
Murphy
, G. J.
, -algebra and operator theory (Academic
, New York
, 1990
).19.
© 2007 American Institute of Physics.
2007
American Institute of Physics
You do not currently have access to this content.
