ABSTRACT
In 1935 Albert Einstein, Boris Podolsky and Nathan Rosen, confronted quantum physics with a profound objection concerning the quantessential property of entanglement. This led to a fierce debate between Bohr and Einstein closely followed by Schrödinger. In those days the problem was presented as a gedanken experiment involving a pair of spins or qubits which are entangled but widely separated in space. One may think of a spin-less particle at rest (a π0 particle for example) decaying into two photons, because of momentum conservation both particles will fly off back to back and because of spin conservation the polarizations of the two photons have to be opposite. This means that without interactions the particles could separate and travel a long way, and we could imagine that one might arrive in New York and the other in Tokyo where Alice and Bob will make polarization measurements. The polarization state of the entangled pair is given by: https://www.w3.org/1998/Math/MathML" display="block"> | ψ N T 〉 = 1 2 ( | 1 , − 1 〉 − | − 1 , 1 〉 ) , where the first entry refers to the NY particle and the second to its Tokyo counterpart, and we for convenience have assumed the particles to be polarized in z-direction. Now Alice in New York decides to make a polarization measurement. Let us suppose that she chooses to do this along the x-axis, and let us also suppose that she finds a value +1. Then we know that the first spin is projected on the |+〉 state. But as the spins are opposite it follows that instantaneously the spin of the particle in Tokyo must have changed to the |−〉 state. That this indeed has to be the case follows from the fact that we could have written the initial state also in the form The Myth of Depth, a 1984 painting by Mark Tensey. It makes you think of unusual, if not magical, ways information may propagate. It is the ‘Spooky action at a distance,' Einstein was so worried about. A painting depicts a group of people on a boat in turbulent water, with one person standing on the waves, symbolizing unusual information propagation. https://www.w3.org/1999/xlink" content-type="colour" xlink:href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003701910/52acb51c-2955-4a2b-9bba-befceb5d8a5c/content/figII_4_1_C.jpg"/> (Source: ANP / Mark Garlick / Science Photo Library) https://www.w3.org/1998/Math/MathML" display="block"> | ψ N T 〉 = 1 2 ( | − , + 〉 − | + . − 〉 ) , and Alice’s projects on the first term as we discussed in the previous section, so after Alice’s measurement we have ψNT ⇒ | +.−〉. If Bob also decides to measure along the x-axis, then he will obtain the value −1. It is clear that the probalities for measurement outcomes can be precisely calculated for all possible independent choices that Alice and Bob could make.
