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Quantum Speed Limit
In quantum mechanics, a quantum speed limit (QSL) is a limitation on the minimum time for a quantum system to evolve between two distinguishable (orthogonal) states. QSL theorems are closely related to time-energy uncertainty relations. In 1945, Leonid Mandelstam and Igor Tamm derived a time-energy uncertainty relation that bounds the speed of evolution in terms of the energy dispersion. Reprinted as Over half a century later, Norman Margolus and Lev Levitin showed that the speed of evolution cannot exceed the mean energy, a result known as the Margolus–Levitin theorem. Realistic physical systems in contact with an environment are known as open quantum systems and their evolution is also subject to QSL. Quite remarkably it was shown that environmental effects, such as non-Markovian dynamics can speed up quantum processes, which was verified in a cavity QED experiment. QSL have been used to explore the limits of computation and complexity. In 2017, QSLs were studied in a quantum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Mechanics
Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science. Quantum mechanics can describe many systems that classical physics cannot. Classical physics can describe many aspects of nature at an ordinary (macroscopic and Microscopic scale, (optical) microscopic) scale, but is not sufficient for describing them at very small submicroscopic (atomic and subatomic) scales. Classical mechanics can be derived from quantum mechanics as an approximation that is valid at ordinary scales. Quantum systems have Bound state, bound states that are Quantization (physics), quantized to Discrete mathematics, discrete values of energy, momentum, angular momentum, and ot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hamiltonian Operator
In quantum mechanics, the Hamiltonian of a system is an operator corresponding to the total energy of that system, including both kinetic energy and potential energy. Its spectrum, the system's ''energy spectrum'' or its set of ''energy eigenvalues'', is the set of possible outcomes obtainable from a measurement of the system's total energy. Due to its close relation to the energy spectrum and time-evolution of a system, it is of fundamental importance in most formulations of quantum theory. The Hamiltonian is named after William Rowan Hamilton, who developed a revolutionary reformulation of Newtonian mechanics, known as Hamiltonian mechanics, which was historically important to the development of quantum physics. Similar to vector notation, it is typically denoted by \hat, where the hat indicates that it is an operator. It can also be written as H or \check. Introduction The Hamiltonian of a system represents the total energy of the system; that is, the sum of the kineti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Superposition
Quantum superposition is a fundamental principle of quantum mechanics that states that linear combinations of solutions to the Schrödinger equation are also solutions of the Schrödinger equation. This follows from the fact that the Schrödinger equation is a linear differential equation in time and position. More precisely, the state of a system is given by a linear combination of all the eigenfunctions of the Schrödinger equation governing that system. An example is a qubit used in quantum information processing. A qubit state is most generally a superposition of the basis states , 0 \rangle and , 1 \rangle: : , \Psi \rangle = c_0, 0\rangle + c_1, 1\rangle, where , \Psi \rangle is the quantum state of the qubit, and , 0 \rangle, , 1 \rangle denote particular solutions to the Schrödinger equation in Dirac notation weighted by the two probability amplitudes c_0 and c_1 that both are complex numbers. Here , 0 \rangle corresponds to the classical 0 bit, and , 1 \r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Qubit
In quantum computing, a qubit () or quantum bit is a basic unit of quantum information—the quantum version of the classic binary bit physically realized with a two-state device. A qubit is a two-state (or two-level) quantum-mechanical system, one of the simplest quantum systems displaying the peculiarity of quantum mechanics. Examples include the spin of the electron in which the two levels can be taken as spin up and spin down; or the polarization of a single photon in which the two spin states (left-handed and the right-handed circular polarization) can also be measured as horizontal and vertical linear polarization. In a classical system, a bit would have to be in one state or the other. However, quantum mechanics allows the qubit to be in a coherent superposition of multiple states simultaneously, a property that is fundamental to quantum mechanics and quantum computing. Etymology The coining of the term ''qubit'' is attributed to Benjamin Schumacher. In the acknow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tommaso Toffoli
Tommaso Toffoli () is an Italian-American professor of electrical and computer engineering at Boston University where he joined the faculty in 1995. He has worked on cellular automata and the theory of artificial life (with Edward Fredkin and others), and is known for the invention of the Toffoli gate. Early life and career He was born in June, 1943 in Montereale Valcellina, in northeastern Italy, to Francesco and Valentina (Saveri) Toffoli, and was raised in Rome, Italy. He received his ''laurea'' in physics (equivalent to a master's degree) from the University of Rome La Sapienza in 1967. Toffoli moved to the United States in 1969. In 1976 he received a PhD in computer and communication science from the University of Michigan, then in 1978 he joined the faculty of Massachusetts Institute of Technology as a principal research scientist. In 1995 he joined the faculty of Boston University. , he is retired. Books * ''Cellular Automata Machines: A New Environment for Modeling'', ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lev B
Lev or LEV may refer to: People and fictional characters *Lev (given name) *Lev (surname) Places *Lev, Azerbaijan, a village *Lev (crater), a tiny lunar crater Religion *an abbreviation for Leviticus, the third book of the Hebrew Bible and the Torah *Lay eucharistic visitor, an extraordinary minister of Holy Communion approved by a church (usually Episcopalian or Lutheran) to bring Communion to the homebound *Libreria Editrice Vaticana, the Vatican Publishing House Transportation * Leyland Experimental Vehicle, a type of British experimental railbus *Light electric vehicle, an electric bicycle *Low emission vehicle, a motor vehicle that emits relatively low levels of motor vehicle emissions *Lunar Excursion Vehicle, an early name for the Apollo Lunar Module Political and other * Lesser evil voting (LEV) *Lev (political party), a now-defunct political party in Israel *LEV (cable system), a submarine cable system linking countries in the eastern Mediterranean *''Lev!'', a Swedis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Review A
