Quantum mechanics cTopic Fundamental concepts In physics , a quantumstate is a set of mathematical variables that fully describes a quantum system . For example, the set of 4 numbers math n , ell , m ... state the mathematical object reflects the operations performed by this apparatus. Quantum states ... on a quantumstate, the result is usually described by a probability distribution , and the form that this distribution takes is completely determined by the quantumstate and the observable ... states It is impossible in quantum mechanics unlike classical mechanics to have any state whose ..., a pure quantumstate is typically represented by a Euclidean vector vector in a Hilbert space , which ... name used to denote a vector which corresponds to a pure quantumstate is chosen to be of the form ... math langle psi math , which is also said to correspond to the same physical quantumstate. Technically ... rang c beta beta rang math is a different quantumstate possibly not normalized . Note that which quantumstate it is depends on both the amplitudes and phases arguments of math c alpha math and math ... rang math for real correspond to the same physical quantumstate, they are not interchangeable , since ... state is a state which can be described by a single ket vector, as described above. A mixed quantumstate is a statistical ensemble of pure states see quantum statistical mechanics . Equivalently, a mixed quantumstate on a given quantum system described by a Hilbert space H naturally arises as a pure quantumstate called a purification on a larger bipartite system H tensor K, the other half of which ... in quantum mechanics are particularly simple to state in terms of density matrices. For example, the ensemble ... context. See also Basic concepts of quantum mechanics Excited state Introduction to quantum mechanics Orthonormal basis Probability amplitude Quantum harmonic oscillator Qubit Stationary state W state ... ph229 Physics 219 at Caltech. DEFAULTSORT QuantumState Category Quantum mechanics ar ... more details
A macroscopic quantumstate is a state of matter in which macroscopic properties, such as Motion physics mechanical motion ref A. D. O Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and A. N. Cleland. Quantum ground state and single phonon control of a mechanical resonator. Nature, 464 697 703, April 2010. ref , thermal conductivity , electrical conductivity ref M. Ansmann, H. Wang, R. C. Bialczak, M. Hofheinz, E. Lucero, M. Neeley, A. D. O Connell, D. Sank, M. Weides, J. Wenner, A. N. Cleland, John M. Martinis. Violation of Bell s inequality in Josephson phase qubits. Nature, 461 504 506 September 2009. ref and viscosity , can be described by quantum mechanics as opposed to classical mechanics . This occurs primarily at low temperatures where there is little thermal motion present to mask the quantum nature of a substance. Macroscopic quantum phenomena can emerge from coherent states of superfluidity superfluids and superconductivity superconductors . Quantum states of motion have been directly observed in a macroscopic mechanical resonator see quantum machine . References reflist Category Quantum mechanics quantum stub ar pt Estado qu ntico macrosc pico ... more details
Of QuantumState Category Linear algebra Category Quantum information science ...In quantum mechanics , especially quantum information , purification refers to the fact that every mixed state acting on finite dimensional Hilbert spaces can be viewed as the partial trace reduced state of some pure state. In purely linear algebraic terms, it can be viewed as a statement about positive semidefinite matrix positive semidefinite matrices . Statement Let be a density matrix acting on a Hilbert space math H A math of finite dimension n . Then there exist a Hilbert space math H B math and a pure state math psi rangle in H A otimes H B math such that the partial trace of math psi rangle langle psi math with respect to math H B math math operatorname tr B left psi rangle langle psi right rho. math Proof A density matrix is by definition positive semidefinite. So can be Diagonalizable matrix diagonalized and written as math rho sum i 1 n p i i rangle langle i math for some orthonormal basis math i rangle math . Let math H B math be another copy of the n dimensional Hilbert space with any orthonormal basis math i rangle math . Define math psi rangle in H A otimes H B math by math psi rangle sum i sqrt p i i rangle otimes i rangle. math Direct calculation gives math operatorname tr B left psi rangle langle psi right operatorname tr B left sum i, j sqrt p ip j i rangle langle j otimes i rangle langle j right sum i,j delta i,j sqrt p i p j i rangle langle j rho. math This proves the claim. Note The vectorial pure state math psi rangle math is in the form specified by the Schmidt decomposition . Since square root decompositions of a positive semidefinite matrix are not unique, neither are purifications. In linear algebraic terms, a square matrix is positive semidefinite if and only if it can be purified in the above sense. The if part of the implication follows ... on completely positive maps and purification of a mixed state, we can recover the Stinespring ... more details
