Coherent spaces, Boolean rings and quantum gates

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• 作者：A. Vourdas ^{a.vourdas@bradford.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Coherence ; Boolean rings ; Gates
• 刊名：Annals of Physics
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：373
• 期：Complete
• 页码：557-580
• 全文大小：514 K

文摘

Coherent spaces spanned by a finite number of coherent states, are introduced. Their coherence properties are studied, using the Dirac contour representation. It is shown that the corresponding projectors resolve the identity, and that they transform into projectors of the same type, under displacement transformations, and also under time evolution. The set of these spaces, with the logical OR and AND operations is a distributive lattice, and with the logical XOR and AND operations is a Boolean ring (Stone’s formalism). Applications of this Boolean ring into classical CNOT gates with n$n$-ary variables, and also quantum CNOT gates with coherent states, are discussed.