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# Questions tagged [channel-capacity]

The highest rate at which quantum information can be communicated over many independent uses of a noisy quantum channel (e.g. a qubit) from a sender to a receiver.

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### What are examples of channels whose Holevo capacity can be computed explicitly?

Given a channel $\Phi:\operatorname{Lin}(\mathbb{C}^n)\to\operatorname{Lin}(\mathbb{C}^m)$, we define its Holevo capacity as $$\chi(\Phi) = \sup_\eta \chi(\Phi(\eta)),$$ with the sup taken with ...
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### Prove that the coherent information of an antidegradable channel is equal to zero

I want to show that antidegradable channels have zero coherent information, based on Exercise 13.5.6 in [1]. So the solution should use the following relationship: For Hilbert spaces $R, B, E$, a pure ...
• 7,123
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### Does no-cloning imply zero capacity of antidegradable channels?

I read that (paraphrasing, see below) "antidegradable channels have zero capacity because of the no-cloning theorem". Is there a formal derivation of the capacity of an antidegradable ...
• 7,123
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### Classical capacity of quantum channel - Holevo quantity vs accessible information of a channel

Just above Eq (20.7) in Mark Wilde's book, while discussing the classical capacity of a quantum channel, he says: These results then suggest that the ultimate classical capacity of the channel is the ...
• 2,997
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### Coherent information is a lower bound of channel capacity. What about coherent information based on Renyi entropies?

It is known that coherent information defined in terms of von Neumann entropies is a lower bound of quantum channel capacity. If we define coherent information in terms of $\alpha$-Renyi entropies, ...
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### Classical capacity of the quantum bitflip channel

I'm looking for references or a derivation for the classical capacity of the quantum bitflip channel, $$\mathcal{N}(\rho) = (1-p)\rho + pX\rho X.$$ Or if this is not known, are some other quantities ...
• 7,123
1 vote
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### Is there a notion of approximate entanglement breaking (EB) channels?

Is there a notion of approximate entanglement breaking (EB) channels? Say, e.g. the output is always close to a separable state. If so, do the nice properties of the EB channels, such as additive ...
• 321
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### Increasing quantum channel capacity

I have a few confusions regarding quantum communication. Please bear with me as I ask what might appear to be basic or naive questions: In the case of classical communication the capacity of wireless ...
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1 vote
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### Is the LOCC-assisted quantum channel capacity of a degradable quantum channel additive?

The LOCC-assisted quantum channel capacity refers to the maximum rate of faithful quantum information transmission through the channel when classical communications and local operations are also ...
156 views

### Twirling of quantum states: Maximally entangled states

I have been reading the paper "Resource theory of unextendibility and non-asymptotic quantum capacity" (https://arxiv.org/pdf/1803.10710.pdf) by Kaur et.al, I have two questions ...
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1 vote
60 views