In this doctoral thesis we provide one of the first theoretical expositions on a 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 applications of entanglement in time.
In this doctoral thesis we provide one of the first theoretical expositions on a 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 applications of entanglement in time.
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.'
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.'
Although the concept of quantum entanglement has been known for about seventy years, it only recently quit the realms of meta-theoretical discussions when it was discovered how entanglement can be exploited to compute and communicate with an unprecedented power. The primary motivation of the work presented in this thesis has been to contribute to the big e#ort that has been done during the last decade to understand and quantify quantum entanglement. We have developed advanced techniques of linear and multilinear algebra to investigate and classify entangled pure and mixed quantum states, and discussed some novel applications in the field of quantum information theory. The results presented in this thesis are mainly of interest from a fundamental point a view: entanglement is the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought [186]. It is however a real privilege that fundamental research in quantum information theory bears the tools of tomorrow's electrical engineers: the ongoing miniaturization of electronic components will soon reach a scale where quantum mechanical e#ects play a major role.
Recently, there has been increased interest in understanding entanglement and quantum communication in black hole spacetimes and in using quantum information techniques to address questions in gravity. Studies on relativistic entanglement show the emergence of conceptually important qualitative differences to a non-relativistic treatment. For instance, entanglement was found to be an observer-dependent property that changes from the perspective of accelerated observers moving in flat spacetime. Relativisitic quantum information theory uses well-known tools coming from quantum information and quantum optics to study quantum effects provoked by gravity to learn information about the spacetime. We can take advantage of our knowledge about quantum correlations and effects produced by the gravitational interaction to set the basis for experimental proposals ultimately aiming at finding corrections due to quantum gravity effects, too mild to be directly observed. This doctoral thesis dissertation summarises most of the research carried out during my PhD on this topic.
Temporal coherence networks represent a paradigm shift in quantum information transmission, moving beyond the limitations of individual particle entanglement. This paper investigates the design and analysis of networks predicated on the temporal coherence of entangled states, proposing a novel mechanism to facilitate faster and more efficient quantum communication. We explore how topological properties can be leveraged to guide information flow across time, offering a potential pathway to overcome inherent challenges in quantum data transfer. The core claim is that these networks will drastically reduce latency and increase bandwidth compared to traditional approaches. This work delves into the mathematical foundations of maintaining and propagating entanglement across time, providing a detailed theoretical framework for future network development. We present a comprehensive analysis of the potential challenges and benefits associated with this approach, ultimately aiming to establish a robust and scalable framework for temporal coherence quantum communication.
Quantum mechanics, which describes the behaviour of matter and energy on very small scales, is one of the most successful theories in the history of science. Einstein's theory of special relativity, which describes the relationship between space and time, is likewise a highly successful and widely accepted theory. And yet there is a well-documented tension between the two theories, to the extent that it is still not clear that the two can ever be reconciled. This thesis is concerned with furthering the current understanding of the relationship between quantum mechanics and special relativity. In the first part of the thesis we study the behaviour of quantum information in relativistic spacetime. The field of quantum information arose from the realisation that quantum information has a number of crucial properties that distinguish it from classical information, such as the no-cloning property, quantum contextuality, and quantum discord. More recently, it has been realised that placing quantum information under relativistic constraints leads to the emergence of further unique features which are not exhibited by either non-relativistic quantum information or relativistic classical information; as part of this ongoing research programme we develop a new relativistic quantum `paradox' which puts pressure on conventional views about the spatiotemporal persistence of quantum states over time. We then study a new set of relativistic quantum protocols which involve the distribution of entangled states over spacetime, defining one task involving the distribution of the two halves of a known entangled state, and another task involving the distribution of the two halves of an unknown entangled state. The second part of the thesis deals with relativistic quantum cryptography, a field which first began attracting serious attention when it was realised that a cryptographic task known as `bit commitment,' can be implemented with perfect security under relativistic constraints. This result was highly significant, since it is provably impossible to implement bit commitment with perfect security in a purely classical or purely quantum context, and hence bit commitment is an ideal starting point for probing the power of relativistic quantum cryptography. In this thesis we propose several new relativistic quantum bit commitment protocols which have notable advantages over previously known protocols. We then move to a related task, a generalization of zero-knowledge proving which we refer to as knowledge-concealing evidencing of knowledge of a quantum state; we prove no-go theorems concerning the possibility of implementing this task with perfect security, and then set out a relativistic protocol for the task which is asymptotically secure as the dimension of the state in question becomes large. These results have interesting foundational significance above and beyond their applications in the field of cryptography, providing a new perspective on the connections between knowledge, realism and quantum states.