Unreferenced date December 2009 In quantum mechanics , a two state system also known as a TLS or two level system is a system which has two possible states. More formally, the Hilbert space of a two state ... state system is the Spin physics spin of a spin 1 2 particle such as an electron, whose spin can have values or in units of . The physics of a quantum mechanical two state system is trivial if both ... statequantum systems Spin 1 2 particles are two statequantum systems when only the spin degree ... Two StateQuantum System Category Quantum models de Zweizustandssystem zh ... difference between the two states, then nontrivial dynamics can occur. Two state dynamics If the time independent Hamiltonian quantum mechanics Hamiltonian is math H , math , and we label the two levels ... general state, math left. psi t 0 right rangle c a left. a right rangle c b left. b right rangle , math then after evolving under math H , math , at time math t , math , the state will be center ... hbar left b right rangle , math center The physics of two state systems can be usefully applied to multi state systems where the system is known to have only enough energy available to excite the lowest two states, thus effectively creating a two state system. In fact, in nature, it is difficult to identify any true two state systems merely systems where the energetics of the circumstances isolate ... known as the Bloch sphere . Dynamics of a two state system interacting with a field Free Precession The interaction of a two state system with an external field results in the precession of the state vector. The ability to carefully control the position of the state vector on the Bloch sphere is central ... mu B hbar math , math psi 0 math is the state vector at time math t 0 math , and math e i omega ... math The representation on the Bloch sphere for a state vector math psi 0 math will simply be the vector ... sigma z rangle right math . As an example, consider a state vector math psi 0 math that is a normalized ... more details
Other uses Quantum disambiguation pp move indef In physics , a quantum plural quanta is the minimum amount ... quantization . ref Wiener, N. 1966 . Differential Space, Quantum Systems, and Prediction . Cambridge ... certain discrete values. There is a related term of quantum number . An example of an entity that is quantized ... quantum of light, and is referred to as a light quantum . The energy of an electron bound to an atom .... As incorporated into the theory of quantum mechanics , this is regarded by physicists as part of the fundamental .... Etymology and discovery The word quantum comes from the Latin quantus, for how much. Quanta .... However, the word quantum in general was well known before 1900. ref E. Cobham Brewer 1810 ... by physicians , such as the term quantum satis . Both Helmholtz and Julius von Mayer were physicians as well as physicists. Helmholtz used quantum with reference to heat in his article ref E. Helmholtz ... R Mayer.pdf de icon ref on Mayer s work, and indeed, the word quantum can be found in the formulation ... cite journal last1 Klein first1 Martin J. title Max Planck and the beginnings of the quantum theory ... trunc sys.shtml Real World Quantum Effects Demonstrated ref In the attempt to bring experiment into agreement ... also colbegin 3 Basic concepts of quantum mechanics Elementary particle Graviton Introduction to quantum mechanics Magnetic flux quantum Photon Photon polarization Quantization physics Quantum cellular automata Quantum channel Quantum coherence Quantum chromodynamics Quantum computer Quantum cryptography Quantum dot Quantum electronics Quantum entanglement Quantum immortality Quantum lithography Quantum mechanics Quantum number Quantum sensor Quantumstate Subatomic particle colend References reflist 2 Further reading B. Hoffmann, The Strange Story of the Quantum , Pelican 1963. Lucretius, On the Nature ... Development of Quantum Theory , Vol.1, Part 1, Springer Verlag New York Inc., New York 1982 ...., London 1925 Dover editions 1960 and 1993 including the Nobel lecture. Category Quantum mechanics ... more details
Quantum Chemistry And Solid State Physics Software Category Density functional theory Category Computational ...Quantum chemistry computer programs are used in computational chemistry to implement the methods of quantum chemistry . Most include the Hartree&ndash Fock HF and some post Hartree&ndash Fock methods. They may also include density functional theory DFT , molecular mechanics or semi empirical quantum chemistry method s. The programs include both open source and commercial software. Most of them are large, often containing several separate programs, and have developed over many years. The following table illustrates the capabilities of the most versatile software packages that show an entry in two or more columns of the table. class sortable wikitable style font size 90 Package License sup sup Programming Language Lang. Basis set chemistry Basis Periodic sup sup Molecular mechanics Mol. mech. Semi empirical quantum chemistry method Semi emp. Hartree&ndash Fock HF Post Hartree&ndash Fock Post HF Density functional theory DFT ABINIT GNU General Public License GPL Fortran Basis set chemistry Plane wave basis sets PW 3d yes no no no yes ACES computational chemistry ACES II Academic Fortran Gaussian orbital GTO no no no yes yes yes ACES computational chemistry ACES II MAB Academic Fortran Gaussian orbital GTO no no no yes yes no ACES computational chemistry ACES III GPL Fortran C Gaussian orbital GTO no no no yes yes no Amsterdam Density Functional ADF Commercial Fortran Slater type orbital ... yes yes yes no Quantum ESPRESSO GNU General Public License GPL Fortran Basis set chemistry Plane ... espresso.org Quantum ESPRESSO sup 7 sup Web service integrating MPQC . sup 8 sup TeraChem is the first fully GPU accelerated quantum chemistry software . sup 9 sup Atomistix ToolKit also contains ... Nanostructures modeling programs Semi empirical quantum chemistry methods Semi empirical programs Computational chemical methods in solid state physics Solid state system programs with periodic boundary ... more details
