A classification of classical representations for quantum-like systems

Details A classification of classical representations for quantum-like systems A classification of classical representations for quantum-like systems

2000-08-14

arxiv.org/abs/quant-ph/0008062v2

Helvetica Physica Acta 70, 462-477 (1997)

Physics

Quantum Physics

13 pages; 2 figs

Scientific paper

For general non-classical systems, we study the different classical representations that fulfill the specific context dependence imposed by the hidden measurement system formalism introduced in quant-ph/0008061. We show that the collection of non-equivalent representations has a poset structure. We also show that in general, there exists no 'smallest' representation, since this poset is not a semi-lattice. Then we study the possible representations of quantum-like measurement systems. For example, we show that there exists a classical representation of finite dimensional quantum mechanics with ${\Bbb N}$ as a set of states for the measurement context, and we build an explicit example of such a representation.

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