• Publications
  • Influence
Symmetric informationally complete quantum measurements
TLDR
It is conjecture that a particular kind of group-covariant SIC–POVM exists in arbitrary dimensions, providing numerical results up to dimension 45 to bolster this claim.
Tight informationally complete quantum measurements
We introduce a class of informationally complete positive-operator-valued measures which are, in analogy with a tight frame, 'as close as possible' to orthonormal bases for the space of quantum
Symmetric informationally complete positive-operator-valued measures: A new computer study
We report on a new computer study of the existence of d2 equiangular lines in d complex dimensions. Such maximal complex projective codes are conjectured to exist in all finite dimensions and are the
SIC-POVMs: A new computer study
We report on a new computer study into the existence of d2 equiangular lines in d complex dimensions. Such maximal complex projective codes are conjectured to exist in all finite dimensions and are
Multipartite entanglement, quantum-error-correcting codes, and entangling power of quantum evolutions
TLDR
It is exposed a connection between such measures and quantum-error-correcting codes by deriving a formula relating the weight distribution of the code to the average entanglement of encoded states.
Weighted complex projective 2-designs from bases : Optimal state determination by orthogonal measurements
We introduce the problem of constructing weighted complex projective 2-designs from the union of a family of orthonormal bases. If the weight remains constant across elements of the same basis, then
Optimizing quantum process tomography with unitary 2-designs
We show that weighted unitary 2-designs define optimal measurements on the system-ancilla output state for ancilla-assisted process tomography of unital quantum channels. Examples include complete
Unitary designs and codes
TLDR
In this paper, irreducible representations of the unitary group are used to find a general lower bound on the size of a unitary t-design in U(d), for any d and t.
SICs: Extending the list of solutions
Zauner's conjecture asserts that $d^2$ equiangular lines exist in all $d$ complex dimensions. In quantum theory, the $d^2$ lines are dubbed a SIC, as they define a favoured standard informationally
Fibonacci-Lucas SIC-POVMs
We present a conjectured family of symmetric informationally complete positive operator valued measures which have an additional symmetry group whose size is growing with the dimension. The symmetry
...
...