# Thread: Zero-capacity x 2 = 1 quantum channel

1. ## Zero-capacity x 2 = 1 quantum channel

Originally Posted by arxivblog.com

Quantum communication: when 0 + 0 is not equal to 0

August 5th, 2008 | by KFC |

One of the lesser known cornerstones of modern physics is Claude Shannon’s mathematical theory of communication which he published in 1948 while juggling and unicycling his way around Bell Labs.

Shannon’s theory concerns how a message created at one point in space can be reproduced at another point in space. He calls the conduit for such a process a channel and the limits imposed by the universe on this process the channel capacity.

The capacity of a communications channel is [a] hugely important idea. It tells you, among other things, the rate at which you can send information from one location to another, without loss. If you’ve ever made a phone call, watched television or surfed the internet you’ll have benefited from the work associated with this idea.

In recent years, our ideas about communication have been transformed by the possibility of using quantum particles to carry information. When that happens the strange rules of quantum mechanics govern what can and cannot be sent from one region of space to another. This kind of thinking has has spawned the entirely new fields of quantum communication and quantum computing.

But ask a physicist what the capacity is of a quantum information channel and [they’ll] stare at the floor and shuffle [their] feet. Despite years of trying, nobody has been able to update Shannon’s theory of communication with a quantum version.

Which is why a paper today on the arXiv is so exciting. Graeme Smith at the IBM Watson Research Center in Yorktown Heights NY (a lab that has carried the torch for this problem) and Jon Yard from Los Alamos National Labs have made what looks to be an important breakthrough by calculating that two zero-capacity quantum channels can have a nonzero capacity when used together.

That’s interesting because it indicates that physicists may have been barking up the wrong tree with this problem: perhaps the quantum capacity of a channel does not uniquely specify its ability for transmitting quantum information. And if not, what else is relevant?

That’s going to be a stepping stone to some interesting new thinking in the coming months and years. Betcha!

Ref: arxiv.org/abs/0807.4935: Quantum Communication With Zero-Capacity Channels
Uh huh. So it's about having 2 of these things, or a zero-capacity quantum channel can have a non-zero-capacity if it gets 'cloned'. Interesting; make two edges into a usable gap between, type of thing.

2. In contrast, the problem of
noiseless quantum communication with a noisy quantum
channel is one of the simplest and most natural com-
munication tasks imaginable in a quantum mechanical
context. Our findings uncover a level of complexity in
this simple problem that had not been anticipated and
point towards several fundamentally new questions about
information and communication in the physical world.
They couldn't even isolate Gravity Prope-B from gravitational perturbations by solar flares. How do they expect to isolate quantum-streams from outside interference and maintain valid data transfer? Unless a miraculous alloy allows for amazing containment this will never be plausible.

The only potential I can see for this is local computation.

Where an external detection would alter an internal electrical field to be directly opposite to the external field. Where the actual computation would exist inside an object shielded from the direct effects of the internal field...or is somehow accounted for.

In either case the throughput would only be equal to information transfer speed exported outside of the containment shields.

3. Originally Posted by Graeme Smith & Jon Yard
Although our construction involves systems of unbounded dimension, one can show that any Horodecki channel with positive private capacity can be combined with a finite symmetric channel to give positive quantum capacity. In particular, there is a positive-private-capacity Horodecki channel acting on a four-level system [19].
This channel gives positive quantum capacity when combined with a small symmetric channel – a 50% erasure channel $N_e$ with a four-level input which half of the time delivers the input state to the output, otherwise telling the receiver that an erasure has occurred. The parallel combination of these channels has a quantum capacity greater than 0.01 (see Appendix I).

We find this ‘superactivation’ to be a startling effect. One would think that the question, “can this communication link transmit any information?” would have a straightforward answer. However, with quantum data, the answer may well be “it depends on the context”.

Taken separately, Horodecki and symmetric channels are useless for transmitting quantum information, albeit for entirely different reasons. Nonetheless, each channel has the potential to “activate” the other, effectively canceling the other’s reason for having no capacity. We know of no analog of this effect in the classical theory.

Perhaps each channel transfers some different, but complementary kind of quantum information. If so, can these kinds of information be quantified in an operationally meaningful way? Are there other pairs of zero-capacity channels displaying this effect? Are there triples? Does the private capacity also display superactivation? What new insights does this yield for computing the quantum capacity in general?

--Quantum Communication With Zero-Capacity Channels
hmm.

4. Originally Posted by Vkothii
hmm.
What is the uniqueness of any given channel?

5. Sorry, you might need to qualify the question? What do you mean by "uniqueness"?
There are two channels - each has zero capacity, but together they 'activate' each other.

6. Originally Posted by Vkothii
Sorry, you might need to qualify the question? What do you mean by "uniqueness"?
There are two channels - each has zero capacity, but together they 'activate' each other.
I might be confusing the issue, but the article posted was about use Quantum mechanics in communication. Also it implied its use in quantum processing. Meaning the processor would have to have multiple different channel sets to operate binary, even if it was only two.

What uniqueness exists between the two sets that would allow the channels to not interact with each other?

7. All I can suggest is: read the article.

The intro article from arxivblog.com mentions QP, but it's about a particular kind of channel; the paper (on arxiv) is about communications not about processing.

8. Here's the thing with this supposedly 'new' quantum information channel.

Because of entanglement, quantum information is fundamentally different to classical, the signal/noise ratio is not necessarily a limit for QI, as for a classical channel. This is what these researchers were looking at.

In this case, with two different kinds of channels - that have different reasons for having zero capacity, there's still a correlation if both outputs are measured jointly. A necessary condition is that one channel not have separable states; or this appears to be tied to some kind of separability principle (maybe).

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