dorsal/arxiv
View SchemaA Representation for Compound Quantum Systems as Individual Entities: Hard Acts of Creation and Hidden Correlations
| Authors | Bob Coecke |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0105093 |
| URL | https://arxiv.org/abs/quant-ph/0105093 |
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.)
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"abstract": "We introduce an explicit definition for \u0027hidden correlations\u0027 on individual\nentities in a compound system: when one individual entity is measured, this\ninduces a well-defined transition of the \u0027proper state\u0027 of the other individual\nentities. We prove that every compound quantum system described in the tensor\nproduct of a finite number of Hilbert spaces can be uniquely represented as a\ncollection of individual(ized) (peudo-)entities between which there exist such\nhidden correlations. We investigate the significance of these hidden\ncorrelation representations within the so-called\n``creation-discovery-approach\u0027\u0027 and in particular their compatibility with the\n``hidden measurement formalism\u0027\u0027. This leads us to the introduction of the\nnotions of \u0027soft\u0027 and \u0027hard\u0027 \u0027acts of creation\u0027 and to the observation that our\napproach can be seen as a theory of (pseudo-)individuals when compared to the\nstandard quantum theory. (For a presentation of the ideas proposed in this\npaper within a quantum logical setting, yielding a structural theorem for the\nrepresentation of a compound quantum system in terms of the Hilbert space\ntensor product, we refer to quant-ph/0008054.)",
"arxiv_id": "quant-ph/0105093",
"authors": [
"Bob Coecke"
],
"categories": [
"quant-ph"
],
"title": "A Representation for Compound Quantum Systems as Individual Entities: Hard Acts of Creation and Hidden Correlations",
"url": "https://arxiv.org/abs/quant-ph/0105093"
},
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