Quantum jump may refer to Atomic electron transition or a similar transition between quantumstate s, which is a scientific phenomenon Quantum Jump , a British rock music band disambig ... more details
Unreferenced date December 2009 Orphan date December 2009 In some physics theories, choosing a 3 geometry via spin network and 4 geometry via spin foam , any superposition of spin networks is called a kinematical state and any superposition of spin foams is called a quantum history . DEFAULTSORT Quantum History Category Quantum mechanics Quantum stub ... more details
Context date October 2009 The word quantum refers to the idea of interactions and discrete energy levels of particles at the subatomic level quantum mechanics . Quantum mechanics is a very deep topic, and seeks to describe the state of being of a physical system. The quantum world goes against traditional laws of physics and opens new dimensions of study and possibility. A quantum sensor therefore is an influencing system that can measure the effect of the quantumstate of another physical or particle system on itself. The mere act of measurement influences the quantumstate and alters the probability and uncertainty associated with its state during measurement. A quantum sensor is a device that exploits quantum correlations, such as quantum entanglement , to achieve a sensitivity or resolution that is better than can achieved using only classical systems. ref http merlin.fic.uni.lodz.pl concepts 2005 3 4 2005 3 4 225.pdf K.T.Kapale, et al., Concepts of Physics 2 2005 225 . ref The Defense Advanced Research Projects Agency has recently When date August 2011 launched a research program in optical quantum sensors that seeks to exploit ideas from quantum metrology and quantum imaging , such as quantum lithography and the NOON state , in order to achieve these goals with optical sensor systems such as lidar . ref http www.darpa.mil sto space qsp.html DARPA Quantum Sensor Program . ref ref https www.fbo.gov index?id 9bafd20629bf798e1b084fb2582a4b34 BROAD AGENCY ANNOUNCEMENT BAA 07 22 Quantum Sensors ref Quantum sensor is also a term used in other settings where entangled quantum systems are exploited to make better atomic clocks ref http link.aps.org abstract PRA v54 pR4649 J.J.Bollinger, et al., Phys. Rev. A 54 1996 R4649 . ref or more sensitive magnetometers . ref http link.aps.org abstract PRL v93 e173002 M.Auzinsh et al., Phys. Rev. Lett. 93 2004 173002 . ref ref http link.aps.org ... References Reflist Category Quantum information science Category Quantum mechanics ... more details
A quantum limit in physics is a limit on measurement accuracy at quantum scales ref Vladimir Borisovich Braginski and Farid Ya. Khalili. Quantum Measurement. 1995. ref . Depending on the context, the limit may be absolute such as the Heisenberg limit , or it may only apply when the experiment is conducted with naturally occurring quantumstate s e.g. the standard quantum limit in interferometry and can be circumvented with advanced state preparation and measurement schemes. The terms quantum limit and standard quantum limit are sometimes used interchangeably. Usually, quantum limit is a general term which refers to any restriction on measurement due to quantum effects, while the standard quantum limit in any given context refers to a quantum limit which is ubiquitous in that context. Examples In the context of interferometry or other optical measurements, the standard quantum limit usually refers to the minimum level of quantum noise which is obtainable without Squeezed coherent state squeezed states . ref M. T. Jaekel and S. Reynaud, Quantum limits in interferometric measurements , Europhys. Lett. 13, 301. 1990. ref There is additionally a quantum limit for phase noise , reachable only by a laser at high noise frequencies. In spectroscopy , the shortest wavelength in an X ray spectrum is called the quantum limit. ref Donald Stover Piston, The Polarization of X rays from Thin Targets. 1935. ref Misleading relation to the classical limit Note that due to an overloading of the word limit , the classical limit is not the opposite of the quantum limit. In quantum limit , limit is being used in the sense of a physical limitation e.g. the Armstrong limit . In classical limit , limit is used in the sense of a Limit mathematics limiting process ref Note that there is no simple rigorous mathematical limit which fully recovers classical mechanics from quantum mechanics, the Ehrenfest theorem notwithstanding. ref . See also Classical limit Heisenberg limit Relativistic limit References ... more details
