|
Negativity (quantum Mechanics)
In quantum mechanics, negativity is a measure of quantum entanglement which is easy to compute. It is a measure deriving from the PPT criterion for separability. It has been shown to be an entanglement monotone and hence a proper measure of entanglement. Definition The negativity of a subsystem A can be defined in terms of a density matrix \rho as: :\mathcal(\rho) \equiv \frac where: * \rho^ is the partial transpose of \rho with respect to subsystem A * , , X, , _1 = \text, X, = \text \sqrt is the trace norm or the sum of the singular values of the operator X . An alternative and equivalent definition is the absolute sum of the negative eigenvalues of \rho^: : \mathcal(\rho) = \left, \sum_ \lambda_i \ = \sum_i \frac where \lambda_i are all of the eigenvalues. Properties * Is a convex function of \rho: :\mathcal(\sum_p_\rho_) \le \sum_p_\mathcal(\rho_) * Is an entanglement monotone: :\mathcal(P(\rho)) \le \mathcal(\rho) where P(\rho) is an arbitrary LOCC LOCC ... [...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] |
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] |
Peres–Horodecki Criterion
The Peres–Horodecki criterion is a necessary condition, for the joint density matrix \rho of two quantum mechanical systems A and B, to be separable. It is also called the PPT criterion, for ''positive partial transpose''. In the 2×2 and 2×3 dimensional cases the condition is also sufficient. It is used to decide the separability of mixed states, where the Schmidt decomposition does not apply. The theorem was discovered in 1996 by Asher Peres and the Horodecki family ( Michał, Paweł, and Ryszard) In higher dimensions, the test is inconclusive, and one should supplement it with more advanced tests, such as those based on entanglement witnesses. Definition If we have a general state \rho which acts on Hilbert space of \mathcal_A \otimes \mathcal_B :\rho = \sum_ p^_ , i\rangle \langle j , \otimes , k\rangle \langle l, Its partial transpose (with respect to the B party) is defined as :\rho^ := (I \otimes T) (\rho) = \sum_ p^ _ , i\rangle \langle j , \otimes (, k\ra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Separable State
In quantum mechanics, separable states are multipartite quantum states that can be written as a convex combination of product states. Product states are multipartite quantum states that can be written as a tensor product of states in each space. The physical intuition behind these definitions is that product states have no correlation between the different degrees of freedom, while separable states might have correlations, but all such correlations can be explained as due to a classical random variable, as opposed to being due to entanglement. In the special case of pure states the definition simplifies: a pure state is separable if and only if it is a product state. A state is said to be entangled if it is not separable. In general, determining if a state is separable is not straightforward and the problem is classed as NP-hard. Separability of bipartite systems Consider first composite states with two degrees of freedom, referred to as ''bipartite states''. By a postulate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entanglement Monotone
In quantum information and quantum computation, an entanglement monotone or entanglement measure is a function that quantifies the amount of entanglement present in a quantum state. Any entanglement monotone is a nonnegative function whose value does not increase under local operations and classical communication. Definition Let \mathcal(\mathcal_A\otimes\mathcal_B)be the space of all states, i.e., Hermitian positive semi-definite operators with trace one, over the bipartite Hilbert space \mathcal_A\otimes\mathcal_B. An entanglement measure is a function \mu:\to \mathbb_such that: # \mu(\rho)=0 if \rho is separable; # Monotonically decreasing under LOCC, viz., for the Kraus operator E_i\otimes F_i corresponding to the LOCC \mathcal_, let p_i=\mathrm E_i\otimes F_i)\rho (E_i\otimes F_i)^/math> and \rho_i=(E_i\otimes F_i)\rho (E_i\otimes F_i)^/\mathrm E_i\otimes F_i)\rho (E_i\otimes F_i)^/math>for a given state \rho, then (i) \mu does not increase under the average over all ... [...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] |
Partial Transpose
