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


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 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 she’ll stare at the floor and shuffle her 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

25 Responses to “Quantum communication: when 0 + 0 is not equal to 0”

  1. spispopd says:

    Page 582 of my 2004 printing of “Quantum Computation and Quantum information” by Nielsen and Chuang (ISBN 0 521 63503 9), Figure 12.11 has the following text:

    “Classically, if we have two very noisy channels of zero capacity running side by side, then the combined channel has zero capacity to send information. Quantum mechanically, reversing one of the zero capacity channels can actually allow us to send information!”

    Soo…. what’s the “meat” here? I’m assuming this isn’t a rediscovery, haven’t read the preprint yet :-)

  2. spispopd says:

    Don’t get me wrong, it’s very cool and weird regardless.

  3. SpazmodeusG says:

    It seems it works as well on Horodecki channels with 0 negative information capacity equally as well as it does on channels with 0 positive information capacity. ;)

  4. Markus says:

    Think about the digital world for a minute; two lines can send 4 possible combinations of data, one line can send 2 possible combinations of data, and now quantum communications teach us that zero lines can send 1 possible combination of data (effectively none). But two of those non-existent lines can send two possible combinations of data! Clearly this teaches us that “no” data is the same as .5 data. :p

    Seriously, though. Couldn’t this be useful for having delay-free phone conversations over oceans, using quantum “lines” to carry binary data?

  5. peter says:

    a information negative channel = a state..
    There are no endpoints only combination or sub states from an origin state; in that respect some call it multiverse; other quantum foam.
    Also forget the idea of sending particles, likke matter; matter is pinpointed energey; where energy is only QM information difference.
    On which time is only a combined state solution, what is not combined can have different solutions (until combined).
    The capacity of this system is unlimited; dough its our percepted (time) solution that seams limited (but is not). So here my greetings to you and welcome to a QM multiverse

  6. Paul says:

    Interesting, but is this relevant. Do qauntum particles exist for long enough to travel anywhere. What is a quantum channel?

  7. Phil Lighten says:

    I’m a mathematician well versed in Shannon Information Theory, but unfamiliar with quantum theory and quantum computing. Without recommending I complete a Physics PhD program, can you recommend an insightful article available online to bridge the quantum gap, for people like me?

  8. Albert says:

    Wow.. this is one of the most amazing discoveries of the past century.. and it’s not theirs haha.

  9. xyz says:

    I dont know quantum info. theory, but in communications its always true that two zero capacity channel when used together can have capacity of 1-bit as there is 1-bit information in the fact that which channel is used.

  10. Matt L says:

    Correct me if I’m wrong, but doesn’t Shannon’s theorem define channel capacity by signal switching rate and bandwidth? Now, switching rate could make sense for a quantum channel, but how is the bandwidth of a quantum channel measured?

  11. Phil: Quantum theory in general http://www.ipod.org.uk/reality/index.asp here

    David Deutsch ( mr quantum algorithm) gives video explanations of quantum information

    Quantum computing is basically quantum information right now because there are approx 5 (count them!) algorithms available.

    Paul, all particles have a quantum nature so yes, there are quantum particles that exist for long enough to travel and transmit information. Furthermore this has been done experimentally over distances of kilometres using photons. it’s harder to get photons to do quantum tricks but when you get them into that mode they’re dead good for transmitting information.

    Matt L, there’s special formulations of Shannon’s stuff for quantum purposes. I don’t understand them though for I am a lowly solid state physicist.

  12. Marti says:

    Does this have ramifications for faster than light communications? Sounds so to me, and I’m a very lay person on these matters.

  13. docwatson says:

    It seems that once this is thought through more, teleportation and time travel will be possible.

  14. Hassan Bin Sober says:

    Is this the psychic 411 channeling I’ve heard so much about? Physicist, heal thy self!

  15. erichansa says:

    A very exciting branch of physics that can innovate technology in the near future.

  16. David says:

    Very interesting. I read about channels before… That’s why I’m very pleased with the arXiv paper. Great job!


  17. G says:


    You may want to look at Bennett and Shor’s 1998 review of quantum information theory. It was in IEEE IT, in a special issue commemorating the 50th anniversary of Shannon’s original paper. It’s not on the arXiv, but maybe you have IEEE Trans. Info. Theory available through the library.


  18. Symphony Sid says:

    “The single biggest problem in communication is the illusion that it has taken place”

    George Bernard Shaw

  19. Tanath says:

    “Wow.. this is one of the most amazing discoveries of the past century..”

    In what way is this amazing? This is how quantum theory works, no?

  20. Howard Barnum says:


    Nice observation that Smith-Yard seems related to this Nielsen and Chuang example, but in my opinion a closer examination shows that they’re quite different.

    The difference is that in the Nielsen and Chuang situation, using a zero-capacity channel from Alice to Bob, and another one (which can in fact be an identical channel except with sender and receiver reversed) from Bob to Alice, Alice and Bob can cooperate to transfer quantum information from Alice to Bob at a nonzero rate. In the Smith-Yard situation, both zero-capacity channels run from Alice to Bob, and by using them in parallel, a positive rate of Alice-to-Bob transmission of quantum information is achieved. So there are similarities, but Smith and Yard definitely show something different.

    The two channels used in the Nielsen-Chuang example can be identical, whereas (by the definition of capcity), they *must* be different for the Smith-Yard phenomenon.

    But perhaps the most significant difference is that the backwards channel is used entirely to send *classical* information in the Nielsen-Chuang example. Using an auxiliary channel solely to send classical information from sender to receiver cannot, however, increase the quantum information rate of a quantum channel; Smith and Yard’s auxiliary channel, unlike the back-channel in the Nielsen-Chuang example, helps because it is used for something other than just sending classical information.



  21. Howard Barnum says:

    NB—my previous post is intended as a reply to spispod’s post (the first post regarding the initial KFC post on the Smith-Yard article), not as a reply to the post immediately preceding it…

  22. Erwin's Cat says:

    Go to xxx.lanl.gov and search for the keyword “parrondo” also you can try “quantum” and “parrondo.” You will see papers that say you can combine losing games and yet they win, both in classical and quantum contexts. The Smith and Yard paper seems to have unearthed another Parrondo effect and it seems there is scope for examining it from a game-theoretic viewpoint.

  23. [...] when you tell me that with quantum theory you can take two channels that have zero capacity, and use them together to create a non-zero capacity chann…… Sigh. So zero plus zero equals a positive value? Back to the [...]

  24. Sorry, but what is a quantum channel?

  25. Basisrente says:

    Interesting, but relevant?