Orphan date November 2007 A quantum instrument is a quantum operation with both classical and quantum outputs. It combines the concepts of measurement and quantum operation. Description Usually it is implemented as a weighted collection of completely positive maps the sum of which is trace preserving. Quantum Instrument collection math mathcal E k math acts as math rho AB rightarrow tilde rho AA B sum k mathcal E k left rho AB right otimes vert k rangle langle k vert A math A quantum instrument is more general than a quantum operation because it records the outcome k of which operator acted on the state. References No footnotes date July 2009 E. Davies, J. Lewis. An operational approach to quantum probability, Comm. Math. Phys., vol. 17, pp. 239 260, 1970. http arxiv.org abs quant ph 0306078v1 Distillation of secret key paper http arxiv.org abs quant ph 0501045 Another paper which uses the concept DEFAULTSORT Quantum Instrument Category Quantum mechanics ... more details
theory to the quantum world. Quantum information theory aims to answer the following question blockquote What happens if information is stored in a state of a quantum system? blockquote One of the strengths ..., quantum mechanics does not allow us to read out the state of a quantum system with arbitrary precision. The existence of Bell state Bell correlations between Two statequantum system quantum systems ...for the journal with this title Historical Social Research No footnotes date November 2011 In quantum mechanics , quantum information is physical information that is held in the state of a quantum system . The most popular unit of quantum information is the qubit , a two level quantum system. However, unlike classical digital states which are discrete , a two statequantum system can actually be in a quantum superposition superposition of the two states at any given time. Quantum information differs ... without the state becoming the measured value, An arbitrary state cannot be no cloning theorem cloned , The state may be in a superposition of basis values. However, despite this, the amount of information ... quantum computation that the differentiation occurs. The ability to manipulate quantum information ... secure transmission of information. Quantum information processing is the most general field that is concerned with quantum information. There are certain tasks which classical computer s cannot perform efficiently that is, in polynomial time according to any known algorithm. However, a quantum ... speed up over the best possible classical algorithm. Quantum information, and changes in quantum information ... ensemble of quantum mechanical systems with the density matrix math rho math , it is given ... theory can also be generalized to the quantum case, such as http www.mi.ras.ru holevo eindex.html Holevo entropy and the conditional quantum entropy . Quantum information theory The theory of quantum .... However, this is not the case for quantum information it is not possible, for example, to write ... more details
Quantum cloning is the process that takes an arbitrary, unknown quantumstate and makes an exact copy without altering the original state in any way. In Dirac notation , the process of quantum cloning is described by math U psi rangle A e rangle B psi rangle A psi rangle B math , where math U math is the actual cloning operation, math psi rangle A math is the state to be cloned, and math e rangle B math is the initial state of the copy. Quantum cloning is forbidden by the laws of quantum mechanics as shown by the no cloning theorem , which proves that there is no math U math that can perform the cloning operation for any arbitrary state math psi rangle A math . Though perfect quantum cloning is not possible, it is possible to perform imperfect cloning, where the copies have a non unit Fidelity of quantum states fidelity with the state being cloned. The quantum cloning operation is the best way to make copies of quantum information therefore cloning is an important task in quantum information processing, especially in the context of quantum cryptography. Researchers are seeking ways to build quantum cloning machines, which work at the so called quantum limit. The first cloning machine relied on stimulated emission to copy quantum information encoded into single photons. Teleportation, nuclear magnetic resonance, quantum amplification and superior phase conjugation have been some other methods utilized to realize a quantum cloning machine. References V. Buzek and M. Hillery, http xstructure.inr.ac.ru x bin theme3.py?level 1&index1 373537 Quantum cloning , Physics World 14 11 2001 ... abs quant ph 0205149 Experimental Quantum Cloning of Single Photons , Science 296 5568 2002 ... quant ph 011198 Approximate Quantum Cloning with Nuclear Magnetic Resonance , Phys. Rev. Lett 88 ... Conjugate Inputs , Phys. Rev. Lett 98 170503 2007 See also Quantum no deleting theorem Category Quantum mechanics Category Quantum information science quantum stub ... more details
