Quantum computation and privacy

Quantum mechanics is one of the most intriguing subjects to study. The world works inherently differently on very small scales and can no longer be described by means of classical physics corresponding to our everyday intuition. Contrary to classical computing, quantum computation is based on the rules of quantum mechanics. It not only allows for more efficient local computations, but also has far-reaching effects on multi-party protocols. In this thesis, we investigate two cryptographic primitives for privacy protection using quantum computing: private information retrieval and anonymous transmissions

Supporting polyrepresentation in a quantum-inspired geometrical retrieval framework

The relevance of a document has many facets, going beyond the usual topical one, which have to be considered to satisfy a user's information need. Multiple representations of documents, like user-given reviews or the actual document content, can give evidence towards certain facets of relevance. In this respect polyrepresentation of documents, where such evidence is combined, is a crucial concept to estimate the relevance of a document. In this paper, we discuss how a geometrical retrieval framework inspired by quantum mechanics can be extended to support polyrepresentation. We show by example how different representations of a document can be modelled in a Hilbert space, similar to physical systems known from quantum mechanics. We further illustrate how these representations are combined by means of the tensor product to support polyrepresentation, and discuss the case that representations of documents are not independent from a user point of view. Besides giving a principled framework for polyrepresentation, the potential of this approach is to capture and formalise the complex interdependent relationships that the different representations can have between each other

mARC: Memory by Association and Reinforcement of Contexts

This paper introduces the memory by Association and Reinforcement of Contexts (mARC). mARC is a novel data modeling technology rooted in the second quantization formulation of quantum mechanics. It is an all-purpose incremental and unsupervised data storage and retrieval system which can be applied to all types of signal or data, structured or unstructured, textual or not. mARC can be applied to a wide range of information clas-sification and retrieval problems like e-Discovery or contextual navigation. It can also for-mulated in the artificial life framework a.k.a Conway "Game Of Life" Theory. In contrast to Conway approach, the objects evolve in a massively multidimensional space. In order to start evaluating the potential of mARC we have built a mARC-based Internet search en-gine demonstrator with contextual functionality. We compare the behavior of the mARC demonstrator with Google search both in terms of performance and relevance. In the study we find that the mARC search engine demonstrator outperforms Google search by an order of magnitude in response time while providing more relevant results for some classes of queries

On quantum statistics in data analysis

Originally, quantum probability theory was developed to analyze statistical phenomena in quantum systems, where classical probability theory does not apply, because the lattice of measurable sets is not necessarily distributive. On the other hand, it is well known that the lattices of concepts, that arise in data analysis, are in general also non-distributive, albeit for completely different reasons. In his recent book, van Rijsbergen argues that many of the logical tools developed for quantum systems are also suitable for applications in information retrieval. I explore the mathematical support for this idea on an abstract vector space model, covering several forms of data analysis (information retrieval, data mining, collaborative filtering, formal concept analysis...), and roughly based on an idea from categorical quantum mechanics. It turns out that quantum (i.e., noncommutative) probability distributions arise already in this rudimentary mathematical framework. We show that a Bell-type inequality must be satisfied by the standard similarity measures, if they are used for preference predictions. The fact that already a very general, abstract version of the vector space model yields simple counterexamples for such inequalities seems to be an indicator of a genuine need for quantum statistics in data analysis.Comment: 7 pages, Quantum Interaction 2008 (Oxford, April 2008) v3: added two diagrams, changed some wording