von Neumann entropy and change of basis - Mathematics Stack …
Given that the von Neumann entropy can also be written as $\rho = -\sum_j \eta_j \log \eta_j $ where, $\eta_j$ are the eigenvalues of $\rho$, the only thing that remains to be proved is that eigenvalues are invariant under a change of basis.
Von Neumann Entropy: Temperature & Info Explained - Physics …
2006年2月11日 · What is the significance of Von Neumann Entropy in information theory? In information theory, Von Neumann Entropy is used to quantify the amount of uncertainty or unpredictability in a system. It is a measure of the average amount of information needed to describe the state of a system. Can Von Neumann Entropy be negative? No, Von Neumann ...
quantum mechanics - Von Neumann entropy vs Shannon entropy ...
2024年7月2日 · The entropy of a quantum state $\rho$ is defined as the Shannon entropy of the probability distribution defined by its eigenvalues. Observe that since a state is a posivitive matrix, all the eigenvalues are non-negative real numbers.
matrix calculus - Derivative of the von Neumann entropy
2019年2月23日 · Derivative of the von Neumann entropy. Ask Question Asked 5 years, 10 months ago.
How to compute Von Neumann entropy? - Physics Forums
2014年4月6日 · What is Von Neumann entropy? Von Neumann entropy is a measure of the uncertainty or randomness in a quantum system. It is named after John von Neumann, a mathematician who made significant contributions to quantum mechanics. How is Von Neumann entropy computed? Von Neumann entropy is computed by taking the trace of the system's …
Maximum value of Von Neumann Entropy - Physics Forums
2016年4月22日 · The maximum value of Von Neumann Entropy is closely related to other measures of entropy, such as Shannon entropy and Boltzmann entropy. However, it differs in the fact that it takes into account the quantum nature of the system and is applicable to both pure and mixed quantum states.
What is the definition of log(P) in the von neumann entropy …
2005年3月29日 · Von Neumann entropy is calculated using the formula S = -Tr(ρln(ρ)), where S is the entropy, ρ is the density matrix of the system, and ln is the natural logarithm. This formula is derived from the von Neumann entropy formula for a discrete probability distribution.
Showing that the Shannon entropy is a special case of the von …
2024年4月3日 · This gives that we have the trace operator, $\text{Tr}\rho=1$, which gives the von Neumann entropy of $\mathcal{D}(\rho)=1\ln 1=0$ for the element with two outcomes. This is a pure state, with lowest possible entropy.
Interpreting von Neumann Entropy in Schrodinger's Cat-type …
2011年9月13日 · The von Neumann entropy is indeed an extension of classical entropy, and it can be interpreted as a measure of the uncertainty in a quantum system. In the case of Schrodinger's cat experiment, the sudden decrease in the joint entropy of the system can be explained by the fact that the system has undergone a measurement.
On the definition of Von Neumann entropy - Physics Forums
2009年7月12日 · I am confused by the definition of the Von Neumann entropy. In Nielson and Chung's book page 510, the Von Neumann entropy is defined as S (\\rho) = - tr(\\rho \\log \\rho) where \\rho is the density matrix. What is the definition of the logrithm of a matrix? Is it some series expansion of a...