Partial may refer to: Mathematics *Partial derivative, derivative with respect to one of several variables of a function, with the other variables held constant ** ∂, a symbol that can denote a partial derivative, sometimes pronounced "partial dee" **Partial differential equation, a differential equation that contains unknown multivariable functions and their partial derivatives Other uses *Partial application, in computer science the process of fixing a number of arguments to a function, producing another function *Partial charge or net atomic charge, in chemistry a charge value that is not an integer or whole number *Partial fingerprint, impression of human fingers used in criminology or forensic science *Partial seizure or focal seizure, a seizure that initially affects only one hemisphere of the brain * Partial or Part score, in contract bridge a trick score less than 100, as well as other meanings * Partial or Partial wave, one sound wave of which a complex tone is composed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trace Norm
Trace may refer to: Arts and entertainment Music * ''Trace'' (Son Volt album), 1995 * ''Trace'' (Died Pretty album), 1993 * Trace (band), a Dutch progressive rock band * ''The Trace'' (album), by Nell Other uses in arts and entertainment * ''Trace'' (magazine), British hip-hop magazine * ''Trace'' (manhwa), a Korean internet cartoon * ''Trace'' (manga), a Japanese manga series by Kei Koga * ''Trace'' (novel), a novel by Patricia Cornwell * ''The Trace'' (film), a 1994 Turkish film * ''The Trace'' (video game), 2015 video game * ''Sama'' (film), alternate title ''The Trace'', a 1988 Tunisian film * Trace, a fictional character in the game ''Metroid Prime Hunters'' * Trace, the protagonist of ''Axiom Verge'' * Trace, another name for Portgas D. Ace, a fictional character in the manga ''One Piece'' * Trace, the main brand for a number of music channels such as Trace Urban Language * Trace (deconstruction), a concept in Derridian deconstruction * Trace (linguistics), a s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Function
In mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of a function, graph of the function lies above or on the graph between the two points. Equivalently, a function is convex if its epigraph (mathematics), ''epigraph'' (the set of points on or above the graph of the function) is a convex set. In simple terms, a convex function graph is shaped like a cup \cup (or a straight line like a linear function), while a concave function's graph is shaped like a cap \cap. A twice-differentiable function, differentiable function of a single variable is convex if and only if its second derivative is nonnegative on its entire domain of a function, domain. Well-known examples of convex functions of a single variable include a linear function f(x) = cx (where c is a real number), a quadratic function cx^2 (c as a nonnegative real number) and an exponential function ce^x (c as a nonnegative real number). Convex functions pl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
LOCC
LOCC, or local operations and classical communication, is a method in quantum information theory where a local (product) operation is performed on part of the system, and where the result of that operation is "communicated" classically to another part where usually another local operation is performed conditioned on the information received. Mathematical properties The formal definition of the set of LOCC operations is complicated due to the fact that later local operations depend in general on all the previous classical communication and due to the unbounded number of communication rounds. For any finite number r\geq1 one can define \operatorname_r, the set of LOCC operations that can be achieved with r rounds of classical communication. The set becomes strictly larger whenever r is increased and care has to be taken to define the limit of infinitely many rounds. In particular, the set LOCC is not topologically closed, that is there are quantum operations that can be approximat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PPT Criterion
PPT may refer to: Organizations * Parti Progressiste Tchadien, a political party active in Chad between 1947 and 1973 * Partido del Pueblo Trabajador (Working People's Party of Puerto Rico), a political party in Puerto Rico * Patria Para Todos, a left-wing political party in Venezuela * Permanent Peoples' Tribunal, an international opinion tribunal founded in Bologna, 1979 * Plunge Protection Team, a nickname of the United States President's Working Group on Financial Markets * Porin Pallo-Toverit, the former name of the Finnish football club FC Jazz * PTT Public Company Limited, Thai state-owned oil and gas company Science and technology * .ppt, the file format used by Microsoft PowerPoint presentation software * Parts-per notation for ''parts-per-trillion'' (more common) or ''parts-per-thousand'' (less common) * PerlPowerTools, a revitalized of the classic Unix command set in pure Perl * Positive partial transpose, a criterion used in quantum mechanics * Power point tr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
