Abstract
Recently, new types of independence of a pair of C *- or W *-subalgebras \(({\mathcal{A}}_{1},{\mathcal{A}}_{2})\) 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.
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Rédei, M. Operational Independence and Operational Separability in Algebraic Quantum Mechanics. Found Phys 40, 1439–1449 (2010). https://doi.org/10.1007/s10701-010-9447-x
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DOI: https://doi.org/10.1007/s10701-010-9447-x