unreferenced date June 2011 Coupling in molecules Quantum Coupling is an effect in quantum mechanics in which two or more quantum systems are bound such that a change in one of the quantum states in one of the systems will cause an instantaneous change in all of the bound systems. It is a state similar to quantum entanglement but whereas quantum entanglement can take place over long distances quantum coupling is restricted to quantum scales. Quantum coupling in action Trapped ion quantum computers utilize the quantum coupling effect by suspending particles representing qubits in an array of ion traps. These particles are then induced into a state of quantum coupling by using optical pumping by a laser. Information can be stored in this state by coupling two or more qubits. While the individual particles may fluctuate their values, the quantum states of the two qubits remain locked in relation to each other, via Coulomb force . Any action by one of the coupled ions instantaneously alters the other to maintain the relative value. This allows the computer to hold information despite the instability of the individual particles. Other examples In benzene , C sub 6 sub H sub 6 sub , the charges of the individual carbon atoms exhibit coupling. There are three double bonds and three single bond s in alternating positions around the ring. The measurement of the energy in any individual bond will result in a puzzling result resembling an impossible one and a half bond . This is because the bonds are in a quantum superposition of double and single bonds at any particular bond position. The coupling effect causes the charge at all points on the ring to be altered when a bond at any one point is altered, in order to maintain the relative charge between atoms . This results in an illusionary bond and a half bond between all 6 carbon atoms. Category Quantum mechanics sl Kvantna sklopitev ... more details
of the coherent state as a quantum description of laser light and the realization that some states ... quantumstate of light with certain advantages over any classical state, Squeezed coherent state ... Squeezed coherent state squeezed light . Other important quantum aspects are related to correlations ... of it that draws not from atomic physics but from solid state physics. Its usage overlapped Quantum ...No footnotes date April 2009 Quantum optics is a field of research in physics , dealing with the application of quantum mechanics to phenomena involving light and its interactions with matter . History of quantum optics Light is made up of particles called photons and hence inherently is grainy quantized . Quantum optics is the study of the nature and effects of light as quantized photons. The first ... between light and matter following these developments not only formed the basis of quantum optics but was also crucial for the development of quantum mechanics as a whole. However, the subfields of quantum mechanics dealing with matter light interaction were principally regarded as research into matter rather than into light hence one rather spoke of atom physics and quantum electronics ... became an important field, and the quantum mechanics underlying the laser s principles was studied now with more emphasis on the properties of light, and the name quantum optics became customary. As laser ... very fruitful, interest in quantum optics rose. Following the work of Paul Dirac Dirac in quantum field theory , George Sudarshan , Roy J. Glauber , and Leonard Mandel applied quantum theory to the electromagnetic ... the first source of light which required a quantum description a single atom that emitted ... fast ultrafast processes. Applications for solid state research e.g. Raman spectroscopy ... of quantum entanglement , quantum teleportation , and recently, in 1995 quantum logic gate s. The latter are of much interest in quantum information theory , a subject which partly emerged from ... more details
quantumQuantum Darwinism is a theory explaining the emergence of the Classical physics classical world from the Quantum mechanics quantum world as due to a process of Charles Darwin Darwinian natural selection where the many possible quantum states are selected against in favor of a stable pointer state ... reality and exist in the macroscopic realm in a state able to undergo further evolution. As a quantum ... to achieve consensual agreement concerning their information of the quantumstate. This aspect of einselection ... topics pursued over the course of twenty five years including pointer state s, einselection and decoherence . A study in 2010 has provided preliminary supporting evidence of quantum Darwinism with scars of a quantum dot becoming a family of mother daughter states indicating they could stabilize into multiple pointer states. ref name urlNew evidence for quantum Darwinism found in quantum dots cite web url http www.physorg.com news192693808.html title New evidence for quantum Darwinism found in quantum dots format work accessdate 2010 05 12 ref Implications Along with Zurek s related theory of envariance , quantum Darwinism explains how the classical world emerges from the quantum world and proposes to answer the quantum measurement problem , the main interpretational challenge for quantum theory. The measurement problem arises because the quantumstate vector, the source of all knowledge concerning quantum systems, evolves according to the Schr dinger equation into a linear superposition ... never experienced in our classical world. Quantum theory has traditionally treated this problem as being resolved by a non unitarity physics unitary transformation of the quantumstatestate vector at the time of measurement into a definite state. It provides an extremely accurate means of predicting the value of the definite state that will be measured in the form of a probability for each possible measurement value. The physical nature of the transition from the quantum superposition of states ... more details
