PhD thesis: Non-contextual inequalities and dimensionality
by
Johan Ahrens(Fysikum)
→
Europe/Stockholm
FB42
FB42
Description
Abstract
This PhD-thesis is based on the ve experiments I have performed during my
time as a PhD-student. Three experiments are implementations of non-contextual
inequalities and two are implementations of witness functions for classical- and
quantum dimensions of sets of states.
A dimension witness is an operator function that produce a value when
applied to a set of states. This value has dierent upper bounds depending on
the dimension of the set of states and also depending on if the states are classical
or quantum. Therefore a dimension witness can only give a lower bound on the
dimension of the set of states.
The rst dimension witness is based on the CHSH-inequality and has the
ability of discriminating between classical and quantum sets of states of two and
three dimensions, it can also indicate if a set of states must be of dimension four
or higher.
The second dimension witness is based on a set theoretical representation
of the possible combinations of states and measurements and grows with the
dimension of the set of states you want to be able to identify, on the other hand
there is a formula for expanding it to arbitrary dimension.
Non-contextual hidden variable models is a family of hidden variable models
which include local hidden variable models, so in a sence non-contextual inequal-
ities are a generalisation of Bell-inequalities. The experiments presented in this
thesis all use single particle quantum systems.
The rst experiment is a violation of the KCBS-inequality, this is the sim-
plest correlation inequality which is violated by quantum mechanics.
The second experiment is a violation of the Wright-inequality which is the
simplest inequality violated by quantum mechanics, it contains only projectors
and not correlations.
The nal experiment of the thesis is an implementation of a Hardy-like equal-
ity for non-contextuality, this means that the operators in the KCBS-inequality
have been rotated so that one term in the sum will be zero for all non-contextual
hidden variable models and we get a contradiction since quantum mechanics
gives a non-zero value for all terms.
Keywords: Quantum information, quantum optics, non-contextuality, dimen-
sion witness.
Johan Ahrens
