Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Natural majorization of the Quantum Fourier Transformation in
  phase-estimation algorithms   We prove that majorization relations hold step by step in the Quantum Fourier
Transformation (QFT) for phase-estimation algorithms considered in the
canonical decomposition. Our result relies on the fact that states which are
mixed by Hadamard operators at any stage of the computation only differ by a
phase. This property is a consequence of the structure of the initial state and
of the QFT, based on controlled-phase operators and a single action of a
Hadamard gate per qubit. As a consequence, Hadamard gates order the probability
distribution associated to the quantum state, whereas controlled-phase
operators carry all the entanglement but are immaterial to majorization. We
also prove that majorization in phase-estimation algorithms follows in a most
natural way from unitary evolution, unlike its counterpart in Grover's
algorithm.

21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc