dorsal/arxiv
View SchemaProperty lattices for independent quantum systems
| Authors | Boris Ischi |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0204095 |
| URL | https://arxiv.org/abs/quant-ph/0204095 |
| DOI | 10.1016/S0034-4877(02)80052-0 |
Abstract
We consider the description of two independent quantum systems by a complete atomistic ortho-lattice (cao-lattice) L. It is known that since the two systems are independent, no Hilbert space description is possible, i.e. $L\ne P(H)$, the lattice of closed subspaces of a Hilbert space (theorem 1). We impose five conditions on L. Four of them are shown to be physically necessary. The last one relates the orthogonality between states in each system to the ortho-complementation of L. It can be justified if one assumes that the orthogonality between states in the total system induces the ortho-complementation of L. We prove that if L satisfies these five conditions, then L is the separated product proposed by Aerts in 1982 to describe independent quantum systems (theorem 2). Finally, we give strong arguments to exclude the separated product and therefore our last condition. As a consequence, we ask whether among the ca-lattices that satisfy our first four basic necessary conditions, there exists an ortho-complemented one different from the separated product.
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"abstract": "We consider the description of two independent quantum systems by a complete\natomistic ortho-lattice (cao-lattice) L. It is known that since the two systems\nare independent, no Hilbert space description is possible, i.e. $L\\ne P(H)$,\nthe lattice of closed subspaces of a Hilbert space (theorem 1). We impose five\nconditions on L. Four of them are shown to be physically necessary. The last\none relates the orthogonality between states in each system to the\northo-complementation of L. It can be justified if one assumes that the\northogonality between states in the total system induces the\northo-complementation of L. We prove that if L satisfies these five conditions,\nthen L is the separated product proposed by Aerts in 1982 to describe\nindependent quantum systems (theorem 2). Finally, we give strong arguments to\nexclude the separated product and therefore our last condition. As a\nconsequence, we ask whether among the ca-lattices that satisfy our first four\nbasic necessary conditions, there exists an ortho-complemented one different\nfrom the separated product.",
"arxiv_id": "quant-ph/0204095",
"authors": [
"Boris Ischi"
],
"categories": [
"quant-ph"
],
"doi": "10.1016/S0034-4877(02)80052-0",
"title": "Property lattices for independent quantum systems",
"url": "https://arxiv.org/abs/quant-ph/0204095"
},
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