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No-communication Theorem
In physics, the no-communication theorem or no-signaling principle is a no-go theorem from quantum information theory which states that, during measurement of an entangled quantum state, it is not possible for one observer, by making a measurement of a subsystem of the total state, to communicate information to another observer. The theorem is important because, in quantum mechanics, quantum entanglement is an effect by which certain widely separated events can be correlated in ways that, at first glance, suggest the possibility of communication faster-than-light. The no-communication theorem gives conditions under which such transfer of information between two observers is impossible. These results can be applied to understand the so-called paradoxes in quantum mechanics, such as the EPR paradox, or violations of local realism obtained in tests of Bell's theorem. In these experiments, the no-communication theorem shows that failure of local realism does not lead to what could ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physics
Physics is the natural science that studies matter, its 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." Physics is one of the most fundamental scientific disciplines, with its main goal being to understand how the universe behaves. "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 physic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Density Matrix
In quantum mechanics, a density matrix (or density operator) is a matrix that describes the quantum state of a physical system. It allows for the calculation of the probabilities of the outcomes of any measurement performed upon this system, using the Born rule. It is a generalization of the more usual state vectors or wavefunctions: while those can only represent pure states, density matrices can also represent ''mixed states''. Mixed states arise in quantum mechanics in two different situations: first when the preparation of the system is not fully known, and thus one must deal with a statistical ensemble of possible preparations, and second when one wants to describe a physical system which is entangled with another, without describing their combined state. Density matrices are thus crucial tools in areas of quantum mechanics that deal with mixed states, such as quantum statistical mechanics, open quantum systems, quantum decoherence, and quantum information. Definition an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classical Information Channel
{{Short description, Type of communication channel in quantum information science In quantum information science, a classical information channel (often called simply classical channel) is a communication channel that can be used to transmit classical information (as opposed to quantum channel which can transmit quantum information). An example would be a light travelling over fiber optics lines or electricity travelling over phone lines. Although classical channels cannot transmit quantum information by themselves, they can be useful in combination with quantum channels. Examples of their use are: * In quantum teleportation, a classical channel together with a previously prepared entangled quantum state are used to transmit quantum information between two parties. Neither the classical channel nor the previously prepared quantum state alone can do this task. * In quantum cryptography, a classical channel is used along with a quantum channel in protocols for quantum key exchange. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
No-teleportation Theorem
In quantum information theory, the no-teleportation theorem states that an arbitrary quantum state cannot be converted into a sequence of classical bits (or even an infinite number of such bits); nor can such bits be used to reconstruct the original state, thus "teleporting" it by merely moving classical bits around. Put another way, it states that the unit of quantum information, the qubit, cannot be exactly, precisely converted into classical information bits. This should not be confused with quantum teleportation, which does allow a quantum state to be destroyed in one location, and an exact replica to be created at a different location. In crude terms, the no-teleportation theorem stems from the Heisenberg uncertainty principle and the EPR paradox: although a qubit , \psi\rangle can be imagined to be a specific direction on the Bloch sphere, that direction cannot be measured precisely, for the general case , \psi\rangle; if it could, the results of that measurement would b ... [...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 which satisfies a stronger, more robust condition. Definition Let A and B be C*-algebras. A linear map \phi: A\to B is called 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 say that \phi is k-positive if \textrm_ \otimes \phi is a positive map, and \phi is called completely positive if \phi is k-positive for all k. Properties * Po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Separable 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Density Operator
In quantum mechanics, a density matrix (or density operator) is a matrix that describes the quantum state of a physical system. It allows for the calculation of the probabilities of the outcomes of any measurement performed upon this system, using the Born rule. It is a generalization of the more usual state vectors or wavefunctions: while those can only represent pure states, density matrices can also represent ''mixed states''. Mixed states arise in quantum mechanics in two different situations: first when the preparation of the system is not fully known, and thus one must deal with a statistical ensemble of possible preparations, and second when one wants to describe a physical system which is entangled with another, without describing their combined state. Density matrices are thus crucial tools in areas of quantum mechanics that deal with mixed states, such as quantum statistical mechanics, open quantum systems, quantum decoherence, and quantum information. Definition an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Operation
