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Quantum Information Can be Negative
nerdlygirl writes "In a development that would probably even puzzle Claude Shannon,
information can be negative -- at least when the information is quantum.
The discovery, by
Horodecki, Oppenheim, and Winter, appears in the
current edition of the leading journal Nature.
If I tell you negative information, you'll know less. Apparently, researchers hope to use this to gain deeper insights into phenomena such as quantum teleportation and computation, as well as the very structure of the quantum world. More details can be found here and
here
A popular account of the article can be found on Oppenheim's
homepage, and a free version of the article can be found in the arxiv for those of us
without subscriptions to Nature."
This article is not bogus.
The concept of a "quantum eraser" is not a new one. Consider the classic double-slit experiment, where electrons are shot at a double slit and form an interference pattern on a screen which corresponds to the probability distribution of the particle's position. If you were to place detectors so that you knew which slit the particle went through, the interference pattern would disappear-- that is, there would be no uncertainty in the position (because obviously, you know which slit it went through). This is intuitive if you consider the interference pattern to be a probability distribution.
However, if you were to place a 50/50 beam splitter in front of the detectors, the interference pattern would reappear! By destryong the which-path information, the interference pattern (uncertainty) is restored. Bizarre, but true.
Google "quantum eraser" for more info.
Ummm...
...you'll just know far less.
(-2)+(-3)=
-5
Now, if two people containing negative information multiply...
(-2)*(-3)
The result is positive. +6.
This provides a ray of hope for the observation that, "only stupid people are breeding", as noted by the famous song (not that famous, I guess. Cannot recall the song or artist). Eventually, things will come full circle.
FTFA: "It sometimes seems that we become more ignorant after talking to certain individuals. Perhaps they are saying things which are confusing or untrue. Well, after getting negative information, you know less. But not in the same sense as someone who tells you lies are tries to bamboozle you. Remember, that we don't worry about the quality of information (whether it is true or false for example). We just concern ourselves with how much there is. So, if we know less after receiving negative information, the amount of information we have must actually go down. This obviously cannot happen classically, but let me try to explain why it can happen quantumly."
I distinctly remember a lecture by Feynman at Caltech in the early 1980's where he talked about negative information (probability). I am sure I still have notes for it somewhere. Of course, you can never see negative information; any actual measurement has to have positive probility. But it can give quantum interference effects in measured quantities.
Feynman presented it as just a different way of having quantum interference, from negative probability instead of complex amplitudes.
... or, more likely, with his subtraction:
(-2) - (-3) = 1
Geez, don't be so cynical. After I got my PhD from Berkeley, with a dissertation in quantum mechanics, I taught the stuff to graduate students for five years or so. I've published QM papers in PRA and all that, too. So, yeah, I know what they mean. I'm perfectly qualified to review their Nature paper, if it comes to that, and I doubt I'm the only one like this reading /.
I have to say I'm not especially impressed by the work, however. The frisson of defining information as negative emerges ultimately from a semi-deliberate muddling of the distinction between the definition of information in the quantum computing context and information as we use the word in daily life. This is not hard useful scientific discovery so much as the scientific equivalent of making an outrageous pun.
But then I feel similarly about most of what's published in the Bell's Inequality, EPR paradox, quantum tele-whatever field. Getting cynical myself, maybe I am....bah, humbug...grumble...
The trick is that you can use quantum entanglement to have excess unspecified knowledge, which can be converted into specific knowledge. It's like being on a quiz show where you are given a certain number of times you can look up an answer. These bonuses have to count in your total knowledge (I know 100 facts, plus I can look up things twice). If someone tells you something, you get positive information. If you look something up, you get zero information (you trade a bonus lookup for a fact). If you look something up, and you already knew the answer, you get negative information.
Now think about it as if someone else controlled the book. They can tell you things over the phone, and they can cause answers to pop out of the book. If they waste the book on something you actually already knew, your total information goes down, so the information in the transaction is negative.
This paper just provides a hand-waving argument. This maths-free approach, would be swiftly rejected if submitted to the journal where this topic really belongs - IEEE Transactions on Information Theory.
However, I can't wait for the longer technical account. Is it common for Nature to publish exciting results without proof?
BTW, there seems to be a bit of confusion regarding negative entropy and negative information (or rather channel capacity). Entropy is a measure with respect to some coordinates. By changing the scale of the coordinates of a probability distribution, e.g. by changing its variance, you can change its entropy - even making it negative. However, channel capacity is always the same regardless of the coordinates used, as it measures a difference. Its like measuring voltage in a circuit.
Lee Smolin discusses this in Three Roads to Quantum Gravity, as well as its relationship to the Beckenstein Bound.
General Relativity: Space-time tells matter where to go; Matter tells space-time what shape to be.
Here's a straightforward example of negative information.
Suppose there are 3 possible outcomes of an experiment: A, B, and C. A priori you know that A is 98% likely, B is 1% likely and C is 1% likely. Your uncertainty (i.e. entropy) about the outcome is quite low (because you are almost sure that the outcome is A). Now it is revealed that the outcome is not A. Your new probabilities are 50% on B and C. Your new uncertainty about the outcome is now much higher.
Being told that A did not occur thus has negative information because it increases your uncertainty (i.e. entropy) about the outcome.
In order to learn something, you have to make a measurement. Of course, in the quantum world, measuring a system will change it, so you are giving up what you know by measuring. It seems that in negative information situations, you are giving up your certainty in order to measure something, but your aren't learning anything in return. So your net 'gain' of information is negative.
Computers are useless. They can only give you answers.
-- Pablo Picasso
Well, you hit the gist of where pretty much everyone was going. Good example.
I think another example would be religions.
Or the classic Billy Madison line "we are all now stupider for having listened to that" (not sure if I phrased that exactly but it's very close to that).
But you can look at pretty much anything in society and see this being used all the time. Look at how many people think things like Universal Health Care is bad, Schools need local control, taxes are always bad, paying off national debt isn't important, the media is a left wing conspiracy, nuclear power is bad, republicans are good with money , tax cuts jump start the economy etc etc...
(if you found a slant in there, well, sorry those are just the common ones going on today and have caused us to have the officials we have while the continue to screw up on the basis of people believing these things)
People just go with these things, but they would not be able to give you a solid answer as to why, they just hear it so much it sticks. Thats why we have pundents who go on the news and get air time to drive it into peoples heads even more. The more something is said the more it becomes fact even if it has no basis.
Look at myths and urban legends, people here it something so much for so long they just accept them even if common sense would prove it otherwise.
Actually, it has been known for a while that the quantity called quantum conditional entropy (which is defined analogue to the classical conditional entropy) can be negative. The problem was that in the quantum setting, the meaning of this quantity was an open question. This paper gives a nice interpretation that is somewhat analogous to the classical interpretation (using quantum communication instead of classical communication).
A more descriptive title (but more boring for the general public) could have been "Interpretation of Quantum Conditional Entropy".