MV-algebras and quantum computation (Q2498366)

The authors give a generalization of MV-algebras which is motivated by a study of quantum computing, namely of quantum logical gates. A prototypical example is a unit circle with the center \(\langle \frac{1}{2}, \frac{1}{2} \rangle.\) These algebras are called quasi-MV-algebras, and it is shown that they can be embedded into the direct product of an MV-algebra and a special kind of quasi-MV-algebra. In addition, the completeness theorem is proved that says that two terms are the same in every flat quasi-MV-algebra iff they are the same in the above-mentioned ``circle''.