Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlinear Schr\"odinger equations and generalized Heisenberg uncertainty
  principle violating the principle of estimation independence   One of the advantages of a reconstruction of quantum mechanics based on
transparent physical axioms is that it may offer insight to naturally
generalize quantum mechanics by relaxing the axioms. Here, we discuss possible
extensions of quantum mechanics within a general epistemic framework based on
an operational scheme of estimation of momentum given positions under epistemic
restriction. The epistemic restriction is parameterized by a
global-nonseparable random variable on the order of Planck constant, an ontic
extension to the separable classical phase space variables. Within the
estimation scheme, the canonical quantum laws is reconstructed for a specific
estimator and estimation error. In the present work, keeping the Born's
quadratic law intact, we construct a class of nonlinear variants of
Schr\"odinger equation and generalized Heisenberg uncertainty principle within
the estimation scheme by assuming a more general class of estimation errors.
The nonlinearity of the Schr\"odinger equation and the deviation from the
Heisenberg uncertainty principle thus have a common transparent operational
origin in terms of generalizations of estimation errors. We then argue that a
broad class of nonlinearities and deviations from Heisenberg uncertainty
principle arise from estimation errors violating a plausible
inferential-causality principle of estimation independence which is respected
by the standard quantum mechanics. This result therefore constrains possible
extensions of quantum mechanics, and suggests directions to generalize quantum
mechanics which comply with the principle of estimation independence.

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The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
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The categories of this paper are: eess
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
16
The categories of this paper are: stat
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The categories of this paper are: adap-org