Single photons - discrete wavepackets of light - are one of the most fundamental entities in physics. In recent years, the ability to consistently create and manipulate both single photons and pairs of photons has facilitated everything from tests of quantum theory to the implementation of quantum-enhanced precision measurements. These activities all fall within the scope of the rapidly-growing field of quantum information - the exploitation of the properties of quantum states (and specifically their capability to exist in superpositions) to accomplish tasks that would not be possible with classical objects. One stated goal of research in quantum information is to build a device consisting of a network of quantum logic gates that can evaluate quantum algorithms. The photonic implementation of individual logic gates has already been demonstrated. However, partly due to standard methods of preparing single photons, current schemes have severe limitations in terms of scaling up from a single logic gate to multiple concatenated operations. Until now it has not been proven that single photons can be generated in pure and indistinguishable quantum states, something upon which the successful operation of optical quantum logic gates relies. This thesis presents an experimental demonstration of simultaneous generation of almost identical single photons in highly pure states from two independent sources based on parametric downconversion. This is a process of photon pair generation during the passage of a light beam through a nonlinear crystal; one photon from the resulting pair is detected to herald the other. The work herein describes, refines, and implements a technique that minimises the strong quantum correlations usually present within each pair by spectral engineering of the source. This allows the heralded single photons to be in pure states, a property that is confirmed by observing a high-visibility two-photon interference effect without spectral filtering.

Quantum entanglement is a phenomenon which has shown great potential use in modern technical implementations, but there is still much development needed in the field. One major problem is how to measure the amount of entanglement present in a given entangled state. There are numerous different entanglement measures suggested, all satisfying some conditions being of either operational, or more abstract, mathematical nature. However, in contradiction to what one might expect, the measures show discrepancies in the ordering of entangled states. Concretely this means that with respect to one measure, a state can be more entangled than another state, but the ordering may be opposite for the same states using another measure. In this thesis we take a closer look at some of the most commonly occurring entanglement measures, and find examples of states showing inequivalent entanglement ordering for the different measures. / Kvantmekanisk sammanflätning är ett fenomen som visat stor potential för framtida tekniska tillämpningar, men för att kunna använda oss av detta krävs att vi hittar lämpliga modeller att mäta omfattningen av sammanflätningen hos ett givet tillstånd. Detta har visat sig vara en svår uppgift, då de modeller som finns idag är otillräckliga när det gäller att konsekvent avgöra till vilken grad olika tillstånd är sammanflätade. Exempelvis kan en modell visa att ett tillstånd är mer sammanflätat än ett annat, medan en annan modell kan visa på motsatsen - att det första tillståndet är mindre sammanflätat än det andra. En möljig orsak kan ligga i de olika modellernas deifnition, då vissa utgår från operativa definitioner, medan andra grundas på matematiska, abstrakta villkor. I denna uppsats tittar vi lite närmre på några av de mätmodeller som finns, och hittar exempel på tillstånd som uppvisar olika ordning av sammanflätningsgrad beroende på vilken modell som används.

This thesis focuses on two aspects of Quantum Information Processing (QIP) and contains experimental implementation by Nuclear Magnetic Resonance (NMR) spectroscopy. The two aspects are: (i) development of novel methodologies for improved or fault tolerant QIP using longer lived states and geometric phases and (ii) implementation of certain quantum algorithms and theorems by NMR. In the first chapter a general introduction to Quantum Information Processing and its implementation using NMR as well as a description of NMR Hamiltonians and NMR relaxation using Redfield theory and magnetization modes are given. The second chapter contains a study of relaxation of Pseudo Pure States (PPS). PPS are specially prepared initial states from where computation begins. These states, being non-equilibrium states, relax with time and hence introduce error in computation. In this chapter we have studied the role of Cross-Correlations in relaxation of PPS. The third and fourth chapters, respectively report observation of cyclic and non-cyclic geometric phases. When the state of a qubit is subjected to evolution either adiabatically or non-adiabatically along the surface of the Bloch sphere, the qubit sometimes gain a phase factor apart from the dynamic phase. This is known as the Geometric phase, as it depends only on the geometry of the path of evolution. Geometric phase is used in Fault tolerant QIP. In these two chapters we have demonstrated how geometric phases of a qubit can be measured using NMR. The fifth and sixth chapters contain the implementations of “No Deletion” and “No Cloning” (quantum triplicator for partially known states) theorems. No Cloning and No Deletion theorems are closely related. The former states that an unknown quantum states can not be copied perfectly while the later states that an unknown state can not be deleted perfectly either. In these two chapters we have discussed about experimental implementation of the two theorems. The last chapter contains implementation of “Deutsch-Jozsa” algorithm in strongly dipolar coupled spin systems. Dipolar couplings being larger than the scalar couplings provide better opportunity for scaling up to larger number of qubits. However, strongly coupled systems offer few experimental challenges as well. This chapter demonstrates how a strongly coupled system can be used in NMR QIP.