Narrow Results

The CAPSL Integrated Protocol Environment effort aims at providing an intuitive and expressive language for specifying cryptographic authentication and key distribution protocols and supporting interfaces to various analysis tools. The CAPSL Intermediate Language (CIL) has been designed with the emphasis on simplifying translators from CIL to other analysis tools. In this paper we describe the design of a CIL-to-Spin connector. We describe how CIL concepts are translated into Spin and propose a general method to model the behaviors of honest principals and the intruder. Based on the method, a prototype connector has been implemented in Gentle, which automatically translates CIL specifications to Promela codes and LTL formulae, thus greatly simplifying the modeling and analysis process.

It is known that a particle shows two different characters, particle-wave duality in the quantum mechanical world. Photons show the character of wave, such as diffraction and interference, but the photo-electric effect and the black-body radiation can be explained only by the particle character of light. In the microscopic world, duality is a property not only inherent in photons but also common in all particles including electrons, protons and neutrons. From this peculiar character of particles, the motion in the microscopic world can be understood only in the probability interpretation, i.e., the particles are described by the wave function ψ with a wave character and the measurements give the probabilities of finding particles in space-time. This is the concept called the Copenhagen interpretation of quantum mechanics, developed by Niels Bohr and his group. In this chapter, we summarize the basic ideas, principles and concepts of quantum mechanics.

We formulate entropic measurements uncertainty relations (MURs) for a spin-1/2 system. When incompatible observables are approximatively jointly measured, we use relative entropy to quantify the information lost in approximation and we prove positive lower bounds for such a loss: there is an unavoidable information loss. Firstly we allow only for covariant approximate joint measurements and we find state-dependent MURs for two or three orthogonal spin-1/2 components. Secondly we consider any possible approximate joint measurement and we find state-independent MURs for two or three spin-1/2 components. In particular we study how MURs depend on the angle between two spin directions. Finally, we extend our approach to infinitely many incompatible observables, namely to the spin components in all possible directions. In every scenario, we always consider also the characterization of the optimal approximate joint measurements.

The following sections are included:

• Wave function and probability interpretation

• Commutation relation and uncertainty relation

• Quantum states of spin ½ particles

• Quantum bit

• Angular momentum, spin and rotation

• Problems