Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the unpredictability of individual quantum measurement outcomes   We develop a general, non-probabilistic model of prediction which is suitable
for assessing the (un)predictability of individual physical events. We use this
model to provide, for the first time, a rigorous proof of the unpredictability
of a class of individual quantum measurement outcomes, a well-known quantum
attribute postulated or claimed for a long time.
  We prove that quantum indeterminism - formally modelled as value
indefiniteness - is incompatible with the supposition of predictability:
measurements of value indefinite observables are unpredictable. The proof makes
essential use of a strengthened form of the Kochen-Specker theorem proven
previously to identify value indefinite observables. This form of quantum
unpredictability, like the Kochen-Specker theorem, relies on three assumptions:
compatibility with quantum mechanical predictions, non-contextuality, and the
value definiteness of observables corresponding to the preparation basis of a
quantum state.
  We explore the relation between unpredictability and incomputability and show
that the unpredictability of individual measurements of a value indefinite
quantum observable complements, and is independent of, the global strong
incomputability of any sequence of outcomes of this particular quantum
experiment.
  Finally, we discuss a real model of hypercomputation whose computational
power has yet to be determined, as well as further open problems.

27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
2
The categories of this paper are: math
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys