Extended quantum logics

Kenji Tokuo

C. S. Sharma, M K Mukherjee

Two theorems are proved. In the first properties of an important mapping from an orthocomplemented lattice to itself are studied. In the second the authors extend the characterisation theorem of Zierler (1961) to get a very useful theorem characterising orthomodular lattices Since quantum logics are merely sigma -complete orthomodular lattices, the principal result is, for application in quantum physics, a characterisation theorem for quantum logics.

Richard J. Greechie, Stanley Gudder

Amandeep Singh

In the present communication, I deal with the modelling of Generalized Parametric R-Norm Information measure in quantum logic. This information measure is extended to Joint and Conditional measure in quantum logic.

Richard J. Greechie, Stanley Gudder

Canh Minh Do, Tsubasa Takagi, Kazuhiro Ogata

While constructing practical quantum computers by big companies remains a challenge, the application of quantum communication and cryptography has made remarkable progress. Therefore, it is crucial to verify quantum protocols before they can be trusted in safety and security-critical applications. We have proposed Basic Dynamic Quantum Logic (BDQL) to formalize and verify sequential models of quantum protocols with a support tool developed in Maude. However, BDQL does not support concurrency in its formalization. This article introduces Concurrent Dynamic Quantum Logic (CDQL), an extension of BDQL, to formalize and verify concurrent models of quantum protocols. CDQL is more expressive than BDQL by considering concurrent behavior and communication among participants in quantum protocols. Since CDQL is a conservative extension of BDQL, we extend the syntax of BDQL to CDQL and make a transformation from CDQL to BDQL without interrupting the semantics of BDQL. We also extend the implementation of BDQL to support CDQL, making a new support tool in Maude. The new support tool is equipped with a lazy rewriting strategy to make the verification process significantly faster. Several quantum communication protocols are successfully formalized and verified in BDQL/CDQL, demonstrating the effectiveness of our automated approach and tool in verifying quantum protocols.