## Heisenberg’s uncertainty principle and quantum memories;

There is a very good post here that tries to explain a paper that was published by scientists from LMU and the ETH in Zurich, in which they argue that **we can do** measurements in quantum physics systems that “violate” the uncertainty principle that Heisenberg has introduced.

## Heisenberg’s uncertainty principle

About the uncertainty principle I will give an example which is wrong as an explanation of the principle¹, but I hope you will understand what uncertainty means;

Assume that we have a dark room and in the room there is one ball of unknown color. We want to learn where excactly the ball² is located in the room and what color it is. For this purpose we have only two choices; there are two agents that we can use to measure, one agent (“cat”), can tell you only about the position of the ball but in order to find the position it needs to change the color of the ball. The second agent (“dog”), it can tell you about the color of the ball but in-order to do that it relocates the ball.

This way you cannot know the position and the color of the ball in a specific point of time; If you use the cat and the cat returns saying, that the ball is under the center of the table then you know that most possible the ball color has changed. If you use the dog and the dog returns saying, that the ball is blue then you know that the position of the ball has changed.

Two points that you need to know here;

First, you can use the dog after the cat (or the other way around) and after the last measurement you know exactly were the ball is and what is the color. The problem of the uncertainty is that **you don’t know what the initial position and color of the ball was. **Using one of the two agents you introduce “uncertainty” in either the position or the color of the ball, depending what you use first. Of course you cannot use the two agents together (cat and dogs don’t work together :-)) so you cannot know where the ball is and what color it has in the same point of time.

Second, let’s “quantify” our example; When you ask the cat to measure the position of the ball, the cat will ask you; “how accurate you want the results?” if you respond that you want the exact position of the ball then the cat will say that it can repaint the ball to any possible color. That means that after the exact measurement of the position of the ball the uncertainty of the color is huge; you do not have any clue about the color! If you respond to the cat that you want to know the position within an error of 1 meter, let’s say, then the cat (because it does not have to do much work!) will respond; “OK, then I will repaint the ball in a tone of red”. This way you know at least after the measurement that the color of the ball is a tone of red, you do not know the exact color but you have a clue at least, so the uncertainty in this case is smaller.** That means that position and color in our example are somehow competitive; After one measurement, the more you know about the one the less you know about the other, that is the core meaning of the uncertainty principle.**

## quantum *entanglement*

Now there is another “feature” in quantum theory that seems to make things really strange; entanglement.

Assume that in the previous example of the ball before you ask of any agent to do a measurement, you know that there is another ball (“ball1”) that has interacted briefly with our ball and they shared colors. If both balls were the normal (“classical”) balls that we know we would know that both of the balls have the same color. So after the cat would have measured the position of the ball, most definitely ball1 would have different color from ball (remember that the cat agent change the color). In quantum theory simple things like that don’t happen;

the property of quantum entanglement says that ball1 would change its color to be the same color with our ball after the cat measurement!!! Confused? **Quantum entanglement says that if two particles (the balls) are entangled then, the specific property that they are entangled with, it will have the same value for both particles despite how far the two particles are!** You can understand that by supposing that when you measure the first particles spin and you find it to be up, then at the same time the second particle’s spin is changing to up! So in our case whenever you measure the color of ball1 then you know what the color of ball is!

## Violation of the uncertainty principle

The idea is actually very old, since the first steps of quantum theory, and actually it was a

direct outcome of the famous EPR experiment that was the last act of the famous **Bohr-Einstein debate** about the completeness of quantum theory. Nobody back then has payed attention that in the EPR experiment we can circumvent the uncertainty principle.

In the example of the entangled balls above, entanglement gives a great opportunity to measure both qualities in the same time; Assume that after the entanglement we use the dog to measure the exact color of ball1 and the dog returns with the answer red. Then we ask the cat to do an exact measurement of the position of the ball (not ball1), and the cat returns with the ball’s position. We know now that the exact position of the ball (the cat cannot change its position). What about the color? After the cat did the measurement we know that the color can be anything, but we want to know the color before the cat interfered! We have it! It is the color of ball1; red! Since the two balls are entangled we know that when the dog was measuring the color of ball1 it was also measuring the color of ball without changing balls position (since it was doing a measurement on ball1 not ball)

This way quantum entanglement help us to get more information from a quantum system than we could normally get!

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¹ In quantum physics theory the uncertainty does not happen because the equipment that we use to measure is imperfect and it disturbs the fragile subatomic particles when they measure them. Uncertainty is a very important part of the theory itself and it has nothing to do with the technology of the measurement.

