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Topic Review
Lieb-Robinson Bounds
The Lieb-Robinson bound is a theoretical upper limit on the speed at which information can propagate in non-relativistic quantum systems. It demonstrates that information cannot travel instantaneously in quantum theory, even when the relativity limits of the speed of light are ignored. The existence of such a finite speed was discovered mathematically by Elliott H. Lieb and Derek W. Robinson (de) in 1972. It turns the locality properties of physical systems into the existence of, and upper bound for this speed. The bound is now known as the Lieb-Robinson bound and the speed is known as the Lieb-Robinson velocity. This velocity is always finite but not universal, depending on the details of the system under consideration. For finite-range, e.g. nearest-neighbor, interactions, this velocity is a constant independent of the distance travelled. In long-range interacting systems, this velocity remains finite, but it can increase with the distance travelled. In the study of quantum systems such as quantum optics, quantum information theory, atomic physics, and condensed matter physics, it is important to know that there is a finite speed with which information can propagate. The theory of relativity shows that no information, or anything else for that matter, can travel faster than the speed of light. When non-relativistic mechanics is considered, however, (Newton's equations of motion or Schrödinger's equation of quantum mechanics) it had been thought that there is then no limitation to the speed of propagation of information. This is not so for certain kinds of quantum systems of atoms arranged in a lattice, often called quantum spin systems. This is important conceptually and practically, because it means that, for short periods of time, distant parts of a system act independently. One of the practical applications of Lieb-Robinson bounds is quantum computing. Current proposals to construct quantum computers built out of atomic-like units mostly rely on the existence of this finite speed of propagation to protect against too rapid dispersal of information. 
  • 562
  • 20 Oct 2022
Topic Review Peer Reviewed
Integrated Fabry–Perot Cavities: A Quantum Leap in Technology
Integrated Fabry–Perot cavities (IFPCs), often referred to as nanobeams due to their form factor and size, have profoundly modified the landscape of integrated photonics as a new building block for classical and quantum engineering. In this entry, the main properties of IFPCs will be summarized from the classical and quantum point of view. The classical will provide some of the main results obtained in the last decade, whereas the quantum point of view will exp
  • 540
  • 29 Mar 2024
Topic Review
Causal Fermion System
The theory of causal fermion systems is an approach to describe fundamental physics. It provides a unification of the weak, the strong and the electromagnetic forces with gravity at the level of classical field theory. Moreover, it gives quantum mechanics as a limiting case and has revealed close connections to quantum field theory. Therefore, it is a candidate for a unified physical theory. Instead of introducing physical objects on a preexisting spacetime manifold, the general concept is to derive spacetime as well as all the objects therein as secondary objects from the structures of an underlying causal fermion system. This concept also makes it possible to generalize notions of differential geometry to the non-smooth setting. In particular, one can describe situations when spacetime no longer has a manifold structure on the microscopic scale (like a spacetime lattice or other discrete or continuous structures on the Planck scale). As a result, the theory of causal fermion systems is a proposal for quantum geometry and an approach to quantum gravity. Causal fermion systems were introduced by Felix Finster and collaborators.
  • 527
  • 28 Oct 2022
Topic Review
Two-Dimensional Quantum Billiards
Two-dimensional quantum billiards are one of the most important paradigms for exploring the connection between quantum and classical worlds. Researchers are mainly focused on nonintegrable and irregular shapes to understand the quantum characteristics of chaotic billiards. The emergence of the scarred modes relevant to unstable periodic orbits (POs) is one intriguing finding in nonintegrable quantum billiards. On the other hand, stable POs are abundant in integrable billiards. The quantum wavefunctions associated with stable POs have been shown to play a key role in ballistic transport. 
  • 512
  • 19 Oct 2023
Topic Review
SCOP Formalism
The SCOP formalism or State Context Property formalism is an abstract mathematical formalism for describing states of a system that generalizes both quantum and classical descriptions. The formalism describes entities, which may exist in different states, which in turn have various properties. In addition there is a set of "contexts" (corresponding to measurements) by which an entity may be observed. The formalism has primarily found use outside of physics as a theory of concepts, in particular in the field of quantum cognition, which develops quantum-like models of cognitive phenomena (such as the conjunction fallacy) that may seem paradoxical or irrational when viewed from a perspective of classical states and logic.
