Quantum physics is now one hundred years old, and this description of physical phenomena, which has transformed our vision of the world, has never been found at fault, which is exceptional for a scientific theory. Its predictions have always been verified by experiment with impressive accuracy. The basic concepts of quantum physics such as probability amplitudes and linear superpositions of states, which seem so strange to our intuition when encountered for the first time, remain fundamental. However, during the last few decades an important evolution has occurred. The spectacular progress made in observational techniques and methods of manipulating atoms now makes it possible to perform experiments so delicate that they were once considered as only “thought experiments” by the founders of quantum mechanics. The existence of “nonseparable” quantum correlations, which forms the basis of the Einstein–Podolsky–Rosen “paradox” and which violates the famous Bell inequalities, has been confirmed experimentally with high precision. “Entangled” states of two systems which manifest such quantum correlations are now better understood and even used in practical applications such as quantum cryptography. The entanglement of a measuring device with its environment reveals an interesting new pathway to better understanding of the measurement process. In parallel with these conceptual advances, our everyday world is being invaded by devices which function on the basis of quantum phenomena. The laser sources used to read compact disks, in ophthalmology, and in optical telecommunications are based on light amplification by atomic systems with population inversion. Nuclear magnetic resonance is widely used in hospitals to obtain ever more detailed images of the organs of the human body.
Quantum physics is now one hundred years old, and this description of physical phenomena, which has transformed our vision of the world, has never been found at fault, which is exceptional for a scientific theory. Its predictions have always been verified by experiment with impressive accuracy. The basic concepts of quantum physics such as probability amplitudes and linear superpositions of states, which seem so strange to our intuition when encountered for the first time, remain fundamental. However, during the last few decades an important evolution has occurred. The spectacular progress made in observational techniques and methods of manipulating atoms now makes it possible to perform experiments so delicate that they were once considered as only “thought experiments” by the founders of quantum mechanics. The existence of “nonseparable” quantum correlations, which forms the basis of the Einstein–Podolsky–Rosen “paradox” and which violates the famous Bell inequalities, has been confirmed experimentally with high precision. “Entangled” states of two systems which manifest such quantum correlations are now better understood and even used in practical applications such as quantum cryptography. The entanglement of a measuring device with its environment reveals an interesting new pathway to better understanding of the measurement process. In parallel with these conceptual advances, our everyday world is being invaded by devices which function on the basis of quantum phenomena. The laser sources used to read compact disks, in ophthalmology, and in optical telecommunications are based on light amplification by atomic systems with population inversion. Nuclear magnetic resonance is widely used in hospitals to obtain ever more detailed images of the organs of the human body.
When the revolutionary conceptual structure for the description of the physical world which we know as quantum mechanics was first formulated nearly 90 years ago, and its predictions tested in the laboratory, most of the experiments in question were on systems which were both very well characterized and reasonably well isolated from their environments, such as single electrons and atoms, small molecules and near-perfect crystalline solids. While from the very start most physicists have taken it for granted that the formalism of quantum mechanics, when combined with appropriate system-specific information, can “in principle” account for all phenomena occurring in the physical world, including those usually regarded as the subject-matter of biology, until quite recently the overwhelmingly majority opinion has been that in a biological context the role of quantum theory is confined to elucidating the equilibrium structures of the relevant molecules and their reaction processes, and that subtle phenomena such as superposition and entanglement, of which we can now routinely exhibit spectacular effects at the level of a few well-isolated photons or atoms, play at most a very indirect role in any phenomena of biological interest. A major reason conventionally given for this view has been that biological systems, at least working ones, are by their very nature “warm and wet” – a phrase which in the physicist's lexicon translates to “prone to massive decoherence”; it looks as though any interesting superposition, say of different energy eigenstates of one's system, would be rapidly decohered by the ever-present, and usually microscopically very complex, environment.
