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W-state
The W state is an entangled quantum state of three qubits which in the bra-ket notation has the following shape : , \mathrm\rangle = \frac(, 001\rangle + , 010\rangle + , 100\rangle) and which is remarkable for representing a specific type of multipartite entanglement and for occurring in several applications in quantum information theory. Particles prepared in this state reproduce the properties of Bell's theorem, which states that no classical theory of local hidden variables can produce the predictions of quantum mechanics. The state is named after Wolfgang Dür, who first reported the state together with Guifré Vidal, and Ignacio Cirac in 2002. Properties The W state is the representative of one of the two non-biseparable classes of three-qubit states, the other being the Greenberger–Horne–Zeilinger state In physics, in the area of quantum information theory, a Greenberger–Horne–Zeilinger state (GHZ state) is a certain type of entangled quantum state that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multipartite Entanglement
In the case of systems composed of m > 2 subsystems, the classification of quantum-entangled states is richer than in the bipartite case. Indeed, in multipartite entanglement apart from fully separable states and fully entangled states, there also exists the notion of partially separable states. Full and partial separability The definitions of fully separable and fully entangled multipartite states naturally generalizes that of separable and entangled states in the bipartite case, as follows. Full ''m''-partite separability (''m''-separability) of ''m'' systems The state \; \varrho_ of \; m subsystems \; A_1, \ldots, A_m with Hilbert space \; \mathcal_=\mathcal_\otimes\ldots\otimes \mathcal_ is fully separable if and only if it can be written in the form :\; \varrho_ = \sum_^k p_i \varrho_^i \otimes \ldots \otimes \varrho_^i. Correspondingly, the state \; \varrho_ is fully entangled if it cannot be written in the above form. As in the bipartite case, the set of \; m-separ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multipartite Entanglement
In the case of systems composed of m > 2 subsystems, the classification of quantum-entangled states is richer than in the bipartite case. Indeed, in multipartite entanglement apart from fully separable states and fully entangled states, there also exists the notion of partially separable states. Full and partial separability The definitions of fully separable and fully entangled multipartite states naturally generalizes that of separable and entangled states in the bipartite case, as follows. Full ''m''-partite separability (''m''-separability) of ''m'' systems The state \; \varrho_ of \; m subsystems \; A_1, \ldots, A_m with Hilbert space \; \mathcal_=\mathcal_\otimes\ldots\otimes \mathcal_ is fully separable if and only if it can be written in the form :\; \varrho_ = \sum_^k p_i \varrho_^i \otimes \ldots \otimes \varrho_^i. Correspondingly, the state \; \varrho_ is fully entangled if it cannot be written in the above form. As in the bipartite case, the set of \; m-separ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Entanglement
Quantum entanglement is the phenomenon that occurs when a group of particles are generated, interact, or share spatial proximity in a way such that the quantum state of each particle of the group cannot be described independently of the state of the others, including when the particles are separated by a large distance. The topic of quantum entanglement is at the heart of the disparity between classical and quantum physics: entanglement is a primary feature of quantum mechanics not present in classical mechanics. Measurements of physical properties such as position, momentum, spin, and 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 gives ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum State
In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Knowledge of the quantum state together with the rules for the system's evolution in time exhausts all that can be predicted about the system's behavior. A mixture of quantum states is again a quantum state. Quantum states that cannot be written as a mixture of other states are called pure quantum states, while all other states are called mixed quantum states. A pure quantum state can be represented by a ray in a Hilbert space over the complex numbers, while mixed states are represented by density matrices, which are positive semidefinite operators that act on Hilbert spaces. Pure states are also known as state vectors or wave functions, the latter term applying particularly when they are represented as functions of position or momentum. For example, when dealing with the energy spectrum of the electron in a hydrogen at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Qubits
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 states can be taken to be the vertical polarization and the horizontal 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 both 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 acknowledgments of his 1995 paper, Schumacher states that the term ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Information Theory
Quantum information is the information of the quantum state, 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 Observable, observables cannot be precisely mea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Guifré Vidal
Guifré Vidal is a Spanish physicist who is working on quantum many-body physics using analytical and numerical techniques. In particular, he is one of the leading experts of tensor network state implementations such as time-evolving block decimation (TEBD) and multiscale entanglement renormalization ansatz (MERA). He was previously a faculty member of Perimeter Institute Perimeter Institute for Theoretical Physics (PI, Perimeter, PITP) is an independent research centre in foundational theoretical physics located in Waterloo, Ontario, Canada. It was founded in 1999. The institute's founding and major benefactor i ... in Waterloo, Canada. However as of September 2019, he is now a research scientist at Sandbox @ Alphabet. External linksScience Watch interview [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Juan Ignacio Cirac Sasturain
Juan Ignacio Cirac Sasturain (born 11 October 1965), known professionally as Ignacio Cirac, is a Spanish physicist. He is one of the pioneers of the field of quantum computing and quantum information theory. He is the recipient of the 2006 Prince of Asturias Award in technical and scientific research. Career Cirac graduated from the Complutense University of Madrid in 1988 and moved to the United States in 1991 to work as a postdoctoral scientist with Peter Zoller in the Joint Institute for Laboratory Astrophysics in University of Colorado at Boulder. Between 1991 and 1996, he was teaching physics in the Ciudad Real Faculty of Chemistry, University of Castilla-La Mancha. In 1996, Cirac became professor in the Institut für Theoretische Physik in Innsbruck, Austria, and in 2001 he became a director of the Max Planck Institute of Quantum Optics in Garching, Germany, where he heads the Theory Division. At the same time, he was appointed honorary professor at the Technical Unive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Product State
In quantum mechanics, separable states are quantum states belonging to a composite space that can be factored into individual states belonging to separate subspaces. 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 of quantum mechanics these can be described as vectors in the tensor product space H_1\otimes H_2. In this discussion we will focus on the case of the Hilbert spaces H_1 and H_2 being finite-dimensional. Pure states Let \_^n\subset H_1 and \_^m \subset H_2 be orthonormal bases for H_1 and H_2, respectively. A basis for H_1 \otimes H_2 is then \, or in more compact notation \. From the very definition of the tensor product, any vector of norm 1, i.e. a pure state of the composite system, can be written a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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