Operational Independence and Operational Separability in Algebraic Quantum Mechanics

Foundations of Physics 40 (9-10):1439-1449 (2010)

Authors
Miklós Rédei
London School of Economics
Abstract
Recently, new types of independence of a pair of C *- or W *-subalgebras (1,2) of a C *- or W *-algebra have been introduced: operational C *- and W *-independence (Rédei and Summers, http://arxiv.org/abs/0810.5294, 2008) and operational C *- and W *-separability (Rédei and Valente, How local are local operations in local quantum field theory? 2009). In this paper it is shown that operational C *-independence is equivalent to operational C *-separability and that operational W *-independence is equivalent to operational W *-separability. Specific further sub-types of both operational C *- and W *-separability and operational C *- and W *-independence are defined and the problem of characterization of the logical interdependencies of the independence notions is raised.
Keywords Operator algebras  Independence  Quantum mechanics
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DOI 10.1007/s10701-010-9447-x
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References found in this work BETA

Subsystems and Independence in Relativistic Microscopic Physics.Stephen J. Summers - 2009 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 40 (2):133-141.
Subsystems and Independence in Relativistic Microscopic Physics.Stephen J. Summers - 2009 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 40 (2):133-141.

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Citations of this work BETA

How Local Are Local Operations in Local Quantum Field Theory?Miklós Rédei & Giovanni Valente - 2010 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 41 (4):346-353.

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