Quantum learning: optimal classification of qubit states

Pattern recognition is a central topic in Learning Theory with numerous applications such as voice and text recognition, image analysis, computer diagnosis. The statistical set-up in classification is the following: we are given an i.i.d. training set $(X_{1},Y_{1}),... (X_{n},Y_{n})$ where $X_{i}$ represents a feature and $Y_{i}\in \{0,1\}$ is a label attached to that feature. The underlying joint distribution of $(X,Y)$ is unknown, but we can learn about it from the training set and we aim at devising low error classifiers $f:X\to Y$ used to predict the label of new incoming features. Here we solve a quantum analogue of this problem, namely the classification of two arbitrary unknown qubit states. Given a number of `training' copies from each of the states, we would like to `learn' about them by performing a measurement on the training set. The outcome is then used to design mesurements for the classification of future systems with unknown labels. We find the asymptotically optimal classification strategy and show that typically, it performs strictly better than a plug-in strategy based on state estimation. The figure of merit is the excess risk which is the difference between the probability of error and the probability of error of the optimal measurement when the states are known, that is the Helstrom measurement. We show that the excess risk has rate $n^{-1}$ and compute the exact constant of the rate.Comment: 24 pages, 4 figure

A Novel Clustering Algorithm Based on Quantum Games

Enormous successes have been made by quantum algorithms during the last decade. In this paper, we combine the quantum game with the problem of data clustering, and then develop a quantum-game-based clustering algorithm, in which data points in a dataset are considered as players who can make decisions and implement quantum strategies in quantum games. After each round of a quantum game, each player's expected payoff is calculated. Later, he uses a link-removing-and-rewiring (LRR) function to change his neighbors and adjust the strength of links connecting to them in order to maximize his payoff. Further, algorithms are discussed and analyzed in two cases of strategies, two payoff matrixes and two LRR functions. Consequently, the simulation results have demonstrated that data points in datasets are clustered reasonably and efficiently, and the clustering algorithms have fast rates of convergence. Moreover, the comparison with other algorithms also provides an indication of the effectiveness of the proposed approach.Comment: 19 pages, 5 figures, 5 table

Quantum Tasks in Minkowski Space

The fundamental properties of quantum information and its applications to computing and cryptography have been greatly illuminated by considering information-theoretic tasks that are provably possible or impossible within non-relativistic quantum mechanics. I describe here a general framework for defining tasks within (special) relativistic quantum theory and illustrate it with examples from relativistic quantum cryptography and relativistic distributed quantum computation. The framework gives a unified description of all tasks previously considered and also defines a large class of new questions about the properties of quantum information in relation to Minkowski causality. It offers a way of exploring interesting new fundamental tasks and applications, and also highlights the scope for a more systematic understanding of the fundamental information-theoretic properties of relativistic quantum theory

A Literature Survey and Classifications on Data Deanonymisation

The problem of disclosing private anonymous data has become increasingly serious particularly with the possibility of carrying out deanonymisation attacks on publishing data. The related work available in the literature is inadequate in terms of the number of techniques analysed, and is limited to certain contexts such as Online Social Networks. We survey a large number of state-of-the-art techniques of deanonymisation achieved in various methods and on different types of data. Our aim is to build a comprehensive understanding about the problem. For this survey, we propose a framework to guide a thorough analysis and classifications. We are interested in classifying deanonymisation approaches based on type and source of auxiliary information and on the structure of target datasets. Moreover, potential attacks, threats and some suggested assistive techniques are identified. This can inform the research in gaining an understanding of the deanonymisation problem and assist in the advancement of privacy protection

Dynamic Modeling of Location Privacy Protection Mechanisms

International audienceMobile applications tend to ask for users’ location in order to improve the service they provide. However, aside from increasing their service utility, they may also store these data, analyze them or share them with external parties. These privacy threats for users are a hot topic of research, leading to the development of so called Location Privacy Protection Mechanisms. LPPMs often are configurable algorithms that enable the tuning of the privacy protection they provide and thus the leveraging of the service utility. However, they usually do not provide ways to measure the achieved privacy in practice for all users of mobile devices, and even less clues on how a given configuration will impact privacy of the data given the specificities of everyone’s mobility. Moreover, as most Location Based Services require the user position in real time, these measures and predictions should be achieved in real time. In this paper we present a metric to evaluate privacy of obfuscated data based on users’ points of interest as well as a predictive model of the impact of a LPPM on these measure; both working in a real time fashion. The evaluation of the paper’s contributions is done using the state of the art LPPM Geo-I on synthetic mobility data generated to be representative of real-life users’ movements. Results highlight the relevance of the metric to capture privacy, the fitting of the model to experimental data, and the feasibility of the on-line mechanisms due to their low computing complexity

A Predictive Differentially-Private Mechanism for Mobility Traces

International audienceWith the increasing popularity of GPS-enabled hand-held devices, location-based applications and services have access to accurate and real-time location information, raising serious privacy concerns for their millions of users. Trying to address these issues, the notion of geo-indistinguishability was recently introduced, adapting the well-known concept of Differential Privacy to the area of location-based systems. A Laplace-based obfuscation mechanism satisfying this privacy notion works well in the case of a sporadic use; Under repeated use, however, independently applying noise leads to a quick loss of privacy due to the correlation between the location in the trace. In this paper we show that correlations in the trace can be in fact exploited in terms of a prediction function that tries to guess the new location based on the previously reported locations. The proposed mechanism tests the quality of the predicted location using a private test; in case of success the prediction is reported otherwise the location is sanitized with new noise. If there is considerable correlation in the input trace, the extra cost of the test is small compared to the savings in budget, leading to a more efficient mechanism. We evaluate the mechanism in the case of a user accessing a location-based service while moving around in a city. Using a simple prediction function and two budget spending stategies, optimizing either the utility or the budget consumption rate, we show that the predictive mechanim can offer substantial improvements over the independently applied noise