  • 503
  • 11 Oct 2022
Topic Review
Englert–Greenberger–Yasin Duality Relation
The Englert–Greenberger–Yasin duality relation, often called the Englert–Greenberger relation, relates the visibility, [math]\displaystyle{ V }[/math], of interference fringes with the definiteness, or distinguishability, [math]\displaystyle{ D }[/math], of the photons' paths in quantum optics. As an inequality: Although it is treated as a single relation, it actually involves two separate relations, which mathematically look very similar. The first relationship was first experimentally shown by Greenberger and Yasin in 1988. It was later theoretically derived by Jaeger, Shimony, and Vaidman in 1995. This relation involves correctly guessing which of the two paths the particle would have taken, based on the initial preparation. Here [math]\displaystyle{ D }[/math] can be called the predictability, and is sometimes denoted by [math]\displaystyle{ P }[/math]. A year later Englert, in 1996, apparently unaware of this result, derived a related relation which dealt with knowledge of the two paths using an apparatus. Here [math]\displaystyle{ D }[/math] is called the distinguishability. The significance of the relation is that it expresses quantitatively the complementarity of wave and particle viewpoints in double slit experiments. The complementarity principle in quantum mechanics, formulated by Niels Bohr, says that the wave and particle aspects of quantum objects cannot be observed at the same time. The Englert–Greenberger relation makes this more precise; an experiment can yield partial information about the wave and particle aspects of a photon simultaneously, but the more information a particular experiment gives about one, the less it will give about the other. The distinguishability [math]\displaystyle{ D }[/math] which expresses the degree of probability with which path of the particle is known, is a measure of the particle information, while the visibility of the fringes [math]\displaystyle{ V }[/math] is a measure of the wave information. The relation shows that they are inversely related, as one goes up, the other goes down.
  • 501
  • 18 Oct 2022
Topic Review
Wave-particle Duality Relation
The Wave–particle duality relation, often loosely referred to as the Englert–Greenberger–Yasin duality relation, or the Englert–Greenberger relation, relates the visibility, [math]\displaystyle{ V }[/math], of interference fringes with the definiteness, or distinguishability, [math]\displaystyle{ D }[/math], of the photons' paths in quantum optics. As an inequality: Although it is treated as a single relation, it actually involves two separate relations, which mathematically look very similar. The first relation, derived by Greenberger and Yasin in 1988, is expressed as [math]\displaystyle{ P^2+ V^2\le 1 \, }[/math]. It was later extended by Jaeger, Shimony, and Vaidman in 1995. This relation involves correctly guessing which of the two paths the particle would have taken, based on the initial preparation. Here [math]\displaystyle{ P }[/math] can be called the predictability. An year later Englert, in 1996, derived a related relation which dealt with experimentally acquiring knowledge of the two paths using an apparatus, as opposed to predicting the path based on initial preparation This relation is [math]\displaystyle{ D^2+ V^2\le 1 \, }[/math]. Here [math]\displaystyle{ D }[/math] is called the distinguishability. The significance of the relations is that they express quantitatively the complementarity of wave and particle viewpoints in double slit experiments. The complementarity principle in quantum mechanics, formulated by Niels Bohr, says that the wave and particle aspects of quantum objects cannot be observed at the same time. The wave–particle duality relations makes Bohr's statement more quantitative – an experiment can yield partial information about the wave and particle aspects of a photon simultaneously, but the more information a particular experiment gives about one, the less it will give about the other. The predictability [math]\displaystyle{ P }[/math] which expresses the degree of probability with which path of the particle can be correctly guessed, and the distinguishability [math]\displaystyle{ D }[/math] which is the degree to which one can experimentally acquire information about the path of the particle, are measures of the particle information, while the visibility of the fringes [math]\displaystyle{ V }[/math] is a measure of the wave information. The relations shows that they are inversely related, as one goes up, the other goes down.
  • 479
  • 27 Sep 2022
Topic Review
Dirac Equation in the Algebra of Physical Space
The Dirac equation, as the relativistic equation that describes spin 1/2 particles in quantum mechanics, can be written in terms of the Algebra of physical space (APS), which is a case of a Clifford algebra or geometric algebra that is based on the use of paravectors. The Dirac equation in APS, including the electromagnetic interaction, reads Another form of the Dirac equation in terms of the Space time algebra was given earlier by David Hestenes. In general, the Dirac equation in the formalism of geometric algebra has the advantage of providing a direct geometric interpretation.
