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Unextendible Product Basis
In 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 ..., an unextendible product basis is a set of orthogonal, non- entangled state vectors for a multipartite system, with the property that local operations and classical communication are insufficient to distinguish one member of the set from the others. Because these states are product states and yet local measurements cannot tell them apart, they are sometimes said to exhibit "nonlocality without entanglement". They provide examples of non-entangled states that pass the Peres–Horodecki criterion for entanglement. See also * Bound entanglement References {{Quantum-stub Quantum information theory Quantum states ... [...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] |
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] |
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] |
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] |
Bound Entanglement
Bound entanglement is a weak form of quantum entanglement, from which no singlets can be distilled with local operations and classical communication (LOCC). Bound entanglement was discovered by M. Horodecki, P. Horodecki, and R. Horodecki. Bipartite entangled states that have a non-negative partial transpose are all bound-entangled. Moreover, a particular quantum state for 2x4 systems has been presented. Such states are not detected by the Peres-Horodecki criterion as entangled, thus other entanglement criteria are needed for their detection. There are a number of examples for such states. There are also multipartite entangled states that have a negative partial transpose with respect to some bipartitions, while they have a positive partial transpose to the other partitions, nevertheless, they are undistillable. The possible existence of bipartite bound entangled states with a negative partial transpose is still under intensive study. Properties of bound entangled states wit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Information Theory
Quantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information refers to both the technical definition in terms of Von Neumann entropy and the general computational term. It is an interdisciplinary field that involves quantum mechanics, computer science, information theory, philosophy and cryptography among other fields. Its study is also relevant to disciplines such as cognitive science, psychology and neuroscience. Its main focus is in extracting information from matter at the microscopic scale. Observation in science is one of the most important ways of acquiring information and measurement is required in order to quantify the observation, making this crucial to the scientific method. In quantum mechanics, due to the uncertainty principle, non-commuting observables cannot be precisely measured simultaneously, as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
