In quantum channels, zero plus zero can equal non-zero
October 6th, 2008 By Lisa Zyga
Two quantum channels that have zero capacity when used individually (orange and yellow figures) can enable communication when used together (green figure). Image credit: Graeme Smith and Jon Yard. ©2008 Science.
(PhysOrg.com) -- Physicists have discovered a strange characteristic of quantum communication channels. If two quantum channels each have a transmission capacity of zero, they may still have a nonzero capacity when used together. This effect, which has no classical counterpart, reveals a new complexity in the fundamental nature of quantum communication.
The coauthors of the study, Graeme Smith of the IBM T.J. Watson Research Center in Yorktown Heights, New York, and Jon Yard of Los Alamos National Laboratory in Los Alamos, New Mexico, have published their research in a recent issue of Science.
Smith and Yard explain that one of the most important challenges in designing communication networks of any kind is taking steps to correct for noise. By decreasing noise levels in communication channels, developers can increase channel capacity, which is defined as the number of bits (or qubits, in quantum channels) that one channel can transmit. For a channel with zero capacity, no bits are transmitted.
For several decades, scientists have used a well-known formula developed by Claude Shannon in 1948 for developing error-correction techniques in classical communication channels. This formula guides the design of modern communication schemes used in cell phones, the Internet, and deep-space communication. In this classical formula, capacity is additive: when two channels are used simultaneously to transmit data, the capacities of the channels are added to obtain the total capacity.
But even today, physicists don’t understand quantum communication nearly as well as the classical kind. In the current study, Smith and Yard show that some pairs of zero-capacity channels can have a positive quantum capacity when used together. As the physicists explain, that would be like two cut telephone cables being able to transmit data when used together. Their finding shows two things: that quantum capacity is not additive like classical capacity, and that the quantum capacity of a single channel does not completely specify its capability for transmitting quantum information.
“To me, the strange thing is that you have these two things that you would have thought were useless – I mean, you'd usually think that a zero-capacity channel was good for nothing – and when you put them together, somehow there's a kind of synergy and they develop a very quantifiable value,” Smith told PhysOrg.com. “This doesn't happen when you work with classical channels, and since my intuition was based on that case, I was really surprised when it happened here.”
The scientists account for this “superactivation” property by explaining that quantum channels have two different kinds of capacity. “Private capacity” is the rate at which a channel can send secure classical data. “Assisted capacity” is the transmission rate in which multiple symmetric channels can assist a given channel in sending quantum data.
As the physicists demonstrated, a channel’s assisted capacity is always at least half as large as its private capacity. As an example of superactivation, the scientists showed that combining a private “Horodecki” channel and a symmetric channel (each with zero capacity) can give a quantum capacity of more than 0.01 qubits per channel. It’s as if each channel has the potential to activate the other, canceling the other’s reason for having zero capacity.
“The effect has something to do with the existence of something called ‘private Horodecki channels,’” Smith said. “These channels have the weird property that, even though they're too noisy to allow quantum communication, somehow they still allow you to send classical messages that are completely private. Roughly speaking, we figured out that there's this second kind of channel – a symmetric channel – that also can't send any quantum messages on its own, but can be used to transform the private classical communication of the Horodecki channel into noiseless quantum communication.”
Superactivation raises some interesting questions about the nature of communication. For instance, you would think that the question “can this communication link transmit any information?” would have a straightforward answer. However, with quantum data, the answer may be that it depends on the context. If identifying a quantum channel’s capacity is not as straightforward as previously thought, then new ideas will be needed for designing error-correction techniques in quantum channels.
These results lead to other questions, such as what the effect of combing three channels might be. The overall complexity of quantum channel capacity will keep the researchers investigating the fundamental characteristics of communication in the physical world.
“First, I'd like to understand the role of privacy in this whole thing, and whether it's necessary to achieve a superactivation,” Smith said. “In the longer term, I'd like to see if we can turn the improved understanding of quantum error correction that comes out of this into some practical ways to reduce noise in prototypes for quantum computers.”
More information: Smith, Graeme and Yard, Jon. “Quantum Communication with Zero-Capacity Channels.” Science, 26 September 2008, Vol. 321. 10.1126/science.1164382.
