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State-merging
In quantum information theory, quantum state merging is the transfer of a quantum state when the receiver already has part of the state. The process optimally transfers partial information using entanglement and classical communication. It allows for sending information using an amount of entanglement given by the conditional quantum entropy, H(A, B)\,=\,H(AB)-H(B) \, . with H(A) the Von Neumann entropy, H(A):=-Tr\rho_A\log\rho_A. It thus provides an operational meaning to this quantity. Unlike its classical counterpart, the quantum conditional entropy can be negative. In this case, the sender can transfer the state to the receiver using no entanglement, and as an added bonus, this amount of entanglement can be gained, rather than used. Thus quantum information can be negative. The amount of classical information needed is the mutual information I(A:R):=H(A)+H(R)-H(AR). The case where the classical communication is replaced by quantum communication was considered in. This is k ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Discord
In quantum information theory, quantum discord is a measure of nonclassical correlations between two subsystems of a quantum system. It includes correlations that are due to quantum physical effects but do not necessarily involve quantum entanglement. The notion of quantum discord was introduced by Harold Ollivier and Wojciech H. ZurekWojciech H. Zurek, ''Einselection and decoherence from an information theory perspective'', Annalen der Physik vol. 9, 855–864 (2000abstract/ref>Harold Ollivier and Wojciech H. Zurek, ''Quantum Discord: A Measure of the Quantumness of Correlations'', Physical Review Letters vol. 88, 017901 (2001abstract/ref> and, independently by Leah Henderson and Vlatko Vedral. Olliver and Zurek referred to it also as a measure of ''quantumness'' of correlations. From the work of these two research groups it follows that quantum correlations can be present in certain mixed separable states;Paolo Giorda, Matteo G. A. Paris: ''Gaussian quantum discord'' ... [...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] |
Conditional Quantum Entropy
The conditional quantum entropy is an entropy measure used in quantum information theory. It is a generalization of the conditional entropy of classical information theory. For a bipartite state \rho^, the conditional entropy is written S(A, B)_\rho, or H(A, B)_\rho, depending on the notation being used for the von Neumann entropy. The quantum conditional entropy was defined in terms of a conditional density operator \rho_ by Nicolas Cerf and Chris Adami, who showed that quantum conditional entropies can be negative, something that is forbidden in classical physics. The negativity of quantum conditional entropy is a sufficient criterion for quantum non-separability. In what follows, we use the notation S(\cdot) for the von Neumann entropy, which will simply be called "entropy". Definition Given a bipartite quantum state \rho^, the entropy of the joint system AB is S(AB)_\rho \ \stackrel\ S(\rho^), and the entropies of the subsystems are S(A)_\rho \ \stackrel\ S(\rho^A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Von Neumann Entropy
In physics, the von Neumann entropy, named after John von Neumann, is an extension of the concept of Gibbs entropy from classical statistical mechanics to quantum statistical mechanics. For a quantum-mechanical system described by a density matrix , the von Neumann entropy is : S = - \operatorname(\rho \ln \rho), where \operatorname denotes the trace and ln denotes the (natural) matrix logarithm. If is written in terms of its eigenvectors , 1\rangle, , 2\rangle, , 3\rangle, \dots as : \rho = \sum_j \eta_j \left, j \right\rang \left\lang j \ , then the von Neumann entropy is merely : S = -\sum_j \eta_j \ln \eta_j . In this form, ''S'' can be seen as the information theoretic Shannon entropy. The von Neumann entropy is also used in different forms ( conditional entropies, relative entropies, etc.) in the framework of quantum information theory to characterize the entropy of entanglement. Background John von Neumann established a rigorous mathematical framework for quantum me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mutual Information
In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables. More specifically, it quantifies the " amount of information" (in units such as shannons (bits), nats or hartleys) obtained about one random variable by observing the other random variable. The concept of mutual information is intimately linked to that of entropy of a random variable, a fundamental notion in information theory that quantifies the expected "amount of information" held in a random variable. Not limited to real-valued random variables and linear dependence like the correlation coefficient, MI is more general and determines how different the joint distribution of the pair (X,Y) is from the product of the marginal distributions of X and Y. MI is the expected value of the pointwise mutual information (PMI). The quantity was defined and analyzed by Claude Shannon in his landmark paper "A Mathemati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Channel
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 state of a qubit. An example of classical information is a text document transmitted over the Internet. More formally, quantum channels are completely positive (CP) trace-preserving maps between spaces of operators. In other words, a quantum channel is just a quantum operation viewed not merely as the reduced dynamics of a system but as a pipeline intended to carry quantum information. (Some authors use the term "quantum operation" to also include trace-decreasing maps while reserving "quantum channel" for strictly trace-preserving maps.) Memoryless quantum channel We will assume for the moment that all state spaces of the systems considered, classical or quantum, are finite-dimensional. The memoryless in the section title carries the same meaning as in classical information theory: the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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