# Tag Info

Accepted

### Proof of an Holevo information inequality for a classical-classical-quantum channel

It appears that the statement is not true in general. Suppose $X = Y = \{0,1\}$, $\mathcal{H}$ is the Hilbert space corresponding to a single qubit, and $W$ is defined as \begin{align} W(0,0) & = |...
• 4,568
Accepted

• 5,563
Accepted

### How to prove that $\frac{| x_0 \rangle + | x_1 \rangle}{\sqrt{2}}$ hides one of $x_0$ or $x_1$?

We can bound the amount of information that can be retrieved from $|\psi\rangle$ using Holevo's bound. Alice and Bob Let us first reformulate the situation in the terms usually employed in the context ...
• 14.4k

### What is "linear" in linear entropy?

$S_L$ called linear because it's obtained from the usual definition of von Neumann entropy $S = -\mathrm{Tr}(\rho \ln \rho)$ by taking a linear approximation for the natural log $\ln \rho = \rho - 1$. ...
• 16.3k
Accepted

### Accessible information of system vs system, apparatus and environment

For density matrices $\rho_A$ and $\rho_B$ having eigenvalues $\lambda^{\left(A\right)}$ and $\lambda^{\left(B\right)}$, \begin{align}S\left(\rho_A\otimes\rho_B\right) &= -\rho_A\otimes\rho_B\ln\...
• 3,477

• 2,275
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• 4,212
### Prove that Shannon and von Neumann entropies satisfy $H(P)\ge S(\rho)$ with $P$ diagonal of $\rho$
This can be seen through "twirling" with a bunch of unitaries. Call your density operator $\rho$. Let $U_i$ be a unitary with $\pm 1$ on the diagonal, and zeros everywhere else when ...