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In quantum information theory, the channel-state duality refers to the correspondence between quantum channels and quantum states (described by density matrices).Phrased differently, the duality is the isomorphism between completely positive maps (channels) from A to C n×n, where A is a C*-algebra and C n×n denotes the n×n complex entries, and positive linear functionals on the tensor product
Area served City of license VC RF Callsign Translating Network Notes Cleveland: Eastlake: 25 34 W34FP-D: WVIZ: PBS: Ohio Channel on 25.2, World Channel on 25.3, Create on 25.4, PBS Kids on 25.5, WKSU 89.7 FM Simulcast on 25.7, WCLV 90.3 FM Simulcast on 25.8, Cleveland Sight Center Network on 25.9
In quantum information theory and operator theory, the Choi–Jamiołkowski isomorphism refers to the correspondence between quantum channels (described by completely positive maps) and quantum states (described by density matrices), this is introduced by Man-Duen Choi [1] and Andrzej Jamiołkowski. [2]
In quantum information theory, a quantum channel is a communication channel which can transmit quantum information, as well as classical information. An example of quantum information is the general dynamics of a qubit. An example of classical information is a text document transmitted over the Internet.
The duality represents a major advance in understanding of string theory and quantum gravity. [12] This is because it provides a non-perturbative formulation of string theory with certain boundary conditions and because it is the most successful realization of the holographic principle.
Each theory of quantum gravity uses the term "quantum geometry" in a slightly different fashion. String theory, a leading candidate for a quantum theory of gravity, uses it to describe exotic phenomena such as T-duality and other geometric dualities, mirror symmetry, topology-changing transitions [clarification needed], minimal possible distance scale, and other effects that challenge intuition.
Quantum mechanics is a fundamental theory that describes the behavior of nature at and below the scale of atoms. [2]: 1.1 It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science.
In scattering theory, a scattering channel is a quantum state of the colliding system before or after the collision ().The Hilbert space spanned by the states before collision (in states) is equal to the space spanned by the states after collision (out states) which are both Fock spaces if there is a mass gap.