dorsal/arxiv
View SchemaInformation processing in generalized probabilistic theories
| Authors | Jonathan Barrett |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0508211 |
| URL | https://arxiv.org/abs/quant-ph/0508211 |
Abstract
I introduce a framework in which a variety of probabilistic theories can be defined, including classical and quantum theories, and many others. From two simple assumptions, a tensor product rule for combining separate systems can be derived. Certain features, usually thought of as specifically quantum, turn out to be generic in this framework, meaning that they are present in all except classical theories. These include the non-unique decomposition of a mixed state into pure states, a theorem involving disturbance of a system on measurement (suggesting that the possibility of secure key distribution is generic), and a no-cloning theorem. Two particular theories are then investigated in detail, for the sake of comparison with the classical and quantum cases. One of these includes states that can give rise to arbitrary non-signalling correlations, including the super-quantum correlations that have become known in the literature as Nonlocal Machines or Popescu-Rohrlich boxes. By investigating these correlations in the context of a theory with well-defined dynamics, I hope to make further progress with a question raised by Popescu and Rohrlich, which is, why does quantum theory not allow these strongly nonlocal correlations? The existence of such correlations forces much of the dynamics in this theory to be, in a certain sense, classical, with consequences for teleportation, cryptography and computation. I also investigate another theory in which all states are local. Finally, I raise the question of what further axiom(s) could be added to the framework in order uniquely to identify quantum theory, and hypothesize that quantum theory is optimal for computation.
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"abstract": "I introduce a framework in which a variety of probabilistic theories can be\ndefined, including classical and quantum theories, and many others. From two\nsimple assumptions, a tensor product rule for combining separate systems can be\nderived. Certain features, usually thought of as specifically quantum, turn out\nto be generic in this framework, meaning that they are present in all except\nclassical theories. These include the non-unique decomposition of a mixed state\ninto pure states, a theorem involving disturbance of a system on measurement\n(suggesting that the possibility of secure key distribution is generic), and a\nno-cloning theorem. Two particular theories are then investigated in detail,\nfor the sake of comparison with the classical and quantum cases. One of these\nincludes states that can give rise to arbitrary non-signalling correlations,\nincluding the super-quantum correlations that have become known in the\nliterature as Nonlocal Machines or Popescu-Rohrlich boxes. By investigating\nthese correlations in the context of a theory with well-defined dynamics, I\nhope to make further progress with a question raised by Popescu and Rohrlich,\nwhich is, why does quantum theory not allow these strongly nonlocal\ncorrelations? The existence of such correlations forces much of the dynamics in\nthis theory to be, in a certain sense, classical, with consequences for\nteleportation, cryptography and computation. I also investigate another theory\nin which all states are local. Finally, I raise the question of what further\naxiom(s) could be added to the framework in order uniquely to identify quantum\ntheory, and hypothesize that quantum theory is optimal for computation.",
"arxiv_id": "quant-ph/0508211",
"authors": [
"Jonathan Barrett"
],
"categories": [
"quant-ph"
],
"title": "Information processing in generalized probabilistic theories",
"url": "https://arxiv.org/abs/quant-ph/0508211"
},
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