A language L has a property tester if there exists a probabilistic algorithm that given an input x only asks a small number of bits of x and distinguishes the cases as to whether x is in L and x has large Hamming distance from all y in L. We define a similar notion of quantum property testing and show that there exist languages with quantum property testers but no good classical testers. We also show there exist languages which require a large number of queries even for quantumly testing.

We define and study the complexity of robust polynomials for Boolean functions and the related fault-tolerant quantum decision trees, where input bits are perturbed by noise. We compare several different possible definitions. Our main results are• For every n-bit Boolean function f there is an n-variate polynomial p of degree O(n) that robustly approximates it, in the sense that p(x) remains close to f (x) if we slightly vary each of the n inputs of the polynomial.• There is an O(n)-query quantum algorithm that robustly recovers n noisy input bits. Hence every n-bit function can be quantum computed with O(n) queries in the presence of noise. This contrasts with the classical model of Feige et al., where functions such as parity need Θ(n log n) queries.We give several extensions and applications of these results.

We use techniques for lower bounds on communication to derive necessary conditions (in terms of detector efficiency or amount of super-luminal communication) for being able to reproduce the quantum correlations occurring in EPR-type experiments with classical local hidden-variable theories. As an application, we consider n parties sharing a GHZ-type state and show that the amount of superluminal classical communication required to reproduce the correlations is at least n(log 2 n − 3) bits and the maximum detector efficiency η * for which the resulting correlations can still be reproduced by a local hidden-variable theory is upper bounded by η * ≤ 8/n and thus decreases with n.

We define and study the complexity of robust polynomials for Boolean functions and the related fault-tolerant quantum decision trees, where input bits are perturbed by noise. We compare several different possible definitions. Our main results are• For every n-bit Boolean function f there is an n-variate polynomial p of degree O(n) that robustly approximates it, in the sense that p(x) remains close to f (x) if we slightly vary each of the n inputs of the polynomial.• There is an O(n)-query quantum algorithm that robustly recovers n noisy input bits. Hence every n-bit function can be quantum computed with O(n) queries in the presence of noise. This contrasts with the classical model of Feige et al., where functions such as parity need Θ(n log n) queries.We give several extensions and applications of these results.

This paper presents a new approach for classifying individual video frames as being a 'cartoon' or a 'photographic image'. The task arose from experiments performed at the TREC-2002 video retrieval benchmark: 'cartoons' are returned unexpectedly at high ranks even if the query gave only 'photographic' image examples. Distinguishing between the two genres has proved difficult because of their large intra-class variation. In addition to image descriptors used in prior cartoon-classification work, we introduce novel descriptors like ones based on the pattern spectrum of parabolic size distributions derived from parabolic granulometries and the complexity of the image signal approximated by its compression ratio. We evaluate the effectiveness of the proposed feature set for classification (using Support Vector Machines) on a large set of keyframes from the TREC-2002 video track collection and a set of web images. The paper reports the identification error rates against the number of images used as training set. The system is compared with one that classifies Web images as photographs or graphics and its superior performance is evident.