wave. Within quantum mechanics, such a wave can be approximated with a coherent state . At total ... also coherent stateQuantum optics References references C. W. Gardiner and Peter Zoller , Quantum ...No footnotes date November 2009 Quantum noise is uncertainty of some physical quantity due to its quantum origin. In the case of number of particles photons or electrons , the quantum noise is also called shot noise . Most optical communications use amplitude modulation. In this case, the quantum noise appears as shot noise only. In the case of uncertainty of electric field in some laser s, the quantum noise is not just shot noise uncertainties of both amplitude and phase contribute to the quantum noise. This issue becomes important in the case of noise of a quantum amplifier , which preserves ... with energy of quantum comparable to the energy of a signal which is believed to be more robust with respect to additive noise than an amplitude modulation . Origin of quantum noise Quantum noise may ... suppressed. Generally, quantum noise can be considered as error of description of any physical system within classical not quantum theory. In an electric circuit, the random fluctuations of a signal due to discrete character of electrons can be called quantum noise ref name Zoller C. W. Gardiner and Peter Zoller , Quantum Noise , Springer Verlag 1991, 2000, 2004 ref . The random error of interferometric measurement of position due to discrete character of photons registered can be attributed to quantum noise. Even the uncertainty of position of a probe in probe microscopy may lead to quantum noise ... cases, quantum noise refers to the fluctuations of signal in extremely accurate optical systems with stabilized lasers and efficient detectors. Coherent states and noise of a quantum amplifier Although the coherent states can be realized in wide variety of physical systems, they refer mainly to the state ... error of measurement of intensity due the quantum noise is only of order of 10 sup 5 sup which ... more details
for ex. Signatures of nonclassicality in mixed statequantum computation , Physical Review A vol. ... 77, 042303 2008 http pra.aps.org abstract PRA v77 i4 e042303 abstract ref For pure state s, the quantum ... quantum discord is a criterion for the pointer state s, which constitute preferred effectively classical ... be viewed In operational terms as an entanglement consumption in an extended State merging quantum ... basis for the performance in terms of quantum computation ascribed to certain Quantumstate Mixed states mixed statequantum systems, ref name datta et al 2007 P1 with a mixed quantumstate representing ... for ex. Animesh Datta, Sevag Gharibian Signatures of non classicality in mixed statequantum computation ...In quantum information theory , quantum discord is a measure of nonclassical correlations between two subsystems of a quantum system. It includes correlations that are due to quantum mechanics quantum physical effects but do not necessarily involve quantum entanglement . The notion of quantum discord ... 2 K abstract abstract ref ref name olliver zurek 2001 Harold Ollivier and Wojciech H. Zurek, Quantum ... et al 2007 P1 Animesh Datta, Anil Shaji, Carlton M. Caves Quantum discord and the power of one qubit ... page 1 p. 1 ref by L. Henderson and Vlatko Vedral . ref L. Henderson and V. Vedral Classical, quantum ... that quantum correlations can be present in certain mixed separable states ref name giorda paris 2010 P1 Paolo Giorda, Matteo G. A. Paris Gaussian quantum discord , quant ph arXiv 1003.3207v2 ... page 1 p. 1 ref In other words, separability alone does not imply the absence of quantum effects. The notion of quantum discord thus goes beyond the distinction which had been made earlier between entangled versus separable non entangled quantum states. Definition and mathematical relations ... information I X Y . In mathematical terms, quantum discord is defined in terms of the quantum mutual information . More specifically, quantum discord is the difference between two expressions which ... more details
File Electron probabilities in GaAs quantum well.png thumb Electron probabilities in lowest two quantum states of a 160 GaAs quantum well in a GaAs GaAlAs heterostructure as calculated from Envelope waves envelope functions . ref name Bastard Quantum heterostructure is a heterostructure in a substrate usually a semiconductor material , where size restricts the movements of the charge carrier s forcing them into a quantum confinement. This leads to the formation of a set of discrete energy levels at which the carriers can exist. Quantum heterostructures have sharper density of states than structures of more conventional sizes. Quantum heterostructures are important for fabrication of short wavelength light emitting diode s and diode laser s, and for other optoelectronic applications, eg. high efficiency photovoltaic cell s. Examples of quantum heterostructures confining the carriers in quasi two, one and zero dimensions are Quantum well s Quantum wire s Quantum dot s References reflist refs ref name Bastard cite book title Solid state physics Semiconductor Heterostructures and Nanostructures chapter Figure 10 in Electronic States in Semiconductor Heterostructures author G Bastard, JA Brum, R Ferreira isbn 0126077444 year 1991 editor Henry Ehrenreich, David Turnbull, eds url http books.google.com books?id 6ZffQs8hvt0C&pg PA259 page 259 ref See also http www.ecse.rpi.edu schubert Light Emitting Diodes dot org chap04 chap04.htm phys stub Category Quantum electronics Category Nanomaterials Category Semiconductor structures az Heterostruktur fr H t rostructure quantique ru ... more details
