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Let's recap a bit: In classical information theory, the analogous formula is the Shannon noisy channel coding theorem. It's charming, because it is basically just a very simple optimization of the mutual information. The quantum channel capacity is that it is given by $$ \lim\limits_{n\to\infty} \frac{1}{n}Q(T^{\otimes n}) $$ where $T$ is the quantum ...

Right, they are quite similar. The Holevo bound is a bound on the amount of accessible information between your quantum system and your classical system. The I(X;B) object written in the HSW theorem wikipedia page is actually this bound, while the $\chi$ there is the Holevo rate, or product state capacity. What HSW showed was that if you took many copies of ...

These are not really the definitions of classical and quantum capacity, as I will explain. Before doing that, let me adjust the notation being used slightly: let $\Phi:\text{L}(\mathcal{X}) \rightarrow \text{L}(\mathcal{Y})$ be the channel whose capacities we are interested in and let $\Psi:\text{L}(\mathcal{X}) \rightarrow \text{L}(\mathcal{Z})$ be a ...

In a series of individual works, Lloyd, Shor, and then Devetak developed what is known as the "LSD Theorem," which gives a formula for the quantum capacity of a quantum channel. The result states that the quantum capacity $Q$ of a channel $\Phi$ is the regularization of the coherent information, written $$Q(\Phi)=\frac{\lim_{n\rightarrow \infty}}{n}...

Intuition The expression $\|\mathcal{A} - \mathcal{I}\|_\diamond$ quantifies how close the channel $\mathcal{A}$ is to the identity channel $\mathcal{I}$ which is the channel that preserves quantum information perfectly. In order for a channel to transfer quantum information well, it must preserve both diagonal and off-diagonal elements of the input density ...

TL;DR Quantum capacity of $\mathcal{N}_2\circ\mathcal{N}_1$ can be anywhere between zero and the minimum of the quantum capacities of $\mathcal{N}_1$ and $\mathcal{N}_2$. Background Quantum capacity of a quantum channel $\mathcal{N}$ is defined as the greatest real number $Q(\mathcal{N})$ such that for any $R < Q(\mathcal{N})$ (representing a transmission ...

The paper Superactivation of Multipartite Unlockable Bound Entanglement, presented the first experimental realization of the following superactivation: Alice and Charlie have zero entanglement. Bob and Charle have zero entanglement. But Alice, Bob, and Charlie have non-zero tripartite entanglement. Six years earlier was the experimental demonstration of a ...