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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 ...


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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 ...


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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 ...


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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}...


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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 ...


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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 ...


3

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 ...


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