''Physical Review A'' (also known as PRA) is a monthly peer-reviewed scientific journal published by the American Physical Society covering atomic, molecular, and optical physics and quantum information. the editor was Jan M. Rost ( Max Planck Institute for the Physics of Complex Systems). History In 1893, the '' Physical Review'' was established at Cornell University. It was taken over by the American Physical Society (formed in 1899) in 1913. In 1970, ''Physical Review'' was subdivided into ''Physical Review A'', ''B'', ''C'', and ''D''. At that time, section ''A'' was subtitled ''Physical Review A: General Physics''. In 1990, a process was started to split this journal into two, resulting in the creation of '' Physical Review E'' in 1993. Hence, in 1993, ''Physical Review A'' changed its statement of scope to ''Atomic, Molecular and Optical Physics.'' In January 2007, the section of ''Physical Review E'' that published papers on classical optics was merged into ''Physical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geodesic
In geometry, a geodesic () is a curve representing in some sense the locally shortest path ( arc) between two points in a surface, or more generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a connection. It is a generalization of the notion of a " straight line". The noun '' geodesic'' and the adjective '' geodetic'' come from ''geodesy'', the science of measuring the size and shape of Earth, though many of the underlying principles can be applied to any ellipsoidal geometry. In the original sense, a geodesic was the shortest route between two points on the Earth's surface. For a spherical Earth, it is a segment of a great circle (see also great-circle distance). The term has since been generalized to more abstract mathematical spaces; for example, in graph theory, one might consider a geodesic between two vertices/nodes of a graph. In a Riemannian manifold or submanifold, geodesics are characterised by the property of havi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bures Distance
In mathematics, in the area of quantum information geometry, the Bures metric (named after Donald Bures) or Helstrom metric (named after Carl W. Helstrom) defines an infinitesimal distance between density matrix operators defining quantum states. It is a quantum generalization of the Fisher information metric, and is identical to the Fubini–Study metric when restricted to the pure states alone. Definition The Bures metric may be defined as : _\text(\rho, \rho+d\rho)2 = \frac\mbox( d \rho G ), where G is the Hermitian 1-form operator implicitly given by : \rho G + G \rho = d \rho, which is a special case of a continuous Lyapunov equation. Some of the applications of the Bures metric include that given a target error, it allows the calculation of the minimum number of measurements to distinguish two different states and the use of the volume element as a candidate for the Jeffreys prior probability density for mixed quantum states. Bures distance The Bures distance is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Density Matrix
In quantum mechanics, a density matrix (or density operator) is a matrix used in calculating the probabilities of the outcomes of measurements performed on physical systems. It is a generalization of the state vectors or wavefunctions: while those can only represent pure states, density matrices can also represent mixed states. These arise in quantum mechanics in two different situations: # when the preparation of a system can randomly produce different pure states, and thus one must deal with the statistics of possible preparations, and # when one wants to describe a physical system that is entangled with another, without describing their combined state. This case is typical for a system interacting with some environment (e.g. decoherence). In this case, the density matrix of an entangled system differs from that of an ensemble of pure states that, combined, would give the same statistical results upon measurement. Density matrices are thus crucial tools in areas of quantum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Measure
In mathematics, a probability measure is a real-valued function defined on a set of events in a σ-algebra that satisfies Measure (mathematics), measure properties such as ''countable additivity''. The difference between a probability measure and the more general notion of measure (which includes concepts like area or volume) is that a probability measure must assign value 1 to the entire space. Intuitively, the additivity property says that the probability assigned to the union of two disjoint (mutually exclusive) events by the measure should be the sum of the probabilities of the events; for example, the value assigned to the outcome "1 or 2" in a throw of a dice should be the sum of the values assigned to the outcomes "1" and "2". Probability measures have applications in diverse fields, from physics to finance and biology. Definition The requirements for a set function \mu to be a probability measure on a σ-algebra are that: * \mu must return results in the unit interval ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bures Metric
In mathematics, in the area of quantum information geometry, the Bures metric (named after Donald Bures) or Helstrom metric (named after Carl W. Helstrom) defines an infinitesimal distance between density matrix operators defining quantum states. It is a quantum generalization of the Fisher information metric, and is identical to the Fubini–Study metric when restricted to the pure states alone. Definition The Bures metric may be defined as : _\text(\rho, \rho+d\rho)2 = \frac\mbox( d \rho G ), where G is the Hermitian 1-form operator implicitly given by : \rho G + G \rho = d \rho, which is a special case of a continuous Lyapunov equation. Some of the applications of the Bures metric include that given a target error, it allows the calculation of the minimum number of measurements to distinguish two different states and the use of the volume element as a candidate for the Jeffreys prior probability density for mixed quantum states. Bures distance The Bures distance is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
