Entanglement (II): Non-locality, Hidden Variables and Bell’s Inequalities.

In the first article of this series, we studied Einstein, Podolski and Rosen’s paper, where we encountered for the first time the concept of quantum entangled stated and their “spooky action at a distance”.

As EPR realized, when particles interact (under certain conditions), a new type of non-classical correlations arise. In order to understand why entangled states concerned Einstein so much, you have to remember that he never accepted the Copenhagen Interpretation of Quantum Mechanics.  Among many other things, this interpretation postulated that physical observable properties arise only when they are measured, meaning that the interaction of an apparatus (observer) and the systems causes the wave-function to collapse. A perfect example of this is the so-famous Schrödinger Cat Experiment (I won’t get into any detail as I’m sure you all know what I’m talking about).

However, Einstein believed that in any complete physical theory, one should be able to predict the values of observable properties of quantum systems without the need to perform any measurement or to disturb the system. Said otherwise, physical observable properties should exist and have definite values independent of observation, they should be elements of reality. This is stated explicitly in EPR’s criterion of reality and sometimes recalled in Einstein’s quote:

“I, at any rate, am convinced that He (God) does not throw dice.”

-A. Einstein

In this article we will continue to study quantum entangled states and we will see what was the fundamental mistakes that Einstein, Podolski and Rosen made in the derivation of their “paradox”. Also, we will show why it is that we say that these correlations between quantum systems cannot be accounted for by any classical theory.

EPR’s Paradox Exemplified: Bohm’s Spin Experiment

After my post on Einstein, Podolski and Rosen’s paradox, a few of you guys asked me about how is it possible for both the position and momentum of a particle to be elements of reality at the same time. In particular, I think this confusion may come from the choice of example I used (Eq. (3)). I decided to prepare this addendum to present another example of how entangled particles can apparently allow us to determine the values of two non-commuting operators. Thus, I want to discuss Bohm’s version of the EPR paradox. (Also, this article will be very useful for understanding Bell’s Inequalities).

Before presenting Bohm’s experiment I want you to remember that EPR’s criterion of reality establishes that in order for a physical quantity to have real values we should be able to predict with certainty (i. e. with probability equal to unity) the value of said quantities without the need of measuring or disturbing the system.

Monday Humour: Energy Mass Equivalence is Discovered

Wonder how many breakthroughs were made this way?

I just love the fact that he’s randomly trying different exponents ^^

Have the greatest week everyone!

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Update: Accepted to the V Quantum Information School and Workshop

As I mentioned on this post, the V Quantum Information School and Workshop will be hosted in Paratay Brazil between the 4th and the 8th of August. I applied to participate in both the School and the Workshop and last week I received an email confirming my participation for the School (confirmations for the Workshop won’t be sent until mid-May).

If any of you guys is also going to be participating on the School write me via this blog or via Facebook so we can start getting to know each other. I’m really looking forward to meet fellow physicist working on Quantum Information and Computation!

Hope to see some of you guys there!

Marco Cerezo

Today’s NASA ADOD (Astronomy Picture of the Day).

I would like to congratulate mi dear friend Guatemalan Astrophotographer Sergio Montufar Codoñer for winning Today’s NASA APOD (Astronomy Picture of the Day). To view image in full resolution, click the image or visit his APOD here. Go and like his facebook page here, he’s really talented!

Explanation: The view was worth the trip. Battling high winds, cold temperatures, and low oxygen, the trek to near the top of the volcano Santa Maria in Guatemala — while carrying sensitive camera equipment — was lonely and difficult. Once set up, though, the camera captured this breathtaking vista during the early morning hours of February 28. Visible on the ground are six volcanoes of the Central America Volcanic Arc, including Fuego, the Volcano of Fire, which is seen erupting in the distance. Visible in the sky, in separate exposures taken a few minutes later, are many stars much further in the distance, as well as the central band of our Milky Way Galaxy situated horizontally overhead.

Monday Humour: Miracle Demonstrations.

Have a great week everyone!

I guess we have all been there, personally I can relate to both these characters. I can’t remember how many times I thought to myself “Dang it Landau, that step is most definitely not trivial!, you should be more explicit here”.

Also, we have all been stuck in that middle step, not being able to quite figure it out, hopping for that Eureka moment that allows us to get to that beautiful result/Q.E.D. There’s no greater feeling in the whole world that hitting that sweet enlightenment! (wow, even I am amazed at how nerdy that came out 😉 ).

V Quantum Information School and Workshop – Paraty 2015

As you can see here, there will be a School and Workshop about Quantum Information to be hosted in Paratay, Brasil (if you aren’t sure about wanting to attend, just do a quick google image search on Paratay Prasil, that will do the trick).

Deadline for applications to the V Paraty Quantum Information School and Workshop are getting closer (sorry for the short notice but I also very recently just found out). I just submitted my application for the School and the Workshop, and I hope to see you all there (wink wink nudge nudge selection committee!). If everything goes according to plan I ought to present a poster on our latest work.

The School will take place between the 4th and the 8th of August, and the Workshop between the 11th and the 15th. If you are a student, I hear the courses are very good, this year they will be:

Monday Humour: Dogs and Quantum Mechanics.

Keeping up with our geeky Mondays!

I always felt the same way about my cat =)

Have a great week everyone!

Today’s Quote: How the term “Entanglement” came to be.

“When two systems, of which we know the states by their respective representatives, enter into temporary physical interaction due to known forces between them, and when after a time of mutual influence the systems separate again, then they can no longer be described in the same way as before, viz. by endowing each of them with a representative of its own. I would not call that ‘one’ but rather ‘the’ characteristic trait of quantum mechanics, the one that enforces its  entire departure from classical lines of thought. By the interaction the two representatives (or $\psi$-functions) have become entangled.”

-E. Schrödinger

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Monday Humour: Bob and Alice

What better way to start the week that with some geeky humour? 🙂 This is the first post of a weekly publication: Monday Humour!

Enjoy!

Wonder how long has Bob been holding onto that one ^^.

Have a great week everyone!