Quantum realm is a term of art in physics referring to scales where Quantum mechanics quantum mechanical effects become important ref http www.wired.com science discoveries news 2007 04 quantum New Experiment Probes Weird Zone Between Quantum and Classical . Wired.com. Retrieved on 2010 12 16. ref ref http physicsweb.org articles news 7 2 9 1 Nanowires approach the quantum realm physicsworld.com . Physicsweb.org. Retrieved on 2010 12 16. ref ref name stanford1 http plato.stanford.edu entries qm action distance Action at a Distance in Quantum Mechanics Stanford Encyclopedia of Philosophy . Plato.stanford.edu 2007 01 26 . Retrieved on 2010 12 16. ref . Typically, this means distances of 100 nanometer nanometers nm or less. Not coincidentally, this is the same scale as nanotechnology . While originating on the nanometer scale, such effects can operate on a macro level. The classic example is electron tunneling . Most fundamental processes in molecular electronics , organic electronics and organic semiconductor s also originate in the quantum realm. The quantum realm can also sometimes paradoxically involve quantum entanglement actions at long distances . A well known example is David Bohm s 1951 version of the famous thought experiment that Einstein, Podolsky and Rosen proposed in 1935 EPR paradox . Pairs of particles are emitted from a source in the so called spin singlet state and rush in opposite directions. When the particles are widely separated from each other, they each encounter a measuring apparatus that can be set to measure their spin components along various directions. Although the measurement events are distant from each other, so that no slower than light or light signal can travel between them, the measurement outcomes are curiously correlated. ref name stanford1 See also Classical limit Quantum limit References reflist Category Quantum mechanics it Regno quantico ... more details
the internal state of the quantum machine during execution of the quantum program. qcl dump ... not influence the state of the quantum machine and can be realised only using a simulator. The QCL ...mergefrom Quantum virtual machine discuss Talk Quantum programming Merger proposal date August 2009 Quantum programming is a set of computer programming language s that allow the expression of quantum algorithm s using high level constructs. The point of quantum languages is not so much to provide a tool for programmers, but to provide tools for researchers to understand better how quantum computation works and how to formally reason about quantum algorithms. Efforts are underway to develop functional programming languages for quantum computing . Examples include Selinger s QPL ref name qpl http ... http sneezy.cs.nott.ac.uk qml QML A Functional Quantum Programming Language Bot generated title ref . Higher order quantum programming languages, based on lambda calculus , have been proposed by van Tonder ref http epubs.siam.org SICOMP volume 33 art 43216.html A Lambda Calculus for Quantum Computation ... simon quantumQuantum Programming Languages Survey has more information on the current state of research and a comprehensive bibliography of resources. Imperative quantum programming languages Quantum pseudocode Quantum pseudocode proposed by E. Knill is the first formalised language for description of quantum algorithm s was introduced and, moreover, it was tightly connected with a model of quantum machine called Quantum Random Access Machine QRAM . Quantum computing language http tph.tuwien.ac.at oemer qcl.html QCL Quantum Computation Language is one of the first implemented quantum programming languages . Its syntax resembles syntax of the C programming language and classical data type s are similar to data types in C. You can combine a classical code and a quantum code in one source code. The basic built in quantum data type in QCL is the qureg quantum register . It can ... more details
In quantum computing , quantum walks are the quantum analogue of classical random walks . Like the classical random walk, where the walker s current state is described by a probability distribution over positions, the walker in a quantum walk is in a quantum superposition superposition of positions. Like classical random walks, there are two types of quantum walks, discrete time quantum walks and continuous time quantum walks. Motivation Quantum walks are motivated by the widespread use of classical random walks in the design of randomized algorithms, and are part of several quantum algorithm s. For some oracular problems, quantum walks provide an exponential speedup over any classical algorithm ... Spielman D. A. Spielman , Exponential algorithmic speedup by quantum walk, Proc. 35th ACM Symposium ..., and Umesh Vazirani U. V. Vazirani , Quantum algorithms for hidden nonlinear structures, Proc. 48th IEEE Symposium on Foundations of Computer Science, pp. 395 404, 2007, arXiv 0705.2784. ref Quantum ... distinctness problem , ref Andris Ambainis , Quantum walk algorithm for element distinctness ... 