All Questions
Tagged with quantum-operation channel-capacity
17 questions
5
votes
1
answer
70
views
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 ...
glS♦
- 26.9k
2
votes
0
answers
83
views
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, ...
- 3,284
1
vote
1
answer
63
views
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 ...
- 363
3
votes
0
answers
51
views
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 ...
glS♦
- 26.9k
2
votes
1
answer
114
views
What is the complementary map of a serial concatenation of quantum channels?
I have been studying serial concatenations of quantum channels, i.e. $\mathcal{N}_{A\rightarrow B}=\mathcal{N}_1\circ\mathcal{N}_2=\mathcal{N}_{B'\rightarrow B}\circ\mathcal{N}_{A\rightarrow B'}$. ...
2
votes
0
answers
43
views
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♦
- 26.9k
4
votes
0
answers
167
views
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 ...
3
votes
2
answers
394
views
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 ...
- 3,169
6
votes
1
answer
367
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 ...
8
votes
0
answers
282
views
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 ...
- 419
5
votes
0
answers
182
views
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 ...
- 151
4
votes
0
answers
102
views
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 $\{K_i\}$?
- 391
3
votes
2
answers
344
views
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-...
- 3,169
3
votes
1
answer
659
views
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 ...
- 3,169
7
votes
1
answer
522
views
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) -...
- 681
4
votes
1
answer
85
views
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 ...
10
votes
1
answer
749
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 ...