Copyright 2008 PhysOrg.com.
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Apr 13, 2009 |
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Makes my head hurt...
Although I'm not sure about the rest of the article, the above statement is simply not true. This is because when you combine two channels the signal in the channels is correlated and the noise is uncorrelated. Since uncorrelated level (the noise) adds orthogonally and correlated level (the signal) adds linearly, you get a total increase in SNR when you combine the channels. Also, remember that the Shannon-Hartley equation uses power SNR rather than level SNR as is common technique, so the noise (uncorrelated power) adds linearly and signal (correlated power) adds by its square. And finally, remember that increasing the bandwidth increases the noise power proportionally--because you've widened the receiver's window in the frequency domain.
With all that said we can get down to business: To combine two identical channels into one channel, you take the Shannon-Hartley equation for one channel and double the bandwidth, quadruple the signal power (don't worry, energy is conserved--I just don't have room to get into what this means in the context of the Shannon-Hartley equation; it should be sufficient to say that we've simply added two correlated and identical levels, which effectively quadruples the signal power), and double the noise power.
For example, if the SNR is 10 (shown here as a power ratio, not dB), then doubling the channel increases the channel capacity by a factor of 2.539 . And if the SNR in each channel is only 2 (power ratio), then using two such channels as if they are one channel increases the channel capacity by a factor of 2.93 .
This is one of the many reasons UWB (ultra-wideband) is so cool. Another is that, unlike narrow-band systems, the receiver's window can far more easily be narrowed in the time domain (by reducing the signal duty cycle), which let's the receiver gather the same signal power but proportionally less noise power. The end effect is that using UWB in any given region increases the total channel capacity of that region by, typically, 1000-fold, providing that many more channels. Also UWB gives amazingly precise synthetic aperture radar and position tracking.
-fleem
1. We all feel we do not understand something unless we have some analogy of it. For example, we explain electron orbits to children by describing them as planets orbiting a sun. The problem here, is that ALL of our analogies MUST be classical because our minds are 100% classical. Therefore there will be NO analogies for QM, because classical mechanics is simply a crude estimation of a subset of QM (the average behavior of many low-energy systems). Therefore NOBODY "understands" QM in that way.
2. A closed system is allowed to break any physical law it likes (conservation of energy, etc.) WHILE it remains closed, as long as all laws are obeyed once that closed system again "opens" (i.e. we interact with it, trade information with it, observe it, etc.).
Once you warm-up to the above two statements things get a little easier, I think. The foundation of QM is really laughably simple.
-fleem
But isn't you talking about 'macro' systems here?
And they about QM.
" Their finding shows two things: that quantum capacity is not additive like classical capacity, and that the quantum capacity of a single channel does not completely specify its capability for transmitting quantum information. "
Also you wrote that all of our analogies must be classical?
Nah.
Check general and special relativity and Einsteins reasoning.
We need to get away from the classical interpretations instead.
And construct new that works.
And so we do, at all times, little by little.
That's the scientific approach.
Not believing that the sun goes around our flat earth.
We did believe that some time ago:)
Propose that this be called the Bush-Cheney effect
1. We all feel we do not understand something unless we have some analogy of it. For example, we explain electron orbits to children by describing them as planets orbiting a sun. The problem here, is that ALL of our analogies MUST be classical because our minds are 100% classical. Therefore there will be NO analogies for QM, because classical mechanics is simply a crude estimation of a subset of QM (the average behavior of many low-energy systems). Therefore NOBODY "understands" QM in that way."
I call BS, you can understand quantum mechanics by understanding the universe in terms of being one whole unified flat surface, and "objects" as merely bumps and emergent structures from the volume of spacetime, i.e. things only appear disconnected, when they are everywhere connected.
This comes from the western idea of individualism and objectivism. See: Metaphors we live by, by George Lakoff, and other work in cognitive sciences showing that reality is holistic and can't be understood in terms of reducable to just "atomized" blocks. You need both to explain the universe.
You can explain electrons through smears and merges with the surface of spacetime itself, like ball of wax melting into the surface of spacetime and being in many places at once simultaneously.