Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum phase uncertainty in mutually unbiased measurements and Gauss
  sums   Mutually unbiased bases (MUBs), which are such that the inner product between
two vectors in different orthogonal bases is constant equal to the inverse
$1/\sqrt{d}$, with $d$ the dimension of the finite Hilbert space, are becoming
more and more studied for applications such as quantum tomography and
cryptography, and in relation to entangled states and to the Heisenberg-Weil
group of quantum optics. Complete sets of MUBs of cardinality $d+1$ have been
derived for prime power dimensions $d=p^m$ using the tools of abstract algebra
(Wootters in 1989, Klappenecker in 2003). Presumably, for non prime dimensions
the cardinality is much less. The bases can be reinterpreted as quantum phase
states, i.e. as eigenvectors of Hermitean phase operators generalizing those
introduced by Pegg & Barnett in 1989. The MUB states are related to additive
characters of Galois fields (in odd characteristic p) and of Galois rings (in
characteristic 2). Quantum Fourier transforms of the components in vectors of
the bases define a more general class of MUBs with multiplicative characters
and additive ones altogether. We investigate the complementary properties of
the above phase operator with respect to the number operator. We also study the
phase probability distribution and variance for physical states and find them
related to the Gauss sums, which are sums over all elements of the field (or of
the ring) of the product of multiplicative and additive characters. Finally we
relate the concepts of mutual unbiasedness and maximal entanglement. This
allows to use well studied algebraic concepts as efficient tools in our quest
of minimal uncertainty in quantum information primitives.

27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
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The categories of this paper are: eess
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio