dorsal/arxiv
View SchemaQuantum information processing, operational quantum logic, convexity, and the foundations of physics
| Authors | Howard Barnum |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0304159 |
| URL | https://arxiv.org/abs/quant-ph/0304159 |
Abstract
Quantum information science is a source of task-related axioms whose consequences can be explored in general settings encompassing quantum mechanics, classical theory, and more. Quantum states are compendia of probabilities for the outcomes of possible operations we may perform a system: ``operational states.'' I discuss general frameworks for ``operational theories'' (sets of possible operational states of a system), in which convexity plays key role. The main technical content of the paper is in a theorem that any such theory naturally gives rise to a ``weak effect algebra'' when outcomes having the same probability in all states are identified, and in the introduction of a notion of ``operation algebra'' that also takes account of sequential and conditional operations. Such frameworks are appropriate for investigating what things look like from an ``inside view,'' i.e. for describing perspectival information that one subsystem of the world can have about another. Understanding how such views can combine, and whether an overall ``geometric'' picture (``outside view'') coordinating them all can be had, even if this picture is very different in structure from the perspectives within it, is the key to whether we may be able to achieve a unified, ``objective'' physical view in which quantum mechanics is the appropriate description for certain perspectives, or whether quantum mechanics is truly telling us we must go beyond this ``geometric'' conception of physics.
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"abstract": "Quantum information science is a source of task-related axioms whose\nconsequences can be explored in general settings encompassing quantum\nmechanics, classical theory, and more. Quantum states are compendia of\nprobabilities for the outcomes of possible operations we may perform a system:\n``operational states.\u0027\u0027 I discuss general frameworks for ``operational\ntheories\u0027\u0027 (sets of possible operational states of a system), in which\nconvexity plays key role. The main technical content of the paper is in a\ntheorem that any such theory naturally gives rise to a ``weak effect algebra\u0027\u0027\nwhen outcomes having the same probability in all states are identified, and in\nthe introduction of a notion of ``operation algebra\u0027\u0027 that also takes account\nof sequential and conditional operations. Such frameworks are appropriate for\ninvestigating what things look like from an ``inside view,\u0027\u0027 i.e. for\ndescribing perspectival information that one subsystem of the world can have\nabout another. Understanding how such views can combine, and whether an overall\n``geometric\u0027\u0027 picture (``outside view\u0027\u0027) coordinating them all can be had, even\nif this picture is very different in structure from the perspectives within it,\nis the key to whether we may be able to achieve a unified, ``objective\u0027\u0027\nphysical view in which quantum mechanics is the appropriate description for\ncertain perspectives, or whether quantum mechanics is truly telling us we must\ngo beyond this ``geometric\u0027\u0027 conception of physics.",
"arxiv_id": "quant-ph/0304159",
"authors": [
"Howard Barnum"
],
"categories": [
"quant-ph"
],
"title": "Quantum information processing, operational quantum logic, convexity, and the foundations of physics",
"url": "https://arxiv.org/abs/quant-ph/0304159"
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