  • 421
  • 17 Oct 2022
Topic Review
High-Precision Quantum Tests of the Weak Equivalence Principle
General relativity has been the best theory to describe gravity and space–time and has successfully explained many physical phenomena. At the same time, quantum mechanics provides the most accurate description of the microscopic world, and quantum science technology has evoked a wide range of developments today. Merging these two very successful theories to form a grand unified theory is one of the most elusive challenges in physics. All the candidate theories that wish to unify gravity and quantum mechanics predict the breaking of the weak equivalence principle, which lies at the heart of general relativity. It is therefore imperative to experimentally verify the equivalence principle in the presence of significant quantum effects of matter. Cold atoms provide well-defined properties and potentially nonlocal correlations as the test masses and will also improve the limits reached by classical tests with macroscopic bodies. The results of rigorous tests using cold atoms may tell us whether and how the equivalence principle can be reformulated into a quantum version. 
  • 417
  • 26 Sep 2023
Topic Review
Transition of State
In quantum mechanics, particularly Perturbation theory, a transition of state is a change from an initial quantum state to a final one.
  • 371
  • 08 Nov 2022
Topic Review
Broken/Asymptotic Safety in Quantum Gravity
Asymptotic safety (sometimes also referred to as nonperturbative renormalizability) is a concept in quantum field theory which aims at finding a consistent and predictive quantum theory of the gravitational field. Its key ingredient is a nontrivial fixed point of the theory's renormalization group flow which controls the behavior of the coupling constants in the ultraviolet (UV) regime and renders physical quantities safe from divergences. Although originally proposed by Steven Weinberg to find a theory of quantum gravity, the idea of a nontrivial fixed point providing a possible UV completion can be applied also to other field theories, in particular to perturbatively nonrenormalizable ones. In this respect, it is similar to quantum triviality. The essence of asymptotic safety is the observation that nontrivial renormalization group fixed points can be used to generalize the procedure of perturbative renormalization. In an asymptotically safe theory the couplings do not need to be small or tend to zero in the high energy limit but rather tend to finite values: they approach a nontrivial UV fixed point. The running of the coupling constants, i.e. their scale dependence described by the renormalization group (RG), is thus special in its UV limit in the sense that all their dimensionless combinations remain finite. This suffices to avoid unphysical divergences, e.g. in scattering amplitudes. The requirement of a UV fixed point restricts the form of the bare action and the values of the bare coupling constants, which become predictions of the asymptotic safety program rather than inputs. As for gravity, the standard procedure of perturbative renormalization fails since Newton's constant, the relevant expansion parameter, has negative mass dimension rendering general relativity perturbatively nonrenormalizable. This has driven the search for nonperturbative frameworks describing quantum gravity, including asymptotic safety which — in contrast to other approaches—is characterized by its use of quantum field theory methods, without depending on perturbative techniques, however. At the present time, there is accumulating evidence for a fixed point suitable for asymptotic safety, while a rigorous proof of its existence is still lacking.
  • 368
  • 19 Oct 2022
Topic Review
Quantum Information Education
Quantum information is an emerging scientific and technological discipline attracting a growing number of professionals from various related fields. Although it can potentially serve as a valuable source of skilled labor, the Internet provides a way to disseminate information about education, opportunities, and collaboration.
  • 362
  • 12 May 2023
Topic Review
Conceptual Programs in Physics
Different subfields of physics have different programs for determining the state of a physical system.
  • 322
  • 18 Oct 2022
Topic Review
Solid-State Color Centers for Single-Photon Generation
Single-photon sources are important for integrated photonics and quantum technologies, and can be used in quantum key distribution, quantum computing, and sensing. Color centers in the solid state are a promising candidate for the development of the next generation of single-photon sources integrated in quantum photonics devices. They are point defects in a crystal lattice that absorb and emit light at given wavelengths and can emit single photons with high efficiency. 
  • 285
  • 20 Mar 2024
Topic Review
Preparation of Rare-Earth-Ion-Doped High-Purity Glasses
The main source of impurities in the doped selenide glasses are rare-earth metals and their precursors (halides, chalcogenides). The total optical losses in glasses caused by impurities brought with rare-earth metals at a doping level of 1000 wt ppm can reach 10–85 dB/m.
  • 267
  • 06 Dec 2023
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