A CLASSIFICATION OF CLASSICAL REPRESENTATIONS FOR QUANTUM-LIKE SYSTEMS

For general non-classical systems, we study the different classical re presentations that fulfill the specific context dependence imposed by the hidden measurement system formalism introduced in [6]. We show tha t the collection of non-equivalent representations has a poset structu re. We also show that in general, there exists no 'smallest' represent ation, since this poset is not a semi-lattice. Then we study the possi ble representations of quantum-like measurement systems. For example, we show that there exists a classical representation of finite dimensi onal quantum mechanics with N as a set of states for the measurement c ontext, and we build an explicit example of such a representation.