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Spin Squeezing
Spin squeezing is a quantum process that decreases the variance of one of the angular momentum components in an ensemble of particles with a spin. The quantum states obtained are called spin squeezed states. Such states have been proposed for quantum metrology, to allow a better precision for estimating a rotation angle than classical interferometers. Mathematical definition Spin squeezed states for an ensemble of spins have been defined analogously to squeezed states of a bosonic mode. For any quantum state (not necessarily a pure state), let z be the direction of its mean spin, so that \langle J_x \rangle = \langle J_y \rangle = 0. By the Heisenberg uncertainty relation,(\Delta J_x)^2(\Delta J_y)^2 \geqslant \frac 1 4 , \langle J_z \rangle , ^2,where J_l are the collective angular momentum components defined as J_l=\sum_n j_l^, and j_l^ are the single particle angular momentum components. We say that the state is spin-squeezed in the x-direction, if the variance of the x- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Squeezed State
In physics, a squeezed coherent state is a quantum state that is usually described by two non-commuting observables having continuous spectra of eigenvalues. Examples are position x and momentum p of a particle, and the (dimension-less) electric field in the amplitude X (phase 0) and in the mode Y (phase 90°) of a light wave (the wave's quadratures). The product of the standard deviations of two such operators obeys the uncertainty principle: :\Delta x \Delta p \geq \frac2\; and \;\Delta X \Delta Y \geq \frac4 , respectively. Trivial examples, which are in fact not squeezed, are the ground state , 0\rangle of the quantum harmonic oscillator and the family of coherent states , \alpha\rangle. These states saturate the uncertainty above and have a symmetric distribution of the operator uncertainties with \Delta x_g = \Delta p_g in "natural oscillator units" and \Delta X_g = \Delta Y_g = 1/2. The term squeezed state is actually used for states with a standard deviati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Metrology
Quantum metrology is the study of making high-resolution and highly sensitive measurements of physical parameters using quantum theory to describe the physical systems, particularly exploiting quantum entanglement and quantum Squeezed coherent state, squeezing. This field promises to develop measurement techniques that give better precision than the same measurement performed in a classical framework. Together with quantum hypothesis testing, it represents an important theoretical model at the basis of quantum sensing. Mathematical foundations A basic task of quantum metrology is estimating the parameter \theta of the unitary dynamics : \varrho(\theta)=\exp(-iH\theta)\varrho_0\exp(+iH\theta), where \varrho_0 is the initial state of the system and H is the Hamiltonian of the system. \theta is estimated based on measurements on \varrho(\theta). Typically, the system is composed of many particles, and the Hamiltonian is a sum of single-particle terms : H=\sum_k H_k, where H_k ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum State
In quantum physics, a quantum state is a mathematical entity that embodies the knowledge of a quantum system. Quantum mechanics specifies the construction, evolution, and measurement of a quantum state. The result is a prediction for the system represented by the state. Knowledge of the quantum state, and the rules for the system's evolution in time, exhausts all that can be known about a quantum system. Quantum states may be defined differently for different kinds of systems or problems. Two broad categories are * wave functions describing quantum systems using position or momentum variables and * the more abstract vector quantum states. Historical, educational, and application-focused problems typically feature wave functions; modern professional physics uses the abstract vector states. In both categories, quantum states divide into pure versus mixed states, or into coherent states and incoherent states. Categories with special properties include stationary states for tim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heisenberg Uncertainty
The uncertainty principle, also known as Heisenberg's indeterminacy principle, is a fundamental concept in quantum mechanics. It states that there is a limit to the precision with which certain pairs of physical properties, such as position and momentum, can be simultaneously known. In other words, the more accurately one property is measured, the less accurately the other property can be known. More formally, the uncertainty principle is any of a variety of mathematical inequalities asserting a fundamental limit to the product of the accuracy of certain related pairs of measurements on a quantum system, such as position, ''x'', and momentum, ''p''. Such paired-variables are known as complementary variables or canonically conjugate variables. First introduced in 1927 by German physicist Werner Heisenberg, the formal inequality relating the standard deviation of position ''σx'' and the standard deviation of momentum ''σp'' was derived by Earle Hesse Kennard later that ye ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Entanglement
Quantum entanglement is the phenomenon where the quantum state of each Subatomic particle, particle in a group cannot be described independently of the state of the others, even when the particles are separated by a large distance. The topic of quantum entanglement is at the heart of the disparity between classical physics and quantum physics: entanglement is a primary feature of quantum mechanics not present in classical mechanics. Measurement#Quantum mechanics, Measurements of physical properties such as position (vector), position, momentum, Spin (physics), spin, and polarization (waves), polarization performed on entangled particles can, in some cases, be found to be perfectly correlated. For example, if a pair of entangled particles is generated such that their total spin is known to be zero, and one particle is found to have clockwise spin on a first axis, then the spin of the other particle, measured on the same axis, is found to be anticlockwise. However, this behavior ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Open Systems & Information Dynamics
