3 research outputs found
A sequence of unsharp measurements enabling a real time visualization of a quantum oscillation
The normalized state of a single
two-level system performs oscillations under the influence of a resonant
driving field. It is assumed that only one realization of this process is
available. We show that it is possible to approximately visualize in real time
the evolution of the system as far as it is given by . For this
purpose we use a sequence of particular unsharp measurements separated in time.
They are specified within the theory of generalized measurements in which
observables are represented by positive operator valued measures (POVM). A
realization of the unsharp measurements may be obtained by coupling the
two-level system to a meter and performing the usual projection measurements on
the meter only.Comment: 17 pages, 3 figures, accepted for publication in Phys. Rev. A. Some
typographical corrections are made and a short treatmeant of the fidelity of
our measurements (N-series) is adde
Symmetric Informationally Complete Quantum Measurements
We consider the existence in arbitrary finite dimensions d of a POVM
comprised of d^2 rank-one operators all of whose operator inner products are
equal. Such a set is called a ``symmetric, informationally complete'' POVM
(SIC-POVM) and is equivalent to a set of d^2 equiangular lines in C^d.
SIC-POVMs are relevant for quantum state tomography, quantum cryptography, and
foundational issues in quantum mechanics. We construct SIC-POVMs in dimensions
two, three, and four. We further 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.Comment: 8 page
Complete measurements of quantum observables
We define a complete measurement of a quantum observable (POVM) as a
measurement of the maximally refined version of the POVM. Complete measurements
give information from the multiplicities of the measurement outcomes and can be
viewed as state preparation procedures. We show that any POVM can be measured
completely by using sequential measurements or maximally refinable instruments.
Moreover, the ancillary space of a complete measurement can be chosen to be
minimal.Comment: Based on talk given in CEQIP 2012 conferenc