Uncertainty in the presence of quantum memory

[msumm21]

I am looking at the paper "The uncertainty principle in the presence of quantum memory" by Berta and others. It states that if Bob maximally entangles a particle P with a quantum memory M then he can beat the bound of the uncertainty principle on P. The argument is that, if Bob gives P to Alice and she measures some property then Bob can determine her result by performing the same measurement on M, all she has to tell him is what she measured, but not the results of the measurement. He can determine the result from M.

I'm not questioning the last statement above, but I'm having trouble seeing how this beats the bound of the uncertainty principle, or even relates to the uncertainty principle. As I understood it the uncertainty principle gives a lower bound on the product of the standard deviation of two observables -- it limits how well you can SIMULTANEOUSLY know the value of both observables. In this case, all I see is Bob being able to determine the value of one observable, not two.

Anyone know why they are saying that Bob can beat the bound of the uncertainty principle. An example using spin entangled electrons might be good if it is sufficient. Are they saying Bob can simultaneously determine the spin about two different axes? All I see is him being able to determine the spin about one or the other.

 

[DrChinese]

Link to the paper:

http://arxiv.org/abs/0909.0950

 

[DrChinese]

I have to admit that after reviewing their paper, I really am not sure what they are asserting nor how it beats the HUP. I certainly don't see how a quantum memory changes anything.

 

[Demystifier]

I certainly don't see how a quantum memory changes anything.

Can one, at least, explain what quantum memory is? I don't understand even that.

 

[msumm21]

I wonder if the problem is simply that the example and explanation they provide early in the paper is not good / oversimplified -- there are quite a few links out there if you Google for the title of the paper and they all restate the conclusion that the uncertainty principle is violated and none of them I found question it. I will try to look in more detail in the arxiv link above since the original paper I had did not go into the details like that one.

 

[unusualname]

afaics they are talking about an "entropic uncertainty principle" rather than a violation of the HUP in its strict form. The theory has been verified according to this paper:

http://arxiv.org/abs/1012.0332 "Experimental investigation of the uncertainty principle in the presence of quantum memory"

see Baez's blog article for more info http://johncarlosbaez.wordpress.com/2010/10/19/entropy-and-uncertainty/

and further discussions http://www.alphagalileo.org/ViewItem.aspx?ItemId=82019&CultureCode=en and here