lecturenotes14 - CSE 599d Quantum Computing Quantum...

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Unformatted text preview: CSE 599d - Quantum Computing Quantum Entanglement and Bell’s Theorem Dave Bacon Department of Computer Science & Engineering, University of Washington ...contemporary physicists come in two varieties. Type 1 physicists are bothered by EPR and Bell’s The- orem. Type 2 (the majority) are not, but one has to distinguish two subvarieties. Type 2a physicists explain why they are not bothered. Their explanations tend either to miss the point entirely (like Born’s to Einstein) or to contain physical assertions that can be shown to be false. Type 2b are not bothered and refuse to explain why. —David Mermin Today we get to talk about one of my favorite subjects, quantum entanglement. I’ve been dreaming about quantum entanglement for so long now that I sometimes forget how really truly marvellous it is. I came to entanglement in the similar route that many take to the subject: it was presented as the premiere example in physics of a result which defies our common notions of how the world should work. Because entanglement challenges our common sense, it acquired a reputation among physicists as a little taboo. This was probably a tragedy, in retrospect, since we now know that quantum entanglement seems to play a central role in quantum information science. Indeed there is a real way in which quantum entanglement is the fuel which powers quantum computers. I. THE GHZ GAME We will begin our study of the strangeness of entanglement with a simple game. Alice, Bob, and Charlie, while out looking for Dave one day, found themselves trapped at the hands of an evil Wizard (the details of how this came to be are not relevant to us.) The Wizard was evil because he liked to play games with his captives. But he wasn’t so evil that he liked to play games that always resulted in the captives losing. On this day he decided to play the following game with his three captives. The three captives would be locked away in three separate rooms, without the ability to communicate with each other. The Wizard would then come around and give each of the captives a slip of paper with the letter X or Y written on the slip. At midnight, the captives are then to shout out either the value +1 or the value- 1. The Wizard explains to the captives that he either two of them have received Y ’s on their slips of paper or none of them have received Y ’s. The captives will win the game and be released if, when they are all given slips with X on them, the product of what they shout out is +1, and if two of them were given Y slips, then the product of what they shout out must be- 1. Or to write it all down symbolically, there are four possible combinations of the papers on the slips, { XXX,XY Y,Y XY,Y Y X } , and the products of what they shout must be { +1 ,- 1 ,- 1 ,- 1 } for these corresponding slips. Now Alice, Bob, and Charlie are all told the rules to this game. They are allowed to conspire before they are locked away, but after they are locked away they are not allowed to communicate to each other. The question about this game we would like to answer is whether it is possibleallowed to communicate to each other....
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This note was uploaded on 11/06/2011 for the course CSE 599 taught by Professor Staff during the Fall '08 term at University of Washington.

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lecturenotes14 - CSE 599d Quantum Computing Quantum...

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