D. M. Appleby

Publications45
h-index20
Citations1,267
Highly Influential Citations117
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Symmetric informationally complete–positive operator valued measures and the extended Clifford group
We describe the structure of the extended Clifford group [defined to be the group consisting of all operators, unitary and antiunitary, which normalize the generalized Pauli group (or Weyl–Heisenberg…
SIC-POVMs and the Extended Clifford Group
We describe the structure of the extended Clifford Group (defined to be the group consisting of all operators, unitary and anti-unitary, which normalize the generalized Pauli group (or…
The Bell–Kochen–Specker theorem
Galois automorphisms of a symmetric measurement
TLDR
The Galois group of SICs covariant with respect to the Weyl-Heisenberg group is examined and a list of nine conjectures concerning its structure are proposed, representing a considerable strengthening of the theorems actually proved.
Concept of Experimental Accuracy and Simultaneous Measurements of Position and Momentum
The concept of experimental accuracy isinvestigated in the context of the unbiased jointmeasurement processes defined by Arthurs and Kelly. Adistinction is made between the errors of retrodictionand…
SIC‐POVMS and MUBS: Geometrical Relationships in Prime Dimension
The paper concerns Weyl‐Heisenberg covariant SIC‐POVMs (symmetric informationally complete positive operator valued measures) and full sets of MUBs (mutually unbiased bases) in prime dimension. When…
Properties of the extended Clifford group with applications to SIC-POVMs and MUBs
We consider a version of the extended Clifford Group which is defined in terms of a finite Galois field in odd prime power dimension. We show that Neuhauser's result, that with the appropriate choice…
Error Principle
The problem of characterizing the accuracy ofand disturbance caused by a joint measurement ofposition and momentum is investigated. In a previouspaper the problem was discussed in the context of the…
Symmetric informationally complete measurements of arbitrary rank
There has been much interest in so-called SIC-POVMs, i.e., rank 1 symmetric informationally complete positive operator valued measures. In this paper we discuss the larger class of POVMs that are…
Linear dependencies in Weyl–Heisenberg orbits
TLDR
It is proved that linear dependencies will always emerge in Weyl–Heisenberg orbits when the fiducial vector lies in a certain subspace of an order 3 unitary matrix, and this work aligns with recent studies on representations of the Clifford group.
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