47 research outputs found
Structure of Two-qubit Symmetric Informationally Complete POVMs
In the four-dimensional Hilbert space, there exist 16 Heisenberg--Weyl (HW)
covariant symmetric informationally complete positive operator valued measures
(SIC~POVMs) consisting of 256 fiducial states on a single orbit of the Clifford
group. We explore the structure of these SIC~POVMs by studying the symmetry
transformations within a given SIC~POVM and among different SIC~POVMs.
Furthermore, we find 16 additional SIC~POVMs by a regrouping of the 256
fiducial states, and show that they are unitarily equivalent to the original 16
SIC~POVMs by establishing an explicit unitary transformation. We then reveal
the additional structure of these SIC~POVMs when the four-dimensional Hilbert
space is taken as the tensor product of two qubit Hilbert spaces. In
particular, when either the standard product basis or the Bell basis are chosen
as the defining basis of the HW group, in eight of the 16 HW covariant
SIC~POVMs, all fiducial states have the same concurrence of . These
SIC~POVMs are particularly appealing for an experimental implementation, since
all fiducial states can be connected to each other with just local unitary
transformations. In addition, we introduce a concise representation of the
fiducial states with the aid of a suitable tabular arrangement of their
parameters.Comment: 10 pages, 1 figure, 5 table
Towards optimal quantum tomography with unbalanced homodyning
Balanced homodyning, heterodyning and unbalanced homodyning are the three
well-known sampling techniques used in quantum optics to characterize all
possible photonic sources in continuous-variable quantum information theory. We
show that for all quantum states and all observable-parameter tomography
schemes, which includes the reconstructions of arbitrary operator moments and
phase-space quasi-distributions, localized sampling with unbalanced homodyning
is always tomographically more powerful (gives more accurate estimators) than
delocalized sampling with heterodyning. The latter is recently known to often
give more accurate parameter reconstructions than conventional marginalized
sampling with balanced homodyning. This result also holds for realistic
photodetectors with subunit efficiency. With examples from first- through
fourth-moment tomography, we demonstrate that unbalanced homodyning can
outperform balanced homodyning when heterodyning fails to do so. This new
benchmark takes us one step towards optimal continuous-variable tomography with
conventional photodetectors and minimal experimental components.Comment: 9 pages, 4 figure
Numerical Estimation Schemes for Quantum Tomography
Ph.DDOCTOR OF PHILOSOPH