This PhD-thesis is based on the five experiments I have performed during mytime as a PhD-student. Three experiments are implementations of non-contextualinequalities and two are implementations of witness functions for classical- andquantum dimensions of sets of states. A dimension witness is an operator function that produce a value whenapplied to a set of states. This value has different upper bounds depending onthe dimension of the set of states and also depending on if the states are classicalor quantum. Therefore a dimension witness can only give a lower bound on thedimension of the set of states.The first dimension witness is based on the CHSH-inequality and has theability of discriminating between classical and quantum sets of states of two andthree dimensions, it can also indicate if a set of states must be of dimension fouror higher.The second dimension witness is based on a set theoretical representationof the possible combinations of states and measurements and grows with thedimension of the set of states you want to be able to identify, on the other handthere is a formula for expanding it to arbitrary dimension.Non-contextual hidden variable models is a family of hidden variable modelswhich 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 first experiment is a violation of the KCBS-inequality, this is the simplest 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 final experiment of the thesis is an implementation of a Hardy-like equality 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 mechanicsgives a non-zero value for all terms.

Denna doktorsavhandling är baserad på fem experiment jag har utfört undermin tid som doktorand. Tre experiment är realiseringar av icke-kontextuella olikheter och de två övriga är realiseringar av vittnesfunktioner för klassiska och kvantmekaniska dimensioner hos en uppsättning tillstånd. Ett dimensionsvittne är en funktion som tar en uppsättning tillstånd och producerar ett värde. Detta värde har olika övre gränser beroende på dimensionen hos uppsättningen tillstånd och beror även på om tillstånden är klassiska eller kvantmekaniska. På grund av detta kan ett dimensionsvittne endast ge en undre uppskattning på dimensionen hos en uppsättning tillstånd.Det första dimensionsvittnet är baserat på CHSH-olikheten och kan urskiljamellan klassiska och kvantmekaniska tillstånd av två och tre dimensioner, det kan även avgöra ifall uppsättningen av tillstånd har dimension fyra eller högre. Det andra dimensionsvittnet är baserat på en sannolikhetsteoretisk representation av möjliga kombinationer av tillstånd och mätningar. Detta vittne växer med antalet dimensioner som skall kunna urskiljas, å andra sidan finns det en formel för hur man kan expandera vittnet till godtycklig dimension.Icke-kontextuella gömda-variabel-teorier är en familj av gömda-variabel-teorier som innefattar lokala gömda-variabel-teorier, så i en bemärkelse är icke-kontextuella olikheter en generalisering av Bell-olikheter. Experimenteni denna avhandling använder sig alla av en-partikel-kvantsystem. Det första experimentet är en brytning av KCBS-olikheten, det är den en-klaste olikheten baserad på korrelationer som kan brytas av kvantmekanik. Det andra experimentet är en brytning av Wright-olikheten som är den enklaste olikheten som kan brytas av kvantmekanik, den innehåller endast projektorer inga korrelationer. Det sista experimentet i avhandlingen är en realisering av en Hardy-lik olikhet för icke-kontextualitet. Detta betyder att operatorerna i KCBS-olikheten har roterats så att en term i summan är identiskt noll för alla icke-kontextuella gömda-variabel-teorier och vi får en motsägelse då kvantmekaniken ger ettnoll-skiljt värde för alla termer.

The rapidly developing interdisciplinary field of quantum information, which merges quantum and information science, studies non-classical aspects of quantum systems. These studies are motivated by the promise that the non-classicality can be used to solve tasks more efficiently than classical methods would allow. In many quantum informational studies, non-classical behaviour is attributed to the notion of entanglement.

In this thesis we use photons to experimentally investigate fundamental questions such as: What happens to the entanglement in a system when it is affected by noise? In our study of noisy entanglement we pursue the challenging task of creating bound entanglement. Bound entangled states are created through an irreversible process that requires entanglement. Once in the bound regime, entanglement cannot be distilled out through local operations assisted by classical communication. We show that it is possible to experimentally produce four-photon bound entangled states and that a violation of a Bell inequality can be achieved. Moreover, we demonstrate an entanglement-unlocking protocol by relaxing the condition of local operations.

We also explore the non-classical nature of quantum mechanics in several single-photon experiments. In these experiments, we show the violation of various inequalities that were derived under the assumption of non-contextuality. Using qutrits we construct and demonstrate the simplest possible test that offers a discrepancy between classical and quantum theory. Furthermore, we perform an experiment in the spirit of the Kochen-Specker theorem to illustrate the state-independence of this theorem. Here, we investigate whether or not measurement outcomes exhibit fully contextual correlations. That is, no part of the correlations can be attributed to the non-contextual theory. Our results show that only a small part of the experimental generated correlations are amenable to a non-contextual interpretation.