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No-communication Theorem
In physics, the no-communication theorem (also referred to as the no-signaling principle) is a no-go theorem in quantum information theory. It asserts that during the measurement of an entangled quantum state, it is impossible for one observer to transmit information to another observer, regardless of their spatial separation. This conclusion preserves the principle of causality in quantum mechanics and ensures that information transfer does not violate special relativity by exceeding the speed of light. The theorem is significant because quantum entanglement creates correlations between distant events that might initially appear to enable faster-than-light communication. The no-communication theorem establishes conditions under which such transmission is impossible, thus resolving paradoxes like the Einstein-Podolsky-Rosen (EPR) paradox and addressing the violations of local realism observed in Bell's theorem. Specifically, it demonstrates that the failure of local realism doe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physics
Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." It is one of the most fundamental scientific disciplines. "Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Density State
In quantum mechanics, a density matrix (or density operator) is a Matrix (mathematics), matrix used in calculating the probabilities of the outcomes of Measurement in quantum mechanics, 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 quantum entanglement, entangled with another, without describing their combined state. This case is typical for a system interacting with some environment (e.g. quantum decoherence, 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 statis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Faster-than-light Communication
Faster-than-light communication, also called superluminal communication, is a hypothetical process in which information is conveyed at faster-than-light speeds. The current scientific consensus is that faster-than-light communication is not possible, and to date it has not been achieved in any experiment. Faster-than-light communication other than possibly through wormholes is likely impossible because, in a Lorentz-invariant theory, it could be used to transmit information into the past. This would complicate causality, but no theoretical arguments conclusively preclude this possibility. A number of theories and phenomena related to faster-than-light communication have been proposed or studied, including tachyons, neutrinos, quantum nonlocality, wormholes, and quantum tunneling. Proposed mechanisms Tachyons Tachyonic particles are hypothetical particles that travel faster than light, which could conceivably allow for superluminal communication. Because such a particle woul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spacetime
In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects, such as how different observers perceive ''where'' and ''when'' events occur. Until the turn of the 20th century, the assumption had been that the three-dimensional geometry of the universe (its description in terms of locations, shapes, distances, and directions) was distinct from time (the measurement of when events occur within the universe). However, space and time took on new meanings with the Lorentz transformation and special theory of relativity. In 1908, Hermann Minkowski presented a geometric interpretation of special relativity that fused time and the three spatial dimensions into a single four-dimensional continuum now known as Minkowski space. This interpretation proved vital t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Field Theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles. The current standard model of particle physics is based on QFT. History Quantum field theory emerged from the work of generations of theoretical physicists spanning much of the 20th century. Its development began in the 1920s with the description of interactions between light and electrons, culminating in the first quantum field theory—quantum electrodynamics. A major theoretical obstacle soon followed with the appearance and persistence of various infinities in perturbative calculations, a problem only resolved in the 1950s with the invention of the renormalization procedure. A second major barrier came with QFT's apparent inabili ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Causality
Causality is an influence by which one Event (philosophy), event, process, state, or Object (philosophy), object (''a'' ''cause'') contributes to the production of another event, process, state, or object (an ''effect'') where the cause is at least partly responsible for the effect, and the effect is at least partly dependent on the cause. The cause of something may also be described as the reason for the event or process. In general, a process can have multiple causes,Compare: which are also said to be ''causal factors'' for it, and all lie in its past. An effect can in turn be a cause of, or causal factor for, many other effects, which all lie in its future. Some writers have held that causality is metaphysics , metaphysically prior to notions of time and space. Causality is an abstraction that indicates how the world progresses. As such it is a basic concept; it is more apt to be an explanation of other concepts of progression than something to be explained by other more fun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Space-like
In mathematical physics, the causal structure of a Lorentzian manifold describes the possible causal relationships between points in the manifold. Lorentzian manifolds can be classified according to the types of causal structures they admit (''causality conditions''). Introduction In modern physics (especially general relativity) spacetime is represented by a Lorentzian manifold. The causal relations between points in the manifold are interpreted as describing which events in spacetime can influence which other events. The causal structure of an arbitrary (possibly curved) Lorentzian manifold is made more complicated by the presence of curvature. Discussions of the causal structure for such manifolds must be phrased in terms of smooth curves joining pairs of points. Conditions on the tangent vectors of the curves then define the causal relationships. Tangent vectors If \,(M,g) is a Lorentzian manifold (for metric g on manifold M) then the nonzero tangent vectors at each p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Qubit
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 spin states (left-handed and the right-handed circular polarization) can also be measured as horizontal and vertical linear 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 multiple 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 acknow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bell State
In quantum information science, the Bell's states or EPR pairs are specific quantum states of two qubits that represent the simplest examples of quantum entanglement. The Bell's states are a form of entangled and normalized basis vectors. This normalization implies that the overall probability of the particles being in one of the mentioned states is 1: \langle \Phi, \Phi \rangle = 1. Entanglement is a basis-independent result of superposition. Due to this superposition, measurement of the qubit will " collapse" it into one of its basis states with a given probability. Because of the entanglement, measurement of one qubit will "collapse" the other qubit to a state whose measurement will yield one of two possible values, where the value depends on which Bell's state the two qubits are in initially. Bell's states can be generalized to certain quantum states of multi-qubit systems, such as the GHZ state for three or more subsystems. Understanding of Bell's states is useful in a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximally Entangled State
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] |
No-cloning Theorem
In physics, the no-cloning theorem states that it is impossible to create an independent and identical copy of an arbitrary unknown quantum state, a statement which has profound implications in the field of quantum computer, quantum computing among others. The theorem is an evolution of the 1970 no-go theorem authored by James L. Park, in which he demonstrates that a non-disturbing measurement scheme which is both simple and perfect cannot exist (the same result would be independently derived in 1982 by William Wootters and Wojciech H. Zurek as well as Dennis Dieks the same year). The aforementioned theorems do not preclude the state of one system becoming quantum entanglement, entangled with the state of another as cloning specifically refers to the creation of a separable state with identical factors. For example, one might use the controlled NOT gate and the Hadamard transform#Quantum computing applications, Walsh–Hadamard gate to entangle two qubits without violating the no-cl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Completely Positive Map
In mathematics a positive map is a map between C*-algebras that sends positive elements to positive elements. A completely positive map is one that satisfies a stronger, more robust condition. Definition Let A and B be C*-algebras. A linear map \phi: A\to B is called a positive map if \phi maps positive elements to positive elements: a\geq 0 \implies \phi(a)\geq 0. Any linear map \phi:A\to B induces another map :\textrm \otimes \phi : \mathbb^ \otimes A \to \mathbb^ \otimes B in a natural way. If \mathbb^\otimes A is identified with the C*-algebra A^ of k\times k-matrices with entries in A, then \textrm\otimes\phi acts as : \begin a_ & \cdots & a_ \\ \vdots & \ddots & \vdots \\ a_ & \cdots & a_ \end \mapsto \begin \phi(a_) & \cdots & \phi(a_) \\ \vdots & \ddots & \vdots \\ \phi(a_) & \cdots & \phi(a_) \end. We then say \phi is k-positive if \textrm_ \otimes \phi is a positive map and completely positive if \phi is k-positive for all k. Properties * Positive maps are mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