The development of quantum mechanics and quantum physics in general is one of the greatest intellectual achievements of the 20th century. Initially, quantum physicists focused on mathematically describing and understanding the laws of a micro-world, comprised of atoms, molecules and photons. Nuclei and sub-atomic particles were discovered, particle physics evolved, and complex quantum systems in chemistry and solid-state physics are now described in terms of quantum physics. Within a century, quantum physics became the framework, which allows us to describe and predict, albeit with probabilities, the behavior of the microscopic world as we know it. The powerful quantum framework led to revolutionary technical advances for a century, such as semiconductor technology and the entire electronics industry based on it, enabling computers and the information age. The development of lasers found applications in many areas of our current technologies; we use them for printers, storing and retrieving information using CDs, industrial welding, medical surgery, and for range finding and communication purposes. Medical imaging using MRI is now a routine instrument, as are precision measurements using tunneling and atomic force microscopes. Superconducting technologies are used for high magnetic fields and many more current technologies are based on and enabled by the laws of quantum physics. While the framework of quantum physics has thus proven to be extremely successful and powerful, throughout the last century there were many conceptual, and to some extent philosophical, discussions on our understanding of quantum physics. As early as the 1930s, Einstein and Schrödinger realized that quantum physics allows for some peculiar states, which Schrödinger called “entangled”, which have a non-local character and thus do find an easy interpretation in our classical world. It took a few more decades until John Bell conceived a way to quantify such states, which thus became amenable to measurements. Only in the eighties and nineties of the last century did the generation of entangled states, their characterization and their subsequent application become feasible and accessible in laboratories. Early on, Bell states were proposed for applications in quantum communication, employing protocols based on teleportation. Soon, entanglement was recognized to be useful also for sensing, for precision measurements and eventually for quantum information processing. Starting with the early concept of a trapped-ion quantum computer introduced by Ignacio Cirac and Peter Zoller in 1995, many other platforms were proposed for quantum information processing, based on superconducting quantum bits, photonic processes, engineered quantum dots and many more. The first decade of the 21st century saw an explosive development of quantum information physics, which is by now a mature field and increasingly focuses on applications. Worldwide efforts are ongoing to realize quantum networks for secure communication and to implement quantum computers. Enhanced sensing has been demonstrated using advanced quantum states, and quantum simulators have been developed, already tackling problems that are hard to compute with classical computers. While architectures for full-fledged quantum computers are already available, the realization of such computers still requires the routine implementation of error correction, which is not yet available, for full scalability. Currently, noisy intermediate-scale quantum (NISQ) processors are already used for computations and are even accessible via cloud services. Since about 2000, quantum technologies have been developed for many platforms with the aim to surpass the capablities of their classical counterparts. Many such devices now make use of entangled states, which are seen as the new resource for advanced quantum technologies. For this, describing, understanding and generally mastering the generation and manipulation of entanglement is a key element. Moreover, both hardware and software technologies have to be improved in order to better control quantum devices. Mastering quantum phenomena for communication, metrology, simulation and computation purposes is currently one of the hottest topics in science since the wide applicability of quantum technologies will revolutionize these fields. The development of advanced quantum technologies is thus seen worldwide as a strategic area for generating technical knowledge and industrial evolution. This special issue intends to showcase the breadth and impact of the ongoing research in advancing quantum technologies. We have invited a selection of renowned scientists to present their work, and we are confident that this issue will find a broad readership and attract much interest within the scientific community.
