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."

Affects black holes!

[sconeu]

Since a black hole's entropy is directly proportional to it's information content, this, if true, would have an effect on black holes.

If I recall correctly (and I may not -- my physics isn't what it used to be), the amount of information contained by a black hole is directly proportional to its surface area -- specifically, I believe that the total number of bits contained is equal to 1/4 of its surface area as measured in Planck units.

Now, if information can be negative, that would provide another method of shrinking a black hole, in addition to Hawking radiation.

Lao Tzu figured this out millenia ago

[benna]

He wrote, "The scholar learns something every day, the man of tao unlearns something every day, until he gets back to non-doing."

Re:Ouch!

[glowworm]

IANAQM (I am not a quantum mechanic) but lets say you know a set of information about something and someone else knows a different set of information about the same thing and together these sets of information add up to more information than is actually needed to describe that something then it stands to reason there is also a third set of information that is negative, that is, it describes what you shouldn't know about something in order to be able to describe it properly!

The phone digit analogy used in Oppenheim's homepage is pretty good. If Bob knows 15 digits of Alices 10 digit phone number then Alice needs to tell Bob that 5 digits with a certain configuration are not needed - and in doing so makes future communications about telephone numbers easier!

Escort Web Pages

[pyrrhonist]

From the author's homepage:

This web page has about 2500 English words, so it is

convoying more information (although I can't speak to the quality of that information).
But English is a very silly language...

That's not really how you use that word. His spell checker must have provided negative information.

Re:Implication on Information Theory and Probabili

[Chrispy1000000 the 2]

Well, there are particles in QM that have to be roatated a full 720 degrees to complete a full rotation.

Couldn't a probability of 2.0 be taken to mean that two atoms are going to be created using one atoms complete energy to create antimatter. One atom being the antimatter, and one being normal matter. When these two pieces of information meet, they anhilate each other and all the information about each other if their informations are completely equal.

I could be completely and utterly wrong, but I think that's what happens when they make antimatter.

Re:I think Feynman thought of this first

[khallow]

Nope. Even though Feynman had negative probabilities, the information was still positive. He used negative AND positive probabilities, and the net effect would still lead to positive information (if you added everything up). The authors say that information is due to entanglement. Feynman was only talking about single particles going through slits, so there could be no entanglement in his example (entanglement requires two particles).

Two things. First, can we observe negative information? Sounds to me like we still just observe nonnegative information. That hasn't changed. Appears to me that negative information is virtual which is quite in line with Feynman's points.

Second, single particles going through slits? Sounds like self entanglement, ie, the states of the particle going through two slits considered seperately are entangled with one another.

Re:Implication on Information Theory and Probabili

[chemistry]

Since you have defined a system with at most two states because you are using log2. Why not extend this to Shannons Entropy and say:

H = -sum(plog2p)

Now one method that I have recently used to help solve a data-mining/similarty problem in chemistry is to use an Information Gain metric to select a set of features that are useful in searching for compounds with similar properties to a query set:

I = H1 - H2;

In essnece I want to select features from the query subset the show a low Entropy in H2 but a high Entrpy in H1. Thus creating a net gain in information.

Now what if we plug your -2 in for H2? Net negative information gain?

Not really sure what the implications of this are but it is interesting non-the-less.

Re:Bad Analogy

[Lil-Bondy]

so, therefor, if we know negative information, it leads to (the possibility of*) knowing more? *could we perhaps die or something before we learnt the resulting information

Re:Bad Analogy

[bentcd]

I think this may be close, but inaccurate. It doesn't reduce the psychic's information (unless he didn't know he was a psychic), but rather the information in the system.
Let's say there exists a person, Alfred, who is a psychic. Nobody knows he is a psychic (except perhaps himself), but he is. He is approached by Bill, who has Â$55 in his wallet. Alfred senses the $55. There is now information in the system that "Alfred is a psychic" because if he tells Bill about the $55 without Bill showing them to him first, Bill will know that Alfred is a psychic.
Before this can happen, however, Bill shows Alfred the contents of his wallet. If Alfred now tells Bill about the $55, Bill will not be impressed and will have no reason to believe that Alfred is a psychic. So by opening his wallet, Bill removed information from the system. The system in this case being Alfred and Bill.
(Of course, they really should be handling this experiment in a proper, scientific manner before anyone went out and pronounced Alfred a psychic, but the point remains the same.)