# Questions tagged [entropy]

For questions about the various kinds of entropies --- as defined in the context of quantum information theory and quantum statistical mechanics.

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### Schumacher compression - comparing with Shannon compression

Background Shannon's source coding theorem tells us the following. We shall consider a binary alphabet for simplicity. Suppose Alice has $n$ independent and identically distributed instances of a ...
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### What is the classical cost of simulating an arbitrary quantum state?

The past couple of years has seen various groups claim quantum advantage/utility only to have their experiments efficiently simulated with classical methods, notably using tensor networks. My question ...
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### Proof that the relative entropy satisfies $S(\rho\|\sigma)=S(T\rho\|T\sigma)$ iff $\hat TT\rho=\rho$, $\hat TT\sigma=\sigma$ for some $\hat T$

To prove the saturation condition for the strong subadditivity of the von Neumann entropy, the authors of [HJPW2004] make use of the following characterisation of when the monotonicity of the ...
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### What does a quantum mutual information larger than its classical upper bound represent?

Let $\rho$ be a bipartite state. Its quantum mutual information is defined as $$\newcommand{\tr}{\operatorname{tr}}I(\rho) = S(\tr_B(\rho)) + S(\tr_A(\rho)) - S(\rho),$$ where $S(\sigma)$ is the von ...
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### von Neumann entropy of an arbitrary composition system

I understand the von Neumann entropy of a $2$-composite system is that of the reduced density matrix? What is the von Neumann entropy of an entanglement of a more than $3$ composite system?
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