2004. ref the triangle finding problem , ref F. Magniez, M. Santha, and Mario Szegedy M. Szegedy , Quantum ... J. Goldstone , and S. Gutmann, A quantum algorithm for the Hamiltonian NAND tree, Theory of Computing ... can also be viewed as a quantum walk algorithm. Relation to classical random walks Quantum walks ... to limiting distributions and due to the power of quantum interference they may spread significantly faster or slower than their classical equivalents. Continuous time Main Continuous time quantum walk Under particular conditions, continuous time quantum walks can provide a model for universal quantum ... abs 0806.1972 Universal Computation by Quantum Walk . ref Discrete time Expand section date December 2009 Image One dimensional quantum random walk.png thumb right Probability distribution resulting from one dimensional discrete time random walks. The quantum walk created using the Hadamard coin is plotted ... more details
Quantum Content is a concept that describes the complexity, granularity and connectivity of the current state of content creation, consumption and curation. ref cite web last Cotsakos first Christos title The Age of Quantum Content url http www.endplay.com quantum work Speech accessdate 30 November 2011 ref Origins While the exact origins of the term Quantum Content remain unknown, the term was brought to relevance by Christos Cotsakos Dr. Christos M. Cotsakos at the 2011 Gilbane Conference for the Web content management system Web Content Management WCM industry. In his keynote speech, titled The Age of Quantum Content, Dr. Cotsakos defined Quantum Content as a function of Big data Big Data and its granularity, complexity and connectivity, plus elements of serendipity and sizzle also known as the e or error term in statistics . Quantum Content f Big Data Granularity Complexity Connectivity e ref cite web last Cotsakos first Christos title The Age of Quantum Content url http www.endplay.com quantum work Speech accessdate 30 November 2011 ref Characteristics of Quantum Content Prior to the Age of Quantum Content, there were two elements content creation and audience engagement that focused on three areas a creator or idea, a medium channel and an audience. In the age of Quantum Content ... With Discussion On Quantum Content url http www.1888pressrelease.com endplay ceo keynotes gilbane ... 30 November 2011 ref Similarities with Quantum Physics Quantum physics theory holds that energy ... both like a particle and like a wave, depending on how it s measured. ref cite web title What is Quantum ... 5 December 2011 ref Quantum content is not Big Data but rather it is a function of Big Data ... title The Age of Quantum Content url http www.endplay.com quantum work Speech accessdate 5 December 2011 ref As in quantum physics, even discrete data elements in the Age of Quantum Content have multiple ... Keynotes Gilbane Boston With Discussion On Quantum Content http www.endplay.com quantum The Age of Quantum ... more details
A quantum fluid can refer to a cluster of valence electrons moving together after they undergo fermionic condensate fermionic condensation . Under extremely high pressures and low temperatures electrons may condense into a quantum fluid. In such a state, electrical current can theoretically flow forever with a complete absence of voltage , meaning that its electric potential does not change, as in a superconductor . Like superconductivity this quantum fluid state is the result of a phase transition . Quantum fluids exhibit the remarkable property of remaining liquid at absolute zero temperature and zero pressure. This effect arises from their large zero point energy and the small interatomic forces, both of which prevent the formation of a solid phase. A quantum fluid can also refer to a superfluid made up of atoms . References cite book last Lerner first Rita G. and Trigg, George L. title Encyclopedia of Physics publisher VHC Publishers year 1990 isbn 0 89573 752 3 Category Condensed matter physics ... more details
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 . ref http link.aps.org abstract PRL v96 e010401 V.Giovannetti, et al., Phys. Rev. Lett. 96 2006 010401 . ref This field promises to develop measurement techniques that give better precision than the same measurement performed in a classical framework. One example of note is the use of the so called NOON state in a Mach Zender interferometer to perform accurate phase measurements. ref http www.iop.org EJ abstract 1464 4266 6 8 029 P.Kok et al., J. Opt. B 6 2004 S811 . ref A similar effect can be produced using less exotic states such as squeezed state s. An important application of particular note is the detection of gravitational radiation with projects such as LIGO . Here high precision distance measurements must be made of two widely separated masses. However, currently the measurements described by quantum metrology are usually not used as they are very difficult to implement and there are many other sources of noise which prohibit the detection of gravity waves which must be overcome first. Nevertheless plans may call for the use of quantum metrology in LIGO. ref http link.aps.org abstract PRD v65 e022002 H.J.Kimble, et al., Phys. Rev. D 65 2001 022002 . ref References Reflist Category Quantum information science Category Quantum mechanics physics stub ... more details
Encyclopedia
top
