5 votes

Advances in Quantum Channel Capacity

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 ...
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What exactly is the relation between the Holevo quantity and the mutual information?

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 ...
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Understanding classical vs. quantum channel capacities

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}) \...
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What is meant by a "single-letter" expression for the quantum channel capacity?

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 ...
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4 votes
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Bounding diamond norm distance using probability of error in transmission of classical information

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 ...
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4 votes

Quantum capacity for serial composition of quantum channels

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 ...
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3 votes

Experimental Realization of Superactivation of Quantum Capacity

The paper Superactivation of Multipartite Unlockable Bound Entanglement, presented the first experimental realization of the following superactivation: Alice and Charlie have zero entanglement. Bob ...
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Additivity of degradable and anti-degradable quantum capacities

I have been able to find the answer to this question, so I will post it myself for anyone that would be interested. The result is proven in Useful States and Entanglement Distillation by Leditzky, ...
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Why does entanglement not increase the classical capacity of a channel?

In my understanding, the key part for entanglement to increase capacity is to have a suboptimal channel. Suppose the input of you channel can take value in the set $X$, and note $G(X)$ the graph where ...
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Why does entanglement not increase the classical capacity of a channel?

I will try to succinctly answer your first question given that I possess little knowledge regarding entanglement assistance. Shannon's capacity theorem (the noisy channel coding theorem) states that ...
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