# Questions tagged [information-theory]

The tag is used for questions connected with information theory in classical and/or quantum sense.

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### How to compute the QFI of a thermal state?

Let $\rho=\frac{1}{Z}\exp(-\beta H)$ be the thermal state associated to the Hamiltonian $$H=\hbar\omega\sum_i\left( a_i^\dagger a_i+\frac12\right).$$ I wonder how the quantum Fisher information of ...
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### Prove the equality conditions in the triangle inequality $S(A,B)\ge |S(A)-S(B)|$ for the von Neumann entropy

The triangle inequality or Araki-Lieb inequality of the von Neumann entropy is $$S(A,B)\ge|S(A)-S(B)|$$ this is proven by introducing a system $R$ which purifies systems $A$ and $B$. Applying ...
1 vote
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### Why can't Quantum Fisher Information be negative?

Quantum Fisher Information is proportional to Fidelity susceptibility. Mathematically the equation is: $QFI=-\frac{\partial^2 d_B(\epsilon) }{\partial \epsilon^2}$ where above equation shows QFI is ...
191 views

### Comparison of Quantum Mutual Information and Coherent Information with Classical Mutual Information

Between quantum mutual information and coherent information, which one is more similar to classical mutual information? I understand that both measures have some similarities to classical mutual ...
1 vote
169 views

### Deriving the choi matrix definition of the quantum depolarizing channel

I was reading up on the quantum depolarizing channel (Preskill's Notes) (stack exchaange explanation), and I'm failing to see how the form \begin{align} \sigma &= (\mathcal E \otimes \mathbb I)(|\...
1 vote
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The paper here (Definition 1) defines adversarial channels as $N(\rho)= \sum_i A_i \rho A_i$ with the mention that the $A_i$ is chosen only after a communication strategy is decide. This gives the ...
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### Why is error correction very different for circuits compared to channels?

Background Suppose one wishes to communicate information using a noisy channel $N$ instead of an ideal channel $I$. The general framework to communicate reliably is Take $n$ copies of $N$. For some ...
312 views

### Can $2^n$ bits be sent with $n$ instances of quantum teleportation?

So, right now these are two pieces of information I've been told are correct: Quantum teleportation can send a single qubit from Alice to Bob, with two classical bits $n$ qubits can store $2^n$ ...
### How to show $T(\rho,\sigma)≥\sum_i|r_i − s_i|$ with $r_i,s_i$ eigenvalues of $\rho,\sigma$?
The proof of the Fannes' inequality replies on the formula $T(ρ, σ)≥\sum_i|r_i − s_i|$, where $r_i,s_i$ are the eigenvalues of $\rho,\sigma$, in the descending order. In the proof given in Box 11.2, ...