QC398 : Thermodynamics of entanglement in U(2) quantum walk
Thesis > Central Library of Shahrood University > Physics > MSc > 2017
Authors:
Abstarct: Quantum walk has many advantages to its counterpart, classical random walk. The application of quantum walk in designing advanced algorithms as well as in many other sciences has caused extensive studies made on it. These studies have different aspects, such as dimensions, entanglement between spaces, variance, distribution function, rate of propagation, etc., which are very important for studying because they represent special properties of quantum mechanics in quantum walks. One of the parameters which has been considered recently is entanglement temperature which has been attributed to quantum walk. It has been shown in quantum walks that the reduced density matrix will take an asymptotic form over time, which can be compared with a thermal equilibrium and can be considered as a thermodynamic system. By comparing the matrix of reduced density with the density matrix of systems interacting with the thermal bath, one can introduce a temperature to the reduced density matrix of quantum walk. This temperature is related to the coin- position entanglement and depends on eigenvalues of the reduced density matrix. In this thesis, we examined the thermodynamic components of quantum walks, especially the entanglement temperature. And in particular, the entanglement temperature for circle and one-dimensional systems. We have obtained a formalism for entanglement temperature and then, by changing the coin state by $ U (2) $ operator, we have investigated the effect of the coin on the entanglement temperature. We have also investigated entanglement temperature and transient temperature in Mobius quantum walk (MQW),which is generalization of quantum walk on a cycle.
Keywords:
#Quantum walk #reduced density matrix #entanglement temperature #quantum walk on the cycle #Mobius quantum walk #entanglement transient temperature
Keeping place: Central Library of Shahrood University
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Keeping place: Central Library of Shahrood University
Visitor: