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## Main Question or Discussion Point

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.

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.