While it seems possible that quantum computers may allow for algorithms offering a computational speed-up over classical algorithms for some problems, the issue is poorly understood. We explore thisâ€¦ (More)

The well-known Robertsonâ€“SchrÃ¶dinger uncertainty relations have state-dependent lower bounds, which are trivial for certain states. We present a general approach to deriving tight state-independentâ€¦ (More)

The Deutschâ€“Jozsa problem is one of the most basic ways to demonstrate the power of quantum computation. Consider a Boolean function f : {0,Â 1} n â†’ {0,Â 1} and suppose we have a black-box to computeâ€¦ (More)

In this paper we study von Neumann un-biasing normalisation for ideal and real quantum random number generators, operating on finite strings or infinite bit sequences. In the ideal cases one canâ€¦ (More)

We develop a general, non-probabilistic model of prediction which is suitable for assessing the (un)predictability of individual physical events. We use this model to provide, for the first time, aâ€¦ (More)

Quantum computation has shown much promise at providing, at least in some cases, a significant advantage over classical computation. However, the nature of quantum computation is still far from beingâ€¦ (More)

We present a stronger variant of the Kochen-Specker theorem in which some quantum observables are identified to be provably value indefinite. This result is utilised for the construction andâ€¦ (More)

Due to imperfections in measurement and hardware, the flow of bits generated by a quantum random number generator (QRNG) contains bias and correlation, two symptoms of non-randomness. There is noâ€¦ (More)

Unpredictability is an important concept throughout physics and plays a central role in quantum information theory. Despite this, little effort has been devoted to studying generalised notions orâ€¦ (More)