Clocks and fisher information

In a broad sense, any parametric family of quantum states can be viewed as a quantum clock. The time, which is the parameter, is encoded in the corresponding quantum states. The quality of such a clock depends on how precisely we can distinguish the states or, equivalently, estimate the parameter. In view of the quantum Cramér—Rao inequalities, the quality of quantum clocks can be characterized by the quantum Fisher information. We address the issue of quantum clock synchronization in terms of quantum Fisher information and demonstrate its fundamental difference from the classical paradigm. The key point is the superadditivity of Fisher information, which always holds in the classical case but can be violated in quantum mechanics. The violation can occur for both pure and mixed states. Nevertheless, we establish the superadditivity of quantum Fisher information for any classical-quantum state. We also demonstrate an alternative form of superadditivity and propose a weak form of superadditivity. The violation of superadditivity can be exploited to enhance quantum clock synchronization.     

Valuations and Dedekind's Prague Theorem

To any field K we associate an entailment relation in the sense of Scott (Proceedings of the Tarski Symposium, 1974, pp. 411–435). In this way we can interpret an abstract propositional theory representing a generic valuation ring of a field, and obtain a simple effective proof of Dedekind's Prague theorem (Edwards, Arch. Hist. Ex. Sci (1980) 321–378; Divisor Theory, Birkhäuser, Boston, 1990).     

Knowledge Representation, Reasoning and Integration Using Temporal Logic with Clocks

Representation, reasoning about and integrating knowledge based on multiple time granularities in knowledge-based systems is important, especially when talking about events that take place in the real world. Formal approaches based on temporal logics have been successfully applied in many application domains of knowledge-based systems where the evolution of a system and its environment through time is central. This paper presents a methodology based on temporal logic to deal with knowledge based on multiple time granularities in knowledge-based systems. The temporal logic we consider is especially suitable for modelling events with different rates and/or scales of progress. The methodology includes an approach to the representation of timing systems, a method used for representing facts and rules in a knowledge-based system that involve multiple time granularities using temporal logic, and several deductive reasoning techniques. The work presented in this article has been supported in part by The Australian Research Council and Macquarie University. Note that this paper is an extended and revised version of Orgun, Liu and Nayak [37].