dorsal/arxiv
View SchemaCloning and Broadcasting in Generic Probabilistic Theories
| Authors | Howard Barnum, Jonathan Barrett, Matthew Leifer, Alexander Wilce |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0611295 |
| URL | https://arxiv.org/abs/quant-ph/0611295 |
Abstract
We prove generic versions of the no-cloning and no-broadcasting theorems, applicable to essentially {\em any} non-classical finite-dimensional probabilistic model that satisfies a no-signaling criterion. This includes quantum theory as well as models supporting ``super-quantum'' correlations that violate the Bell inequalities to a larger extent than quantum theory. The proof of our no-broadcasting theorem is significantly more natural and more self-contained than others we have seen: we show that a set of states is broadcastable if, and only if, it is contained in a simplex whose vertices are cloneable, and therefore distinguishable by a single measurement. This necessary and sufficient condition generalizes the quantum requirement that a broadcastable set of states commute.
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"abstract": "We prove generic versions of the no-cloning and no-broadcasting theorems,\napplicable to essentially {\\em any} non-classical finite-dimensional\nprobabilistic model that satisfies a no-signaling criterion. This includes\nquantum theory as well as models supporting ``super-quantum\u0027\u0027 correlations that\nviolate the Bell inequalities to a larger extent than quantum theory. The proof\nof our no-broadcasting theorem is significantly more natural and more\nself-contained than others we have seen: we show that a set of states is\nbroadcastable if, and only if, it is contained in a simplex whose vertices are\ncloneable, and therefore distinguishable by a single measurement. This\nnecessary and sufficient condition generalizes the quantum requirement that a\nbroadcastable set of states commute.",
"arxiv_id": "quant-ph/0611295",
"authors": [
"Howard Barnum",
"Jonathan Barrett",
"Matthew Leifer",
"Alexander Wilce"
],
"categories": [
"quant-ph"
],
"title": "Cloning and Broadcasting in Generic Probabilistic Theories",
"url": "https://arxiv.org/abs/quant-ph/0611295"
},
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