² We are talking about not a normal ball, but about an imaginary “quantum” ball.

** **

bwinwnbwisaid, on September 6, 2010 at 12:55 pmThanks for your comment on my blog. I find the above very interesting, it reaffirms my belief in human ingenuity. First comes the question, then the evaluation, and presto, our knowledge horizons expand. In terms of the observation/measurement problems at the quantum level, however, I’m not sure the increase of precision in the measurements visa vise the uncertainty principle changes much. Below is a cut and past from my Quantum Strangeness blog and when all is said and done I don’t see how the information garnered from this measurement (when you measure the first particles spin and you find it to be up) is any different from information garnered by a measurement/observation made on the “fuzzy world at the quantum level” (the collapse of Schrodinger’s wave equation). In both cases an observation collapses the “fuzzy world at the quantum level,” thus garnering useful information that applies to our human world of predictable events. It’s just that in the former case (quantum entanglement) the collapse allows for a more precise measurement visa vise the uncertainty relations described by Heisenberg’s uncertainty principle.

At the depths of the “material world” there exists a fuzzy world that exhibits only statistical behavior, behavior only when we observe it– when we separate ourselves from it. There we find a physical reality with no uniquely determinable location, a physical reality that exists in several states at the same time, a physical reality structured by a mathematical equation. So the question remains: Is it (or when is it) necessary to include human consciousness in our descriptions of the world? Or, put another way: What role does measurement play in an experiment? Does it provide a description of the world under study or does it actually create that world? Quantum Mechanics has a hard time answering questions like these.

Take care, and thanks for the opportunity to post.

e1samansaid, on September 12, 2010 at 9:46 pmThis is a comment for the post above that I recieved…

Hi e1saman. The article you mention is somewhat misleading, and frankly, the idea is not really new. (Btw, it can also be found for free, although in an older version apparently, here: [http://arxiv.org/abs/0909.0950]).

It is misleading (in the Nature Physics version) when they say in the abstract that “if the particle is prepared entangled with a quantum memory, a device that might be available in the not-too-distant future, it is possible to predict the outcomes for both measurement choices precisely.”

First of all, a “quantum memory” in this case is nothing but a system with which your system of interest is entangled with, and well, that’s actually been done to exhaustion; it’s in the not-too-distant past as opposed to future. Sure, it is a technical challenge to do that for many particles and maintaining the coherence for long times, but all you need for the purpose of that paper is a bipartite entangled state.

Now what is terribly misleading in that abstract is that you can only predict the outcomes of *either* measurement, not both! This is precisely the same situation as with the original EPR paradox.

And furthermore, they didn’t cite other works that have interpreted the EPR paradox in terms of the violation of a conditional Heinsenberg uncertainty principle. This was already done in 1989 by Margaret Reid [1] for the original EPR case of position-momentum. This idea has been extended for the general case by me and Reid in 2007 [2] and we have even recently published a review article about all of that [3]! This apparent violation of HUP also relates to the phenomenon of steering for which I and coauthors have derived criteria [4]. Even the proposed applications (for entanglement witnessing and cryptography) were already part of those earlier efforts as you can see in the review paper.

The novelty of that Nature Physics paper as far as I can see is really only that they write a bound on how much quantum theory allows you to have this apparent violation of the HUP depending on the degree of entanglement, which is a nice result, but hardly worth all the hype.

As far as the unpredictability of the quantum world is concerned, it is still alive and well. In fact entanglement *strengthens* that conclusion instead of weakening it [5].

[1] Physical Review A 40, 913 (1989)

http://link.aps.org/doi/10.1103/PhysRevA.40.913

[2] Journal of Modern Optics 54, 2373 (2007)

http://www.informaworld.com/smpp/content~db=all~content=a787786271

http://arxiv.org/abs/0711.2315

[3] Reviews of Modern Physics 81, 1727–1751 (2009)

http://rmp.aps.org/abstract/RMP/v81/i4/p1727_1

http://arxiv.org/abs/0806.0270

[4] Phys. Rev. A 80, 032112 (2009)

http://link.aps.org/doi/10.1103/PhysRevA.40.913

http://arxiv.org/abs/0907.1109

[5] http://arxiv.org/abs/0911.2504

bwinwnbwisaid, on September 14, 2010 at 2:32 pmThanks for the reply! I sincerely appreciate your effort. You teach and inform at the same time–very impressive.