|
| related topics |
| {observables, space, algebra} |
| {theory, mechanics, state} |
| {algorithm, log, probability} |
| {time, decoherence, evolution} |
| {state, states, entangled} |
| {alice, bob, state} |
| {entanglement, phys, rev} |
| {qubit, qubits, gate} |
| {states, state, optimal} |
| {time, systems, information} |
| {measurement, state, measurements} |
| {group, space, representation} |
| {state, algorithm, problem} |
|
Quantum information processing, operational quantum logic, convexity,
and the foundations of physics
Howard Barnum
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.
- oai_identifier:
- oai:arXiv.org:quant-ph/0304159
- categories:
- quant-ph
- comments:
- 38 pages, LaTeX
- arxiv_id:
- quant-ph/0304159
- report_no:
- LA-UR 03-119
- created:
- 2003-04-24
Full article ▸
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