''Open Systems & Information Dynamics'' (OSID) is a journal published by World Scientific. It covers interdisciplinary research in mathematics, physics, engineering and life sciences based upon the fields of information processing, storage and transmission, in both quantum and classical settings, with a theoretical focus. Topics include quantum information theory, open systems, decoherence, complexity theory of classical and quantum systems and other models of information processing. Abstracting and indexing The journal is abstracted and indexed in: * COMPUMATH Citation Index * Current Contents/Engineering, Computing and Technology * Current Contents/Physical, Chemical and Earth Sciences * Inspec * ISI Alerting Services * MATH * Science Citation Index Expanded (also known as SciSearch) * Statistical Theory and Method Abstracts * Zentralblatt MATH zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and ap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Birefringence
Birefringence, also called double refraction, is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. These optically anisotropic materials are described as birefringent or birefractive. The birefringence is often quantified as the maximum difference between refractive indices exhibited by the material. Crystals with non-cubic crystal structures are often birefringent, as are plastics under mechanical stress. Birefringence is responsible for the phenomenon of double refraction whereby a ray of light, when incident upon a birefringent material, is split by polarization into two rays taking slightly different paths. This effect was first described by Danish scientist Rasmus Bartholin in 1669, who observed it in Iceland spar (calcite) crystals which have one of the strongest birefringences. In the 19th century Augustin-Jean Fresnel described the phenomenon in terms of polarization, understanding ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optical Depth
In physics, optical depth or optical thickness is the natural logarithm of the ratio of incident to ''transmitted'' radiant power through a material. Thus, the larger the optical depth, the smaller the amount of transmitted radiant power through the material. Spectral optical depth or spectral optical thickness is the natural logarithm of the ratio of incident to transmitted spectral radiant power through a material. Optical depth is dimensionless, and in particular is not a length, though it is a monotonically increasing function of optical path length, and approaches zero as the path length approaches zero. The use of the term "optical density" for optical depth is discouraged. In chemistry, a closely related quantity called " absorbance" or "decadic absorbance" is used instead of optical depth: the common logarithm of the ratio of incident to transmitted radiant power through a material. It is the optical depth divided by , because of the different logarithm bases used ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cooperativity
Cooperativity is a phenomenon displayed by systems involving identical or near-identical elements, which act dependently of each other, relative to a hypothetical standard non-interacting system in which the individual elements are acting independently. One manifestation of this is enzymes or receptors that have multiple binding sites where the affinity of the binding sites for a ligand is ''apparently'' increased, positive cooperativity, or decreased, negative cooperativity, upon the binding of a ligand to a binding site. For example, when an oxygen atom binds to one of hemoglobin's four binding sites, the affinity to oxygen of the three remaining available binding sites increases; i.e. oxygen is more likely to bind to a hemoglobin bound to one oxygen than to an unbound hemoglobin. This is referred to as cooperative binding. We also see cooperativity in large chain molecules made of many identical (or nearly identical) subunits (such as DNA, proteins, and phospholipids), when ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electric Field
An electric field (sometimes called E-field) is a field (physics), physical field that surrounds electrically charged particles such as electrons. In classical electromagnetism, the electric field of a single charge (or group of charges) describes their capacity to exert attractive or repulsive forces on another charged object. Charged particles exert attractive forces on each other when the sign of their charges are opposite, one being positive while the other is negative, and repel each other when the signs of the charges are the same. Because these forces are exerted mutually, two charges must be present for the forces to take place. These forces are described by Coulomb's law, which says that the greater the magnitude of the charges, the greater the force, and the greater the distance between them, the weaker the force. Informally, the greater the charge of an object, the stronger its electric field. Similarly, an electric field is stronger nearer charged objects and weaker f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Local Field
In mathematics, a field ''K'' is called a non-Archimedean local field if it is complete with respect to a metric induced by a discrete valuation ''v'' and if its residue field ''k'' is finite. In general, a local field is a locally compact topological field with respect to a non-discrete topology. The real numbers R, and the complex numbers C (with their standard topologies) are Archimedean local fields. Given a local field, the valuation defined on it can be of either of two types, each one corresponds to one of the two basic types of local fields: those in which the valuation is Archimedean and those in which it is not. In the first case, one calls the local field an Archimedean local field, in the second case, one calls it a non-Archimedean local field. Local fields arise naturally in number theory as completions of global fields. While Archimedean local fields have been quite well known in mathematics for at least 250 years, the first examples of non-Archimedean local ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Information Science
Quantum information science is a field that combines the principles of quantum mechanics with information theory to study the processing, analysis, and transmission of information. It covers both theoretical and experimental aspects of quantum physics, including the limits of what can be achieved with quantum information. The term quantum information theory is sometimes used, but it does not include experimental research and can be confused with a subfield of quantum information science that deals with the processing of quantum information. Scientific and engineering studies Quantum teleportation, Quantum entanglement, entanglement and the manufacturing of quantum computers depend on a comprehensive understanding of quantum physics and engineering. Google and IBM have invested significantly in quantum computer hardware research, leading to significant progress in manufacturing quantum computers since the 2010s. Currently, it is possible to create a quantum computer with over 100 qub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
