6.6 THE GHZ PUZZLE using visual studio .net tocreate qr code iso/iec18004 in web,windows application QR Code Safe Use But if Qbit 0 qr bidimensional barcode for .NET did indeed have a predetermined predisposition to give x0 when measured, even before Qbits 1 and 2 were measured to reveal what x0 actually was, then the value of x0 surely would not be altered if Hadamards were applied to Qbits 1 and 2 before they were measured, since the Qbits have ceased to interact, and the predisposition to give x0 was present before the decision to apply Hadamards or not had been made. This means that the value x0 appearing in (6.

34) must indeed be identical to the value of x0 appearing in (6.35). So our question is not meaningless.

The answer is Yes! Such an argument for elements of reality predetermined values was put forth in 1935 (in a different context) by Albert Einstein, Boris Podolsky, and Nathan Rosen (EPR). The controversy and discussion it has given rise to has steadily increased over the past seven decades. The terms incomplete and element of reality originated with EPR.

Today it is Einstein s most cited paper. The wonderful thing about three Qbits in the state (6.26) is that they not only provide a beautiful illustration of the EPR argument, but also, when examined further, reveal that the appealing argument establishing predetermined measurement outcomes cannot be correct.

To see this, note that exactly the same reasoning establishes that the values of x1 appearing in (6.34) and (6.36) must be the same, as well as the values of x2 appearing in (6.

34) and (6.37). And the same line of H thought establishes that the values of x0 in (6.

37) and (6.36) must be H the same, as well as the values of x1 in (6.37) and (6.

35) and the values H of x2 in (6.36) and (6.35).

If all this is true, then adding together the left sides of (6.34) (6.37) H H H must give 0 modulo 2, since each of x2 , x1 , x0 , x2 , x1 , and x0 appears in exactly two of the equations.

But the modulo 2 sum of the right sides is 0 1 1 1 = 1. So the appealing EPR argument must be wrong. There are no elements of reality no predetermined measurement outcomes that a more complete theory would take into account.

The answer to what is mistaken in the simple and persuasive reasoning that led Einstein, Podolsky, and Rosen to the existence of elements of reality is still a matter of debate more than 70 years later. How, after all, can Qbit 0 and its measurement gate know that if they interact only after Qbits 1 and 2 have gone through their own measurement gates (and no Hadamards were applied) then the result of the measurement of Qbit 0 must be given by (6.38) The best explanation anybody has come up with to this day is to insist that no explanation is needed beyond what one can infer from the laws of quantum mechanics.

Those laws are correct. Quantum mechanics works. There is no controversy about that.

What fail to work are attempts to provide underlying mechanisms, that go beyond the quantum-mechanical rules, for how certain strong quantum. P R O T O C O L S T H AT U S E J U S T A F E W Q B I T S correlations Visual Studio .NET QR Code JIS X 0510 can actually operate. One gets puzzled only if one tries to understand how the rules can work not only for the actual situation in which they are applied, but also in alternative situations that might have been chosen but were not.

By concluding with this paradoxical state of affairs, I am not suggesting that there is anything wrong with the quantum-theoretic description of Qbits and the gates that act on them. On the contrary, the quantum theory has to be regarded as the must accurate and successful theory in the history of physics, and there is no doubt whatever among physicists that if the formidable technological obstacles standing in the way of building a quantum computer can be overcome, then the computer will behave exactly as described in the preceding chapters. But I cannot, in good conscience, leave you without a warning that the simple theory of Qbits developed here, though correct, is in some respects exceedingly strange.

The strangeness emerges only when one seeks to go beyond the straightforward rules enunciated in 1. In particular one must not ask for an underlying mechanism that accounts not only for the behavior of the circuit actually applied to a particular collection of Qbits, but also for the possible behavior of other circuits that might have been applied to the very same collection of Qbits, but were not. A good motto for the quantum physicist and for future quantum computer scientists might be What didn t happen didn t happen.

On that rm note I conclude (except for the 16 appendices that follow)..
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