The main focus of this thesis is to explore the advantages of using higher-dimensional quantum systems (qudits) as building blocks for fault-tolerant quantum computation. In particular, we investigate the two main essential ingredients of many state-of-the-art fault-tolerant schemes [133], which are magic state distillation and topological error correction. The theory for both of these componen...

We investigate the notion of uncertainty region using variance based sum relation for qubits and qutrits.We compare qubit (a 2-level system) with that qutrit (3-level by considering two non-commuting Pauli-like observables, acting on dimensional Hilbert space. identify physically valid a is smaller than qutrit. This implies an enhanced precision can be achieved in measurement incompatible obser...

An unexpected connection exists between compatibility criteria for quantum states and Symmetric Informationally Complete quantum measurements (SIC-POVMs). Beginning with Caves, Fuchs and Schack’s "Conditions for compatibility of quantum state assignments", I show that a qutrit SIC-POVM studied in other contexts enjoys additional interesting properties. Compatibility criteria provide a new way t...

Based on the controlled order rearrange encryption (CORE) for quantum key distribution using EPR pairs[Fu.G.Deng and G.L.Long Phys.Rev.A68 (2003) 042315], we propose the generalized controlled order rearrangement encryption (GCORE) protocols of N qubits and N qutrits, concretely display them in the cases using 3-qubit, 2-qutrit maximally entangled basis states. We further indicate that our prot...

Consider a system consisting of n d-dimensional quantum particles (qudits), and suppose that we want to optimize the entanglement between each pair. One can ask the following basic question regarding the sharing of entanglement: what is the largest possible value Emax(n, d) of the minimum entanglement between any two particles in the system? Here we take the entanglement of formation as our mea...

We investigate the state space of bipartite qutrits. For states which are locally maximally mixed we obtain an analog of the “magic” tetrahedron for bipartite qubits—a magic simplex W. This is obtained via the Weyl group which is a kind of “quantization” of classical phase space. We analyze how this simplex W is embedded in the whole state space of two qutrits and discuss symmetries and equival...

Harnessing non-abelian statistics of anyons to perform quantum computational tasks is getting closer to reality. While the existence of universal anyons by braiding alone such as the Fibonacci anyon is theoretically a possibility, accessible anyons with current technology all belong to a class that is called weakly integral—anyons whose squared quantum dimensions are integers. We analyze the co...