38,374 research outputs found
The Minimal Modal Interpretation of Quantum Theory
We introduce a realist, unextravagant interpretation of quantum theory that
builds on the existing physical structure of the theory and allows experiments
to have definite outcomes, but leaves the theory's basic dynamical content
essentially intact. Much as classical systems have specific states that evolve
along definite trajectories through configuration spaces, the traditional
formulation of quantum theory asserts that closed quantum systems have specific
states that evolve unitarily along definite trajectories through Hilbert
spaces, and our interpretation extends this intuitive picture of states and
Hilbert-space trajectories to the case of open quantum systems as well. We
provide independent justification for the partial-trace operation for density
matrices, reformulate wave-function collapse in terms of an underlying
interpolating dynamics, derive the Born rule from deeper principles, resolve
several open questions regarding ontological stability and dynamics, address a
number of familiar no-go theorems, and argue that our interpretation is
ultimately compatible with Lorentz invariance. Along the way, we also
investigate a number of unexplored features of quantum theory, including an
interesting geometrical structure---which we call subsystem space---that we
believe merits further study. We include an appendix that briefly reviews the
traditional Copenhagen interpretation and the measurement problem of quantum
theory, as well as the instrumentalist approach and a collection of
foundational theorems not otherwise discussed in the main text.Comment: 73 pages + references, 9 figures; cosmetic changes, added figure,
updated references, generalized conditional probabilities with attendant
changes to the sections on the EPR-Bohm thought experiment and Lorentz
invariance; for a concise summary, see the companion letter at
arXiv:1405.675
Entanglement-assisted capacity of constrained quantum channel
In this paper we fill the gap in previous works by proving the formula for
entanglement-assisted capacity of quantum channel with additive constraint
(such as bosonic Gaussian channel). The main tools are the coding theorem for
classical-quantum constrained channels and a finite dimensional approximation
of the input density operators for entanglement-assisted capacity. The new
version contains improved formulation of sufficient conditions under which
suprema in the capacity formulas are attained.Comment: Extended version of paper presented at Quantum Informatics Symposium,
Zvenigorod, 1-4.10.200
Nijenhuis tensors in pseudoholomorphic curves neighborhoods
Normal forms of almost complex structures in a neighborhood of
pseudoholomorphic curve are considered. We define normal bundles of such curves
and study the properties of linear bundle almost complex structures. We
describe 1-jet of the almost complex structure along a curve in terms of its
Nijenhuis tensor. For pseudoholomorphic tori we investigate the problem of
pseudoholomorphic foliation of the neighborhood. We obtain some results on
nonexistence of the tori deformation.Comment: 27 page
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