6
votes
Accepted
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 ...
- 1,893
6
votes
Accepted
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 ...
- 76
5
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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5
votes
Accepted
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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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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4
votes
Accepted
Classical capacity of quantum channel - Holevo quantity vs accessible information of a channel
No they are not the same. Given some quantum channel $\mathcal{N}$ we can consider an encoding map $\mathcal{E}$ and a decoding map $\mathcal{D}$ such that $\mathcal{C}_1= \mathcal{D}\circ \mathcal{N} ...
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4
votes
Accepted
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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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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2
votes
Does proving $Q^{(1)}(\mathcal{N}\otimes\mathcal{N})=Q^{(1)}(\mathcal{N})+Q^{(1)}(\mathcal{N})$ imply additivity for arbitrary $n$?
I found out the paper Quantum Channel Capacities (by Graeme Smith) were the author states: "Some entropic function
f(N ) is shown to be an achievable rate, and its regularization
equal to the ...
2
votes
Accepted
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, ...
2
votes
Accepted
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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votes
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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votes
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Classical capacity of the quantum bitflip channel
The classical capacity of the quantum bitflip channel is 1.
The states $|+\rangle\langle+|$ and $|-\rangle\langle-|$ are invariant under bitflip channel.
Let $\mathcal{N}$ be the bitflip map.
$$
\...
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1
vote
Accepted
Is there a notion of approximate entanglement breaking (EB) channels?
This work (https://journals.aps.org/pra/abstract/10.1103/PhysRevA.97.012332) may be relevant to your question. The authors have shown that "approximate additivity" holds for "...
1
vote
Twirling of quantum states: Maximally entangled states
Let $|\psi\rangle = \frac{1}{\sqrt{d}}\sum_{i=0}^{d-1} |ii\rangle_{AB}$ be a maximally entangled state on a bipartite system $AB$.
Such states satisfy the transpose property
$$
(X \otimes I) |\psi\...
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