Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Measurement uncertainty relations: characterising optimal error bounds
  for qubits   In standard formulations of the uncertainty principle, two fundamental
features are typically cast as impossibility statements: two noncommuting
observables cannot in general both be sharply defined (for the same state), nor
can they be measured jointly. The pioneers of quantum mechanics were acutely
aware and puzzled by this fact, and it motivated Heisenberg to seek a
mitigation, which he formulated in his seminal paper of 1927. He provided
intuitive arguments to show that the values of, say, the position and momentum
of a particle can at least be unsharply defined, and they can be measured
together provided some approximation errors are allowed. Only now, nine decades
later, a working theory of approximate joint measurements is taking shape,
leading to rigorous and experimentally testable formulations of associated
error tradeoff relations. Here we briefly review this new development,
explaining the concepts and steps taken in the construction of optimal joint
approximations of pairs of incompatible observables. As a case study, we deduce
measurement uncertainty relations for qubit observables using two distinct
error measures. We provide an operational interpretation of the error bounds
and discuss some of the first experimental tests of such relations.

12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: cs
30
The categories of this paper are: q-alg