Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum uncertainty as classical uncertainty of real-deterministic
  variables constructed from complex weak values and a global random variable   What does it take for real-deterministic c-valued (i.e., classical,
commuting) variables to comply with the Heisenberg uncertainty principle? Here,
we construct a class of real-deterministic c-valued variables out of the weak
values obtained via a non-perturbing weak measurement of quantum operators with
a post-selection over a complete set of state vectors basis, which always
satisfies the Kennard-Robertson-Schr\"odinger uncertainty relation. First, we
introduce an auxiliary global random variable and couple it to the imaginary
part of the weak value to transform the incompatibility between the quantum
operator and the basis into the fluctuation of an `error term', and then
superimpose it onto the real-part of the weak value. We show that this class of
``c-valued physical quantities'' provides a real-deterministic contextual
hidden variable model for the quantum expectation value of a certain class of
operators. We then show that the Schr\"odinger and the Kennard-Robertson lower
bounds can be obtained separately by imposing the classical uncertainty
relation to the c-valued physical quantities associated with a pair of
Hermitian operators. Within the representation, the complementarity between two
incompatible quantum observables manifests the absence of a basis wherein the
error terms of the associated two c-valued physical quantities simultaneously
vanish. Furthermore, quantum uncertainty relation is captured by a specific
irreducible epistemic restriction, foreign in classical mechanics, constraining
the allowed form of the joint distribution of the two c-valued physical
quantities. We then suggest an epistemic interpretation of the two terms
decomposing the c-valued physical quantity as the optimal estimate under the
epistemic restriction and the associated estimation error, and discuss the
classical limit.

35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
2
The categories of this paper are: math
22
The categories of this paper are: chao-dyn