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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 ...
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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 ...
forky40's user avatar
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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 ...
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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 ...
forky40's user avatar
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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 ...
Shadumu's user avatar
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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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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 ...
Josu Etxezarreta Martinez's user avatar
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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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Optimal one-shot input for $\mathcal{N}^{\otimes n}$ and optimal one-shot input for $\mathcal{N}^{\otimes k}$ where $k< n$?

Suppose I have a classical or quantum channel $\mathcal{N}$. I wish to use it for some communication task in the one-shot setting i.e. where I have $n$ i.i.d. copies of $\mathcal{N}$ denoted by $\...
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Why is the quantum capacity quantified by the coherent information?

Most types channel capacities associated to a given quantum channel are quantified using mutual informations (sometimes classical, sometimes quantum, sometimes regularised), which is not surprising ...
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How do Hashing bound, entanglement purification, and QECC, relate to each other?

Could anyone elaborate on how these three concepts relate to each other? According to Charlie Bennett's original paper BDSW96, EPP is equivalent to QEC in the sense that both have the hashing bound as ...
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Is it well known classical communication over a quantum channel at a rate below its classical channel capacity can have an exponentially small error?

Classical channel capacity $C(\mathcal N)$ of a quantum channel $\mathcal N$ is defined to be a rate below which any classical communication can succeed with an arbitrarily small error. Specifically, ...
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Does proving $Q^{(1)}(\mathcal{N}\otimes\mathcal{N})=Q^{(1)}(\mathcal{N})+Q^{(1)}(\mathcal{N})$ imply additivity for arbitrary $n$?

I have been reading the proofs that are usually presented in order to proof the additivity of degradable and conjugate degradable channels, and they usually present that the coherent information is ...
Josu Etxezarreta Martinez's user avatar
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What is the complementary map of a serial concatenation of quantum channels?

I have been studying serial concatenations of quantum channels, i.e. $\mathcal{N}_{A\rightarrow B}=\mathcal{N}_1\circ\mathcal{N}_2=\mathcal{N}_{B'\rightarrow B}\circ\mathcal{N}_{A\rightarrow B'}$. ...
Josu Etxezarreta Martinez's user avatar
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What are channels for which entanglement at the encoder improves communication rates?

In discussing the classical capacity of quantum channels, as e.g. mentioned in Wilde's book (see section 20.6), it is possible that using entanglement at the encoder stage can improve transmission ...
glS's user avatar
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Additivity of degradable and anti-degradable quantum capacities

It is known that for degradable channels $\mathcal{N}$ and $\mathcal{M}$, the single-letter quantum capacity is aditive (Potential Capacities of Quantum Channels), i.e. \begin{equation} Q^{(1)}(\...
Josu Etxezarreta Martinez's user avatar
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2 answers
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What is meant by a "single-letter" expression for the quantum channel capacity?

The quantity $Q_1(\Phi) = max_{\rho} I_C(\rho, \Phi)$, is called one-letter capacity of channel $\Phi$. I want to know, what is meant by the term "single-letter" capacity here, often used in ...
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What is the quantum capacity of the combined amplitude and phase damping channel?

Quantum capacity for the amplitude damping channel and the pure dephasing channel have closed-form formulas as it can be seen in section 24.7.2 of From Classical to Quantum Shannon Theory. However, I ...
Josu Etxezarreta Martinez's user avatar
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Optimality of teleportation for entanglement-assisted quantum channel coding

Setting: Consider a quantum channel $N_{A\rightarrow B}$ between Alice and Bob. Let Alice and Bob also share arbitrary amounts of entanglement assistance through the state $\phi_{A_EB_E}$ (these can ...
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Bounding diamond norm distance using probability of error in transmission of classical information

Let us consider an encode, noisy channel and a decoder such that classical messages $m\in\mathcal{M}$ can be transmitted with some small error. That is, for a message $m$ that is sent by Alice, Bob ...
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What was the meaning of Lossless Quantum compression?

I was reading few questions regarding lossless quantum compression on stack exchange, then out of curiosity, I started reading this article. After reading I end up being confused about what does ...
User1086's user avatar
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1 answer
317 views

Quantum capacity for serial composition of quantum channels

Recently, I have been working with quantum channel capacity for quantum-quantum channels and I was wondering if there exist some results for channel compositions. Specifically, I have been looking for ...
Josu Etxezarreta Martinez's user avatar
6 votes
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What are examples of zero capacity quantum channels with Choi rank less than $d$?

All the currently known examples of quantum channels with zero quantum capacity are either PPT or anti-degradable. These notions can be conveniently defined in terms of the Choi matrix of the given ...
mathwizard's user avatar
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Coherent Information and Entanglement Breaking channels

The book by John Watrous, "The Theory of Quantum Information" is an exciting read for anyone wanting to research quantum information theory. The following question presumes some background ...
K Gautam Shenoy's user avatar
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How to compute the capacity of a quantum channel from its Kraus operators?

Is there a working rule to compute the capacity of a quantum channel described by a set of Kraus operators $\{K_i\}$?
Rob's user avatar
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Why does entanglement not increase the classical capacity of a channel?

In a recent paper, the authors quote an older work of Bennett, Shor and others and make the following statement While entanglement assistance can increase achievable rates for classical point-to-...
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What exactly is the relation between the Holevo quantity and the mutual information?

On this page, it is stated that the Holevo quantity is an upper bound to the accessible information of a quantum state. In the scenario where Alice encodes classical information into a quantum state ...
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Understanding classical vs. quantum channel capacities

The classical channel capacity ($C_{ea}$) and the quantum channel capacity ($Q$) as defined here (eqs. 1 and 2) are given by \begin{equation} C_{ea} = \text{sup}_{\rho} \Big[S(\rho) + S(\Phi_t \rho) -...
Tobias Fritzn's user avatar
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1 answer
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Experimental Realization of Superactivation of Quantum Capacity

The superactivation of quantum capacity is an effect that some quantum channels present such that is two of those channels with zero capacity are combined, a non-zero channel capacity can be achieved ...
Josu Etxezarreta Martinez's user avatar
9 votes
1 answer
620 views

Advances in Quantum Channel Capacity

I have been reading about the Quantum Channel Capacity and it seems to be an open problem to find such capacity in general. Quantum capacity is the highest rate at which quantum information can be ...
Josu Etxezarreta Martinez's user avatar