![]() As can be seen, even though one state translates from one gray dot to the other, the rest usually do not, unless that is they are mere permutations of the said state. If I remember correctly, an early characterization of the von Neumann entropy of a state was as the minimum outcome uncertainty (in the sense of Shannons entropy) among all extremal measurements that can be made on that state (excluding the trivial 1-outcome measurement of course). The two lines represent the two measures, the gray dots each represents a value for the corresponding measure and the respective equivalence class. In the framework of Quantum Field Theory, we provide a rigorous, operator algebraic notion of entanglement entropy associated with a pair of open double cones of the spacetime, where the closure of is contained in. Introduction It is well known that the atomic inversion for a two-level atom interacting with a quantized field suffers collapses and revivals of Rabi oscillations 1, 2, 3. The highway of the development of entropy is marked by many great names, for example, Clausius, Gibbs, Boltzmann, Szilard, von Neumann, Shannon, Jaynes. However, for pure states and the maximally mixed state, there do indeed exist one-to-one correspondences due to the uniqueness in their eigenvalue. von Neumann entropy and change of basis Ask Question Asked 10 years ago Modified 4 years, 11 months ago Viewed 3k times 3 The von Neumann entropy is defined as S() Tr( ln ) S ( ) T r ( ln ), where is density matrix. 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. ![]()
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