# Tag Info

Accepted

### What is a "maximally mixed state"?

The maximally mixed state is a quantum state whose density matrix is proportional to the identity matrix. Physically, it may be interpreted as a uniform mixture of states in an orthonormal basis. The ...
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### 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) & = |...
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• 6,197
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### 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\...
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### Does the quantum Jensen-Shannon divergence appear in any quantum algorithms or texts on quantum computing?

That quantity appears to be identical to Holevo information, which turns out to be the upper bound on how much classical information you can transmit using a quantum channel [1]. More generally the ...
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As you mention pure states will not do. So lets look at a simple example of mixed entangled states, two-qubit Werner states. Let $\rho_{AB} = q |\Psi^- \rangle \langle \Psi^-| + (1-q) I / 4$ where $| \... • 5,988 5 votes Accepted ### Prove the additivity of the Renyi entropy:$H_{\beta}(p \times r) = H_{\beta}(p) + H_{\beta}(r)This only holds if the two distributions are independent. In this case \begin{aligned} H_{\beta}(p \times q) &= \frac{1}{1-\beta} \log\left( \sum_{i,j}(p(i) q(j))^{\beta} \right) \\ &= \... • 5,988 5 votes ### Measuring entanglement entropy using a stabilizer circuit simulator I think stim is the right tool for the job here, because it gives you access to the stabilizer generators and also it defines stim.PauliString which you can use to ... • 40.1k 5 votes ### Understanding the definition of entropy in the joint entropy theorem derivation It is not just the binary entropy that is denoted H(p_i). The quantity that is relevant here is the Shannon entropy of the distribution \{p_i\} which is defined as H(p_i) = - \sum_i p_i \log ... • 5,988 4 votes ### Shannon entropy is least when Measurement basis = Mixture basis My favourite way of proving that the Shannon entropy is minimized for a measurement in the qubit basis is through the notion of majorizaion (see Nielsen and Chuang or the book on Matrix Analysis by ... 4 votes Accepted ### Maximally mixed states for more than 1 qubit The Von Neumann entropy of1/2 (|00\rangle \langle 00| + |11\rangle \langle 11|)$is one bit. For$I/4$it's two bits of entropy instead. The entropy of states that only have entries on the ... • 40.1k 4 votes ### Can an isometry leave entropy invariant? You can always do that. Subspaces$\text{Im}(V)$and$A\otimes |0\rangle$have the same dimension, so there must be some unitary that translates one subspace to another. That is,$\exists W \in \text{...
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After some further consideration I think it's quite clear that the only probability mass function evaluated in the computation of $\mathcal{F}_{\text{XEB}}$ is that of the classically computed ideal ...