A Representation for Compound Quantum Systems as Individual Entities: Hard Acts of Creation and Hidden Correlations

Abstract

We introduce an explicit definition for 'hidden correlations' on individual entities in a compound system: when one individual entity is measured, this induces a well-defined transition of the 'proper state' of the other individual entities. We prove that every compound quantum system described in the tensor product of a finite number of Hilbert spaces can be uniquely represented as a collection of individual(ized) (peudo-)entities between which there exist such hidden correlations. We investigate the significance of these hidden correlation representations within the so-called ``creation-discovery-approach'' and in particular their compatibility with the ``hidden measurement formalism''. This leads us to the introduction of the notions of 'soft' and 'hard' 'acts of creation' and to the observation that our approach can be seen as a theory of (pseudo-)individuals when compared to the standard quantum theory. (For a presentation of the ideas proposed in this paper within a quantum logical setting, yielding a structural theorem for the representation of a compound quantum system in terms of the Hilbert space tensor product, we refer to quant-ph/0008054.)