The Nobel Prize in Physics 2022 was awarded to three experiment physicists: Alain Aspect, John F. Clauser and Anton Zeilinger, for their contributions to “experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science”. In this paper, the history, basics, and applications related with the Bell inequalities are reviewed. The discussion of fundamental issues on quantum mechanics dated back to the year 1927 when the fifth Solvay conference was held, highlighting intense arguments between Albert Einstein and Niels Bohr. At the time, Einstein expressed, publicly for the first time, his critical attitude towards quantum mechanics. While the arguments did not reach a decisive conclusion, Bohr’s probabilistic interpretation of quantum mechanics, the Copenhagen interpretation, had since been well circulated among the community. Einstein’s arguments with Bohr lasted many years after the conference. The arguably most famous one was the Einstein-Podolsky-Rosen (EPR) paradox, proposed in a 1935 paper written by the three authors. They stated, by flawless reasoning, that quantum mechanics is ‘incomplete’. Bohr replied immediately. So did Erwin Schrödinger, who, in particular, coined the term ‘entangled’ for the first time to describe the bizarre quantum mechanical property. Nevertheless, the EPR paper received few citations at its publication, until 1990’s when quantum information science started blossoming. From today’s perspective, the paper resembles the ‘sleeping beauty’ who slumbered for decades before fully awakening. It has been widely accepted that it was John S. Bell who eventually resolved the EPR paradox. But many important figures before him should not go unnoticed, including John A. Wheeler, Chien-Shiung Wu, David Bohm, to name a few. In 1964, Bell wrote down a mathematical inequality which satisfies local hidden variable theory but which can be violated in quantum mechanics. The significance is that Bell’s inequality brings the rather philosophic debates on the EPR paradox down to be experimentally testable. Hence, an experiment is here appealing, as is the case in all fields of physics. To the end, John F. Clauser, alongside Stuart J. Freedman, conducted an experiment in 1972 to test a Bell inequality, the Bell-Clauser-Horne-Shimony-Holt (CHSH) inequality, proposed by him and his collaborators in 1969. The results, however, leaves loopholes open. One of the loopholes was closed in a later experiment led by Alain Aspect in 1982. The Bell-CHSH inequality was later tested under a much stricter condition by Anton Zeilinger’s team. Two most important loopholes were both closed by three teams in 2015 independently. Zeilinger’s team was among them. Almost all experiments to date have confirmed quantum mechanical predictions. Zeilinger’s team also performed the first teleportation of unknown quantum states, the first entanglement swapping, along with other contributions pioneering the quantum information science. In retrospect, the foundational study of quantum theory has been developed over a century. It once drew much of quantum physics founders’ attention, went virtually unnoticed while other physical fields advanced, had for quite a while been considered to have very weak relationship with major physics, and finally revived in recent decades leading to rapid progress in quantum information science and quantum technology. We believe that the Nobel Prize in Physics this year is not only an award and recognition to past achievements, but also heralds a new era of science in future.
Quantum theory is the soul of contemporary physics. It was discovered in an adventurous way, under the urge to solve the puzzles posed by atomic spectra and blackbody radiation. But after its invention, it immediately became clear that it was not just a theory of specific physical systems: it was rather a new language of universal applicability. Already in 1928, the theory had received solid mathematical foundations by Hilbert, von Neumann, and Nordheim, and this work was brought to completion in the monumental work of von Neumann, in the form that we still study nowadays. The theory is extraordinarily successful, and its predictions have been confirmed to an astonishing level of precision in a large spectrum of experiments. However, almost 90 years after von Neumann's book, quantum theory remains mysterious. Its mathematical formulation – based on Hilbert spaces and self-adjoint operators – is far from having an intuitive interpretation. The association of physical systems to Hilbert spaces whose unit vectors represent pure states, the representation of transformations by unitary operators and of observables by self-adjoint operators – all such postulates look artificial and ad hoc . A slightly more operational approach is provided by the C * -algebraic formulation of quantum theory – still, this formulation relies on the assumption that observables form an algebra , where the physical meanings of the multiplication and the sum are far from clear. In short, the postulates of quantum theory impose mathematical structures without providing any simple reason for this choice: the mathematics of Hilbert spaces is adopted as a magic blackbox that “works well” at producing experimental predictions. However, in a satisfactory axiomatization of a physical theory the mathematical structures should emerge as a consequence of postulates that have a direct physical interpretation. By this we mean postulates referring, e.g., to primitive notions like physical system, measurement, or process, rather than notions like, e.g., Hilbert space, C * -algebra, unit vector, or selfadjoint operator. The crucial question thus remains unanswered: why quantum theory? Which are the principles at the basis of the theory? A case that is often invoked in contrast is that of Special Relativity theory, which directly follows from the simple understandable principle of relativity.
