
Supersymmetriç coherent states and superqubit units of quantum information
Title:
Supersymmetriç coherent states and superqubit units of quantum information
Author:
Koçak Özvarol, Aygül, author.
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Physical Description:
x, 182 leaves: charts;+ 1 computer laser optical disc
Abstract:
In this thesis, we study the set of maximally entangled Bell based super-coherent states, involving both fermionic and bosonic components. By extending the supersymmetric annihilation operator introduced by Aragone and Zypmann, we develop four distinct types of supersymmetric coherent states, related to the Bell two-qubit quantum states. These Bell super-qubit states form the basis for the Bell-based supersymmetric coherent states, which are constructed using a displacement operator. When these states are combined with separable bosonic coherent states, represented as points on the super-Bloch sphere, the resulting structure is called Bell-based super-coherent states. The entanglement between the bosonic and fermionic components is analyzed through a displacement bosonic operator, which acts on a super-qubit reference state. For these entangled super-coherent states, uncertainty relations are expressed by concurrence. The monotonic relationship between uncertainty and concurrence $C$ indicates the influence of entanglement on uncertainty relations. Then, we observe quadrature squeezing in the uncertainties of position and momentum. Furthermore, we describe an infinite sequence of super-coherent states, whose uncertainty relations are characterized by the ratio of two Fibonacci numbers. For generalization of previous results, we introduce the generic super-qubit quantum state, where the single super-particle state is defined by a complex parameter $\zeta$. This leads us to description of PK-super-qubit quantum states, which are characterized by two unit spheres. These states form the basis for what we refer to as PK-supersymmetric coherent states, for which we have analyzed the entanglement properties. The pq-deformed super-coherent states and particular case as q-deformed super-coherent states are studied.
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Thesis (Doctoral)--İzmir Institute of Technology:Mathematics.
İzmir Institute of Technology:Mathematics--Thesis (Doctoral).
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