Quantum Randomness

Abstract

DeclarationThis thesis is the result of my own work and includes nothing which is the outcome of work done in collaboration with others, except where specifically indicated in the text.To my parents, Lorelei and John. 5689@AB7BA@9865 AcknowledgementsThe work comprising this thesis was carried out over the course of three years at the Centre For Quantum Computation, DAMTP, Cambridge, under the supervision of Adrian Kent. I am indebted to him for support and guidance. Discussions with Adrian are always a pleasure and his eagerness to find loopholes in any new proposal is second to none. His clear thinking and attention to detail have had huge impact on my work, and indeed my philosophy towards research.It is with great pleasure that I thank the members of the quantum information group for an enjoyable three years. Particular thanks go to Matthias Christandl, Robert König, Graeme Mitchison and Renato Renner for numerous useful discussions from which my work has undoubtedly benefited, and to Jiannis Pachos for his constant encouragement and support.My two office co-inhabitants deserve special mention here, not least for putting up with me! Alastair Kay for withstanding (and almost always answering) a battering of questions on forgotten physics, L A T E X, linux and much more besides, and Roberta Rodriquez for providing unrelenting emotional support on all matters from physics to life itself. I am very grateful to the Engineering and Physical Sciences ResearchCouncil for a research studentship and to Trinity College, Cambridge for a research scholarship and travel money. A junior research fellowship from Homerton College, Cambridge has provided financial support during the final stages of writing this thesis.Finally I would like to thank my examiners Robert Spekkens and Andreas Winter for their thorough analysis of this thesis. AbstractSecure multi-party computation is a task whereby mistrustful parties attempt to compute some joint function of their private data in such a way as to reveal as little as possible about it. It encompasses many cryptographic primitives, including coin tossing and oblivious transfer. Ideally, one would like to generate either a protocol or a no-go theorem for any such task.Very few computations of this kind are known to be possible with unconditional security. However, relatively little investigation into exploiting the cryptographic power of a relativistic theory has been carried out. In this thesis, we extend the range of known results regarding secure multi-party computations. We focus on two-party computations, and consider protocols whose security is guaranteed by the laws of physics. Specifically, the properties of quantum systems, and the impossibility of faster-than-light signalling will be used to guarantee security.After a general introduction, the thesis is divided into four parts. In the first, we discuss the task of coin tossing, principally in order to highlight the effect different physical theories have on security in a straightforward manner, but, also, to introduce a new...

Free will determines the limits of psychological foresight: Review of “Free Will” by Sam Harris

“…5 The only requirement to solve such systems is the detailedness in the utilized prediction model. In contrast, the second type of randomness is nonderivable or true randomness (e.g., Aaronson, 2014), c R2 . 6 It is this randomness that is derived from the observation that quantum mechanics seem to lack any predeterminism: One can never predict a particle's position at any given moment.…”

“…Note that the impact of free will (quantified as b 3 ) is variable.5 For instructive examples, see the butterfly effect(Lorenz, 2000) and chaos theory(Cambel, 1993).6 To be accurate, already specifically generated pseudorandomness (e.g., in long number strings) is de-facto, that is, in practice, nonderivable (also see,Aaronson, 2014). However, the beginning (e.g., number seed) is nonrandom which makes it theoretically derivable.…”

Generating randomness: making the most out of disordering a false order into a real one

“…A BIV can only be explained within local realism when events across history conspire to produce measured outcomes [46, 47]. Free variables are thus used to select measurements [48]. If some processes are “free” in the required sense, then other processes are similarly free [49].…”

“…The data confirmed the violation of Bell inequalities. Measurement-setting independence, provided by human agency, disagrees with causal determinism [44, 48]. The results thus closed the freedom-of-choice loophole—that setting choices are influenced by hidden variables to correlate with the properties of particles [84].…”

Graphical Methods in Device-Independent Quantum Cryptography

“…Precisely, two untrusted quantum devices, together with a perfectly random seed of length N , can be manipulated by a classical user to generate a perfectly random output of size f (N ) > N with negligible error. See [31] for a gentle introduction to this topic and [32] for a discussion of a possible implementation.…”