In quantum mechanics, a quantum operation (also known as quantum dynamical map or quantum process) is a mathematical formalism used to describe a broad class of transformations that a quantum mechanical system can undergo. This was first discussed as a general stochastic transformation for a density matrix by George Sudarshan. The quantum operation formalism describes not only unitary time evolution or symmetry transformations of isolated systems, but also the effects of measurement and transient interactions with an environment. In the context of quantum computation, a quantum operation is called a quantum channel. Note that some authors use the term "quantum operation" to refer specifically to completely positive (CP) and non-trace-increasing maps on the space of density matrices, and the term "quantum channel" to refer to the subset of those that are strictly trace-preserving. Quantum operations are formulated in terms of the density operator description of a quantum mechanica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Density State
In quantum mechanics, a density matrix (or density operator) is a matrix that describes the quantum state of a physical system. It allows for the calculation of the probabilities of the outcomes of any measurement performed upon this system, using the Born rule. It is a generalization of the more usual state vectors or wavefunctions: while those can only represent pure states, density matrices can also represent ''mixed states''. Mixed states arise in quantum mechanics in two different situations: first when the preparation of the system is not fully known, and thus one must deal with a statistical ensemble of possible preparations, and second when one wants to describe a physical system which is entangled with another, without describing their combined state. Density matrices are thus crucial tools in areas of quantum mechanics that deal with mixed states, such as quantum statistical mechanics, open quantum systems, quantum decoherence, and quantum information. Definition and m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bell Test
A Bell test, also known as Bell inequality test or Bell experiment, is a real-world physics experiment designed to test the theory of quantum mechanics in relation to Albert Einstein's concept of local realism. Named for John Stewart Bell, the experiments test whether or not the real world satisfies local realism, which requires the presence of some additional local variables (called "hidden" because they are not a feature of quantum theory) to explain the behavior of particles like photons and electrons. To date, all Bell tests have found that the hypothesis of local hidden variables is inconsistent with the way that physical systems behave. According to Bell's theorem, if nature actually operates in accord with any theory of local hidden variables, then the results of a Bell test will be constrained in a particular, quantifiable way. If a Bell experiment is performed and the results are ''not'' thus constrained, then the hypothesized local hidden variables cannot exist. Such ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Trace
In linear algebra and functional analysis, the partial trace is a generalization of the trace. Whereas the trace is a scalar valued function on operators, the partial trace is an operator-valued function. The partial trace has applications in quantum information and decoherence which is relevant for quantum measurement and thereby to the decoherent approaches to interpretations of quantum mechanics, including consistent histories and the relative state interpretation. Details Suppose V, W are finite-dimensional vector spaces over a field, with dimensions m and n, respectively. For any space A, let L(A) denote the space of linear operators on A. The partial trace over W is then written as \operatorname_W: \operatorname(V \otimes W) \to \operatorname(V). It is defined as follows: For T\in \operatorname(V \otimes W), let e_1, \ldots, e_m , and f_1, \ldots, f_n , be bases for ''V'' and ''W'' respectively; then ''T'' has a matrix representation : \ \quad 1 \leq k, i \le ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trace (linear Algebra)
In linear algebra, the trace of a square matrix , denoted , is defined to be the sum of elements on the main diagonal (from the upper left to the lower right) of . The trace is only defined for a square matrix (). It can be proved that the trace of a matrix is the sum of its (complex) eigenvalues (counted with multiplicities). It can also be proved that for any two matrices and . This implies that similar matrices have the same trace. As a consequence one can define the trace of a linear operator mapping a finite-dimensional vector space into itself, since all matrices describing such an operator with respect to a basis are similar. The trace is related to the derivative of the determinant (see Jacobi's formula). Definition The trace of an square matrix is defined as \operatorname(\mathbf) = \sum_^n a_ = a_ + a_ + \dots + a_ where denotes the entry on the th row and th column of . The entries of can be real numbers or (more generally) complex numbers. The trace is not ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
