Quantum information theory shows that quantum measurements have the essential capability to provide more information than classical ones, as emphasized by many authors [1, 2]. Exploiting the advantages of entanglement makes this possible. Several works based on the concept of quantum measurements have appeared recently [3–5]. However, for the purpose of such measurements, not all the features of quantum entanglement are necessary. For example most quantum measurements require entanglement as primary resource, but not non-locality, which is a different property [6].
Quantum information theory shows that quantum measurements have the essential capability to provide more information than classical ones, as emphasized by many authors [1, 2]. Exploiting the advantages of entanglement makes this possible. Several works based on the concept of quantum measurements have appeared recently [3–5]. However, for the purpose of such measurements, not all the features of quantum entanglement are necessary. For example most quantum measurements require entanglement as primary resource, but not non-locality, which is a different property [6].
Abstract Quantum information theory is built upon the realisation that quantum resources like coherence and entanglement can be exploited for novel or enhanced ways of transmitting and manipulating information, such as quantum cryptography, teleportation, and quantum computing. We now know that there is potentially much more than entanglement behind the power of quantum information processing. There exist more general forms of non-classical correlations, stemming from fundamental principles such as the necessary disturbance induced by a local measurement, or the persistence of quantum coherence in all possible local bases. These signatures can be identified and are resilient in almost all quantum states, and have been linked to the enhanced performance of certain quantum protocols over classical ones in noisy conditions. Their presence represents, among other things, one of the most essential manifestations of quantumness in cooperative systems, from the subatomic to the macroscopic domain. In this work we give an overview of the current quest for a proper understanding and characterisation of the frontier between classical and quantum correlations (QCs) in composite states. We focus on various approaches to define and quantify general QCs, based on different yet interlinked physical perspectives, and comment on the operational significance of the ensuing measures for quantum technology tasks such as information encoding, distribution, discrimination and metrology. We then provide a broader outlook of a few applications in which quantumness beyond entanglement looks fit to play a key role.
Introduction Quantum information theory is the study of how the peculiar features of quantum mechanics can be exploited for the purposes of information processing and transmission. A central theme of such a study is the ways in which quantum mechanics opens up possibilities that go beyond what can be achieved classically. This has in turn led to a renewed interest in, and a new perspective on, the differences between the classical and the quantum. Although much of the work along these lines has been motivated by quantum information theory – and some of it has been motivated by the conviction that quantum theory is essentially about possibilities of information processing and transmission – the results obtained, and the frameworks developed, have interest even for those of us who are not of that conviction. Indeed, much of the recent work echoes, and builds upon, work that predates the inception of quantum information theory. The significance of such work extends beyond the setting of quantum information theory; the work done on distinguishing the quantum from the classical in the context of frameworks that embrace both is something worthy of the attention of anyone interested in the foundational issues surrounding quantum theory. One of the striking features of quantum mechanics lies in its probabilistic character. A quantum state yields, not a definite prediction of the outcome of an experiment, but a probability measure on the space of possible outcomes. Of course, probabilities occur also in a classical context.
We present several physical applications that were generated in the framework of quantum information science. We emphasize the crucial role played, in this approach, by a group of unitary transformations, the generalized Pauli or Heisenberg–Weyl group, and by a non-classical property, called entanglement, which appears to be a basic ingredient in Quantum Information Theory. We sketch the links between entanglement and non-locality, and discuss an analogy between entanglement and (human) relationships.
This thesis establishes a number of connections between foundational issues in quantum theory, and some quantum information applications. It starts with a review of quantum contextuality and non-locality, multipartite entanglement characterisation, and of a few quantum information protocols. Quantum non-locality and contextuality are shown to be essential for different implementations of quantum information protocols known as quantum random access codes and quantum communication complexity protocols. I derive sufficient experimental conditions for tests of these quantum properties. I also discuss how the distribution of quantum information through quantum cloning processes can be useful in quantum computing. Regarding entanglement characterisation, some results are obtained relating two problems, that of additivity of the relative entropy of entanglement, and that of identifying different types of tripartite entanglement in the asymptotic regime of manipulations of many copies of a given state. The thesis ends with a description of an information processing task in which a single qubit substitutes for an arbitrarily large amount of classical communication. This result is interpreted in different ways: as a gap between quantum and classical computation space complexity; as a bound on the amount of classical communication necessary to simulate entanglement; and as a basic result on hidden-variable theories for quantum mechanics. I also show that the advantage of quantum over classical communication can be established in a feasible experiment.
Introduction and overview Much that is studied in quantum measurement theory, and thus in this book, is very different from that studied in its classical counterpart, Bayesian inference. While quantum measurement theory is in one sense a minimal extension of the latter to quantum states, quantum measurements cause dynamical changes that never need appear in a classical theory. This has a multitude of ramifications, many of which you will find in this book. One such consequence is a limit to the information that can be obtained about the state of a quantum system, and this results in relationships between information gained and dynamics induced that do not exist in classical systems. Because of the limits to information extraction, choosing the right kinds of measurements becomes important in a way that it never was for classical systems. Finding the best measurements for a given purpose, and working out how to realize these measurements, is often nontrivial. The relationship between information and disturbance impacts the control of quantum systems using measurements and feedback, and we discuss this application in Chapter 5. The ability to extract information about quantum systems is also important in using quantum systems to make precise measurements of classical quantities such as time, acceleration, and the strengths of electric and magnetic fields. This subject is referred to as quantum metrology, and we discuss it in Chapter 6.
Quantum information theory is gaining interest in different communities where it can provide new tools for computation and concurrency, security, and communication protocols, as well as methods to deal with cognition and decision-making. All these domains take advantage of properties that characterise the quantum framework such as superposition, entanglement, and contextuality. A necessary step to exploit the potential advantage of quantum information theory is to highlight the resources underlying this advantage in a theory-independent way. Indeed, the sharing of quantum resources beyond the local scale takes place in current information and communication systems, which are grounded on classic resources: synergy between these two domains is relevant to prompt the diffusion of quantum methodologies in real applications. The present contribution aims to explore different domains where non-quantum and quantum resources coexist and non-classicality arises in different forms. Here, the term “non-classicality” may refer to the elaboration of information through classical or hybrid quantum-classical computing, but also to the representation of knowledge and applications to decision-making under uncertainty. The objective of this contribution is to identify common structures and formal methods that can be specified in different domains sharing the same technological framework. In this way, non-classicality can connect such domains and represent, by itself, a type of resource, supporting the definition of new techniques to deal with distributed classical and quantum information.