Quantum Entanglement in Time

<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>