A definition of multipartitions of quantum systems into possibly non-factor sub-C* algebras, with a representation theorem showing that some partitions, such as fermionic modes, are not fully representable on tensor-product Hilbert spaces.
Generalised tensors and traces
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abstract
Tensors and traceouts are generalised, so that systems can be partitioned according to almost arbitrary logical predicates. One might have feared that the familiar interrelations between the notions of unitarity, complete positivity, trace-preservation, non-signalling causality, locality and localizability that are standard in quantum theory be jeopardized as the partitioning of systems becomes both logical and dynamical. Such interrelations in fact carry through, although a new notion, consistency, becomes instrumental.
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Partitions in quantum theory
A definition of multipartitions of quantum systems into possibly non-factor sub-C* algebras, with a representation theorem showing that some partitions, such as fermionic modes, are not fully representable on tensor-product Hilbert spaces.