Quantum Relative Entropy
In quantum information theory, quantum relative entropy is a measure of distinguishability between two density matrix, quantum states. It is the quantum mechanical analog of relative entropy. Motivation For simplicity, it will be assumed that all objects in the article are finite-dimensional. We first discuss the classical case. Suppose the probabilities of a finite sequence of events is given by the probability distribution ''P'' = , but somehow we mistakenly assumed it to be ''Q'' = . For instance, we can mistake an unfair coin for a fair one. According to this erroneous assumption, our uncertainty about the ''j''-th event, or equivalently, the amount of information provided after observing the ''j''-th event, is :\; - \log q_j. The (assumed) average uncertainty of all possible events is then :\; - \sum_j p_j \log q_j. On the other hand, the Shannon entropy of the probability distribution ''p'', defined by :\; - \sum_j p_j \log p_j, is the real amount of uncertainty befor ...
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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 ...
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