We propose a conceptual design for a quantum blockchain. Our method involves encoding the blockchain into a temporal GHZ (Greenberger-Horne-Zeilinger) state of photons that do not simultaneously coexist. It is shown that the entanglement in time, as opposed to an entanglement in space, provides the crucial quantum advantage. All the subcomponents of this system have already been shown to be experimentally realized. Furthermore, our encoding procedure can be interpreted as nonclassically influencing the past.

Abstract. The Newman-Janis trick is a procedure, (not even really an ansatz), for obtaining the Kerr spacetime from the Schwarzschild spacetime. This 50 year old trick continues to generate heated discussion and debate even to this day. Most of the debate focusses on whether the Newman-Janis procedure can be upgraded to the status of an algorithm, or even an inspired ansatz, or is it just a random trick of no deep physical significance. (That the Newman-Janis procedure very quickly led to the discovery of the Kerr-Newman spacetime is a point very much in its favour.) In the current article we will not answer these deeper questions, we shall instead present a much simpler alternative variation on the theme of the Newman-Janis trick that might be easier to work with. We shall present a 2-step version of the Newman-Janis trick that works directly with the Kerr-Schild "Cartesian" metric presentation of the Kerr spacetime. That is, we show how the original 4-step Newman-Janis procedure can, (using the interplay between oblate spheroidal and Cartesian coordinates), be reduced to a considerably cleaner 2-step process.

The quantum Pusey-Barrett-Rudolph (PBR) theorem addresses the question of whether the quantum state corresponds to a ψ-ontic model (system's physical state) or to a ψ-epistemic model (observer's knowledge about the system). We reformulate the PBR theorem as a Monty Hall game, and show that winning probabilities, for switching doors in the game, depend whether it is a ψ-ontic or ψ-epistemic game. For certain cases of the latter, switching doors provides no advantage. We also apply the concepts involved to quantum teleportation, in particular for improving reliability.

A thesis submitted to the Victoria University of Wellington in fulfilment of the requirements for the degree of Master of Science in Mathematics.

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<p>This thesis is in the field of quantum information science, which is an area that reconceptualizes quantum physics in terms of information.  Central to this area is the quantum effect of entanglement in space.  It is an interdependence among two or more spatially separated quantum systems that would be impossible to replicate by classical systems.  Alternatively, an entanglement in space can also be viewed as a resource in quantum information in that it allows the ability to perform information tasks that would be impossible or very difficult to do with only classical information.  Two such astonishing applications are quantum communications which can be harnessed for teleportation, and quantum computers which can drastically outperform the best classical supercomputers.   In this thesis our focus is on the theoretical aspect of the field, and we provide one of the first expositions on an analogous quantum effect known as entanglement in time.  It can be viewed as an interdependence of quantum systems across time, which is stronger than could ever exist between classical systems.  We explore this temporal effect within the study of quantum information and its foundations as well as through relativistic quantum information.  An original contribution of this thesis is the design of one of the first quantum information applications of entanglement in time, namely a quantum blockchain.  We describe how the entanglement in time provides the quantum advantage over a classical blockchain.  Furthermore, the information encoding procedure of this quantum blockchain can be interpreted as non-classically influencing the past, and hence the system can be viewed as a `quantum time machine.'</p>

An effect known as time inversion was introduced in Christopher Nolan's film TENET, and here we demonstrate that such an effect exists for quantum information. We do this by investigating the von Neumann entropy of experimentally realized photons that are entangled in time. Using these findings, we design a technology called a Turnstile and apply it to detect Distributed Denial-of-Service (DDoS) attacks in quantum networks. Pragmatically, our work can be viewed as formulating the quantum analogue of the Shannon entropic DDoS detection systems used in classical networks.Introduction.-Quantum information has the astonishing ability to perform information tasks that would be impossible or very difficult to do with only classical information [1]. For instance, the property of superposition is used by quantum computers to drastically outperform the best classical supercomputers on certain tasks [2, 3]. Another example is the realization of secure quantum cryptographic protocols which are predicated on the impossibility to copy quantum information [4]. Perhaps the most radical departure from mere classical information is that quantum information can be teleported [5], recently to distances exceeding a 1000km [6]. Beyond this established work, a central aim of quantum information science is to explore novel aspects of this information and design useful technologies with it. Our main results are to demonstrate progress in this aim.