Talk:Quantum channel

message: Near the top of this article, it states: "We will assume for the moment that all state spaces of the systems considered, classical or quantum, are finite dimensional."  However, later on in the CB norm section it says:
"To make the operator norm even a more undesirable candidate, the quantity
:\| \Phi \otimes I_n \|
may increase without bound as n \rightarrow \infty."
This claim is only true in infinite-dimensional spaces (that is, all linear maps on finite-dimensional spaces are completely bounded). Either this comment should be removed or at least reworded accordingly. JokeySmurf (talk) 19:42, 28 February 2009 (UTC)
thread_title: Unbounded CB norm

message: I'm not sure if this is already there or not, but could a section on the forms a quantum-communication device could take (EG twin photons, electrons) be created? UNIT A4B1 (talk) 20:47, 28 October 2009 (UTC)
thread_title:  Forms of communication devices 

message: I just made it clear in the leader paragraph that a quantum channel is just a quantum operation viewed as a communication channel.  This should be emphasized more in the text.  I don't think that this article should be merged with the one on quantum operations, but we should make sure that this articles doesn't repeat the description of quantum operation unnecessarily.  —Preceding unsigned comment added by Njerseyguy (talk • contribs) 14:43, 23 March 2010 (UTC)
thread_title:  Link to quantum operation 

message: Some things that could be improved:
* The section on instrument should be harmonized with quantum instrument, which needs expansion.
* The section on effects should link to an article on quantum effect or someting similar. Some authors seem to use 'effect' as a synonym for 'bra', others seem to use it as a synonym for a conjugate of a mixed state, some seem to imply its an observable ... all this could be clarified.
* The section treating classical information has several minor errors, and is otherwise quite unsatisfying.  My understanding is that classical info is best described by forbenius algebras, but this would need to be fully developed,
* The article POVM is a walking disaster zone, and needs a total overhaul.  Linking to that form this is bound to lead to confusion.
All the above reflects on this article .. User:Linas (talk) 05:49, 30 November 2013 (UTC)
thread_title: TODO list

message: This article doesn't appear to mention the noise of a quantum channel. But I've seen several articles that refer to "noisy quantum channels" and the correction of such noise (see Quantum error correction and Entanglement distillation and see also Fidelity of quantum states). The specific article on Quantum noise appears to refer to measurements (the classical domain), not superpositions.
The present article needs an explanation of "noisy quantum channels". Are quantum states inherently noisy (I think the answer is no, since uncertainty/nondeterminism is only significant when there is a measurement)? Then, how can quantum channels possibly be noisy? In exactly what basic way do the measurements required for communications generate noise? Can a classical channel be used to send a mixed quantum state from one macroscopic location to another (I think the answer is no)? This article should answer these questions and more, not just give mathematics, IMO. David Spector (talk) 19:35, 23 November 2019 (UTC)
replies: text: I would say the whole article is about noisy quantum channels, since all channels that are not unitary describe some sort of noise or error process. The "ideal quantum channel" is the "identity channel" that sends and quantum state |\psi\rangle unchanged from the sender (Alice) to the receiver (Bob): \Phi_{id}(\rho) = \rho. (the unitary channel and the isometry channel \Phi_{V}(\rho) = V\rho V^\dagger, where V is a unitary or isometry are also noise-free channels. All other completely-positive maps as discussed in the article describe information transmission in the presence of some noise process (=coupling to the environment). I think it would be useful to explain this. All error processes arise from coupling to some other system (="environment") and a basic tenet of quantum mechanics is that if we include all the systems making up the environment, then the total evolution is unitary, i.e., the quantum channel from A to B+environment is noise-free. The "noise" arises from the fact that the environment is not accessible to B ("has to be traced out", in math terminology) which leads to the completely positive map mentioned in the 2nd sentence. The noisyness of the channels is reflected in the fact that their quantum capacity is not maximal: the identity channel for a qubit has one qubit capacity (obviously); all the noisy qubit channels have a smaller quantum capacity. --Qcomp (talk) 00:33, 25 November 2019 (UTC)
thread_title:  Quantum channel noise