q-Deformed three-level quantum logic
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q-Deformed three-level quantum logic Azmi Ali Altintas1 · Fatih Ozaydin2
· Cihan Bayındır3,4,5
Received: 21 February 2020 / Accepted: 8 July 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Three-level information plays an important role in the quantum domain. However, q-deformed three-level quantum logic is missing. Here, we address this problem and following Schwinger representation and using q-deformed harmonic oscillators, we construct three-level quantum system (qutrits), as well as one-, two- and three-qutrit q-deformed quantum logic gates. We believe our findings have a potential to contribute to q-deformed quantum science and technology. Keywords q-deformation · Qutrit · Quantum logic · Quantum gate
1 Introduction Unlike classical computation and communications where two-level information is dominant, three-level information (qutrits) has undeniable importance in the quantum domain. Strikingly, in two-party cryptographic problems, qutrits provide higher security than qubits [1]. Cerf et al. considered qutrits and higher level qudits in quantum cryptography for secure key distribution [2]. Vaziri et al. provided experimental proof that realization of new types of quantum communications which are also more secure can be made possible with higher-dimensional entangled states [3]. In a very recent
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Fatih Ozaydin [email protected] Azmi Ali Altintas [email protected] Cihan Bayındır [email protected]
1
Department of Electrical Engineering, Istanbul Okan University, Tuzla, Istanbul, Turkey
2
Institute for International Strategy, Tokyo International University, 1-13-1 Matoba-kita, Kawagoe, Saitama 350-1197, Japan
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Engineering Faculty, ˙Istanbul Technical University, 34469 Maslak, Istanbul, Turkey
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Engineering Faculty, Bo˘gaziçi University, 34342 Bebek, Istanbul, Turkey
5
CERN, 1211 Geneva, Switzerland 0123456789().: V,-vol
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work, Luo et al. considered arbitrarily high dimensions for quantum teleportation and presented experimental demonstration using qutrits [4]. Since the 1980s, with the idea of quantum groups, namely quantum algebras, in the studies on integrable systems in quantum field theory, quantum inverse scattering method has been used [5]. In order to construct a quantum group, one can use the Drinfeld’s method [6], in which a deformation parameter “q” is defined on Lie algebra. An alternative is the Woronowicz’s method which involves noncommutative co-multiplication [7], and another one is based on linear transformations on quantum plane which is called Manin’s approach [8]. Each approach has its own application area. For example, Manin’s approach is mainly used to construct inhomogeneous quantum invariance groups [9–12]. However, the Drinfeld’s method is the most popular one. Particle algebras are vital for describing the behavior of fermions and bosons, and one can define a deformation parameter on the particle algebras. The early examples are introduced by Arik and Coon [13,14]. Later, the relati
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