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.
Questions tagged [channel-capacity]
35 questions
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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 communicated over many independent uses of a noisy…
Josu Etxezarreta Martinez
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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 channel:
A channel is said to be PPT if its Choi…
mathwizard
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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) - S(\rho,t)\Big],
\end{equation}
and…
Tobias Fritzn
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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 results on what happens to quantum channel…
Josu Etxezarreta Martinez
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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 respect to all ensembles $\eta\equiv (\eta_b)$, with…
glS
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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 additive for two channel uses, i.e.…
Josu Etxezarreta Martinez
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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 information theory? The term can be found for example in…
User101
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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 covered in the book, which I will do my best to…
K Gautam Shenoy
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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
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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 for the combined channel. This is obviously an…
Josu Etxezarreta Martinez
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The relationship between QEC decoding error and capacity
Consider a fixed qubit channel $\mathcal{N}$ and some QECC that prepares a logical state $|\psi_L\rangle$ of $k$ logical qubits using $n$ physical qubits. After transmitting data through the channels, the probability of correctly decoding (and thus…
forky40
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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, given a quantum channel $\mathcal N$ and any…
Doris
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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 am unsure if there exist such a result for the…
Josu Etxezarreta Martinez
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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-point channels in the zero-error and one-shot…
user1936752
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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 and sends it to Bob, the accessible information is…
user1936752
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