The Formal Framework

Tomasz Linowski, Konrad Schlichtholz, Łukasz Rudnicki

The problem of defining a Hermitian quantum phase operator is nearly as old as quantum mechanics itself. Throughout the years, a number of solutions have been proposed, ranging from abstract operator formalisms to phase-space methods. In this work, we make an explicit connection between two of the most prominent approaches by proving that the probability distribution of phase in the Paul formalism follows exactly from the Pegg-Barnett formalism by combining the latter with the quantum-limited amplifier channel. Our findings suggest that the Paul framework may be viewed as a semiclassical limit of the Pegg-Barnett approach.

Amanda Lawson

This paper presents the unified mathematical formalism of the Lawson Doubled Mirror Bidirectional Framework, a branch-coupled bidirectional quantum evolution architecture constructed on a quadrupled Hilbert space with Clifford algebra $\mathrm{Cl}(1,3)$ structure.

Martin Janßen

Sheng Zhang, Yonghui Ma, Chunning Meng +1 more

This paper presents a new formal method for verification of quantum communication protocols. By extending the symbolic system of Petri nets, we can define quantum pure states in Petri-net settings. Therefore, it is possible to emerge a framework from formalizing basic quantum phenomena, which are utilized to achieve communication tasks. We also present an example of applying this framework to the modeling and analyzing quantum communication protocols to show how it works.