In recent decades there has been a resurge of interest in the foundations of quantum theory, partly motivated by new experimental techniques, partly by the emerging field of quantum information science. Old questions, asked since the seminal article by Einstein, Podolsky and Rosen (EPR), are being revisited. The work of John Bell has changed the direction of investigation by recognising that those fundamental philosophical questions can have, after all, input from experiment. Abner Shimony has aptly termed this new field of enquiry experimental metaphysics. The objective of this Thesis is to contribute to that body of research, by formalising old concepts, proposing new ones, and finding new results in well-studied areas. Without losing from sight that the appeal of experimental metaphysics comes from the adjective, every major result is followed by clear experimental proposals with detailed analysis of feasibility for quantum-atom optical setups. After setting the appropriate terminology and the basic concepts, we will start by analysing the original argument of Einstein, Podolsky and Rosen. We propose a general mathematical form for the assumptions behind the EPR argument, namely those of local causality and completeness. That formalisation entails what was termed a Local Hidden State model by Wiseman et al., which was proposed as a formalisation of the concept of steering first introduced by Schrodinger in a reply to the EPR paper. Violation of any consequences that can be derived from the assumption of that model therefore implies a demonstration of the EPR paradox. We will show how one can then re-derive the well-known EPR-Reid criterion for continuous-variables correlations, and derive new ones applicable to the spin setting considered by Bohm. The spin set-up of the EPR-Bohm was used by Bell to derive his now famous theorem demonstrating the incompatibility of the assumption of local causality and the predictions of quantum mechanics. The inequalities which bear his name can be derived for any number of discrete outcomes, but so far there has been no derivation which can be directly applied to the continuous-variables case of the original EPR paradox. We close the circle by deriving a class of inequalities which make no explicit mention about the number of outcomes of the experiments involved, and can therefore be used in continuous-variables measurements with no need for binning the continuous results into discrete ones. Apart from that intrinsic interest, these inequalities could prove important as a means to perform an unambiguous test of Bell inequalities since optical homodyne detection can be performed with high detection efficiency. The technique, which is based on a simple variance inequality, can alsobe used tore-derive alarge class of well-known Bell-type inequalities and at the same time find their quantum bound, making explicit from a formal point of view that the non-commutativity of the local operators is at the heart of the quantum violations. Finally, we address the issue of macroscopic superpositions originally sparked by the infamous cat paradox of Schrodinger. We consider macroscopic, mesoscopic and ‘S -scopic’ quantum superpositions of eigenstates of an observable, and develop some signatures for their existence. We define the extent, or size S of a (pure-state) su-perposition, with respect to an observable X, as being the maximum difference in the outcomes of X predicted by that superposition. Such superpositions are referred to as generalised S -scopic superpositions to distinguish them from the extreme superpo-sitions that superpose only the two states that have a difference S in their prediction for the observable. We also consider generalised S -scopic superpositions of coherent states. We explore the constraints that are placed on the statistics if we suppose a system to be described by mixtures of superpositions that are restricted in size. In this way we arrive at experimental criteria that are sufficient to deduce the existence of a generalised S -scopic superposition. The signatures developed are useful where one is able to demonstrate a degree of squeezing.
Quantum physics is well known for being counter-intuitive, or even bizarre. Quantum correlations have no equivalence in classical physics. This was all well known for years. But several discoveries in the 1990's changed the world. First, in 1991 Artur Ekert, from Oxford University, discovered that quantum correlations could be used to distribute cryptographic keys. Suddenly physicists realized that quantum correlations and its associated bizarre non-locality, could be exploited to achieve a useful task that would be impossible without quantum physics. What a revolution! And this was not the end. Three years later, Peter Shor, from the AT&T Laboratories, discovered an algorithm that breaks the most used public key crypto-systems. Shor's algorithm requires a quantum computer, yet another bizarre quantum device, a kind of computer that heavily exploits the quantum superposition principle. The following year, in 1995, a collaboration between six physicists and computer scientists from three continents led to the discovery of quantum teleportation, a process with a science-fiction flavour. These discoveries and others led to the emergence of a new science, marrying quantum physics and theoretical computer science, called quantum information science. Today, a steadily growing community of physicists, mathematicians and computer scientists develop the tools of this new science. This leads to new experiments and new insights into physics and information theory. It is a fascinating time. Quantum information is still a very young science. In particular, the technology required to build a quantum computer is still unknown. Only quantum key distribution has reached a certain level of maturity, with a few start-ups already offering complete systems. Nevertheless, quantum information has been widely recognised as a source for truly innovative ideas and disruptive technologies.