Quantum Walk in Terms of Quantum Bernoulli Noise and Quantum Central Limit Theorem for Quantum Bernoulli Noise

Dynamic Quantum Bernoulli Random Walks

Quantum Bernoulli random walks can be realized as random walks on the dual of SU(2). We use this realization in order to study a model of dynamic quantum Bernoulli random walk with time dependent transitions. For the corresponding dynamic random walk on the dual of SU(2), we prove several limit theorems (local limit theorem, central limit theorem, law of large numbers, large deviations principl...

Topics in Quantum Measurement and Quantum Noise

In this thesis we consider primarily the dynamics of quantum systems subjected to continuous observation. In the Schrödinger picture the evolution of a continuously monitored quantum system, referred to as a ‘quantum trajectory’, may be described by a stochastic equation for the state vector. We present a method of deriving explicit evolution operators for linear quantum trajectories, and apply...

Conductance in quantum wires by three quantum dots arrays

A noninteracting quantum-dot arrays side coupled to a quantum wire is studied. Transport through the quantum wire is investigated by using a noninteracting Anderson tunneling Hamiltonian. The conductance at zero temperature develops an oscillating band with resonances and antiresonances due to constructive and destructive interference in the ballistic channel, respectively. Moreover, we have fo...

Bernoulli , Euler , permutations and quantum algebras

Quantum Error Correction in correlated quantum noise

The superiority of quantum computation over conventional computation relies on the fact that a quantumbit (qubit) register can be in the superposition of a very large number of classical computational states. At the same time, maintaining coherence of this highly superpositional state poses also the main obstacle for the realization of a quantum computer. For a small number of qubits this diffi...