Quantum Walks for Computer Scientists
Quantum Walks for Computer Scientists
One-dimensional discrete-time quantum walks on random environments
Quantum Information Processing
Localization of an inhomogeneous discrete-time quantum walk on the line
Quantum Information Processing
One dimensional quantum walks with memory
Quantum Information & Computation
Limit theorems for quantum walks with memory
Quantum Information & Computation
Limit theorems and absorption problems for quantum random walks in one dimension
Quantum Information & Computation
Crossovers induced by discrete-time quantum walks
Quantum Information & Computation
Quantum walk on distinguishable non-interacting many-particles and indistinguishable two-particle
Quantum Information Processing
Limit measures of inhomogeneous discrete-time quantum walks in one dimension
Quantum Information Processing
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Since a limit distribution of a discrete-time quantum walk on the line was derived in 2002, a lot of limit theorems for quantum walks with a localized initial state have been reported. On the other hand, in quantum probability theory, there are four notions of independence (free, monotone, commuting, and boolean independence) and quantum central limit theorems associated to each independence have been investigated. The relation between quantum walks and quantum probability theory is still unknown. As random walks are fundamental models in the Kolmogorov probability theory, can the quantum walks play an important role in quantum probability theory? To discuss this problem, we focus on a discrete-time 2-state quantum walk with a non-localized initial state and present a limit theorem. By using our limit theorem, we generate probability laws in the quantum central limit theorems from the quantum walk.