PDF (double-sided) - Physics Department, UCSB - University of ...
PDF (double-sided) - Physics Department, UCSB - University of ... PDF (double-sided) - Physics Department, UCSB - University of ...
(independent of which axis it is), they will yield an opposite outcome with certainty. But since measurements along orthogonal axes do not commute, quantum mechanics not only forbids a simultaneous prediction of the outcome of all possible measurements, but states that this information is not present in the state of the two particles before the measurement. Instead, a measurement of particle A instantaneously collapses the wave-function (changes the state) of particle B despite the fact that they are causally disconnected by their distance. Einstein called this non-local effect of entanglement the “spooky action at a distance”. A possible local hidden variable theory would instead state that the particles agree on all possible measurement outcomes before their separation. This agreement would be contained in the state of the particles in extra unmeasured degrees of freedom, the hidden variables. If the measurements of particles A and B are limited to two possible choices of axes each, a and a ′ as well as b and b ′ , and the outcomes are encoded in binary (1 or 0), this agreement implies that the particles have to choose at the time of separation to belong to one of the 16 possible populations shown in Table 10.1. Next, one defines a correlation measurement E xy which takes the value 1 if the outcome of a measurement of particle A along axis x and particle B along axis y yields the same result for both particles and a value of −1 for opposite results. For experimental implementation, the expectation value 228
Table 10.1: Possible Populations for Locally Deterministic Particle Pairs Pop. a a ′ b b ′ E ab E a ′ b E ab ′ E a ′ b ′ S n 0 0 0 0 0 1 1 1 1 2 n 1 0 0 0 1 1 1 -1 -1 2 n 2 0 0 1 0 -1 -1 1 1 -2 n 3 0 0 1 1 -1 -1 -1 -1 -2 n 4 0 1 0 0 1 -1 1 -1 -2 n 5 0 1 0 1 1 -1 -1 1 2 n 6 0 1 1 0 -1 1 1 -1 -2 n 7 0 1 1 1 -1 1 -1 1 2 n 8 1 0 0 0 -1 1 -1 1 2 n 9 1 0 0 1 -1 1 1 -1 -2 n 10 1 0 1 0 1 -1 -1 1 2 n 11 1 0 1 1 1 -1 1 -1 -2 n 12 1 1 0 0 -1 -1 -1 -1 -2 n 13 1 1 0 1 -1 -1 1 1 -2 n 14 1 1 1 0 1 1 -1 -1 2 n 15 1 1 1 1 1 1 1 1 2 229
- Page 206 and 207: energy landscape (see Chapter 2.2.3
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- Page 250 and 251: Figure 9.11: Resonator T 1 - a) Seq
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Table 10.1: Possible Populations for Locally Deterministic Particle Pairs<br />
Pop. a a ′ b b ′ E ab E a ′ b E ab ′ E a ′ b ′ S<br />
n 0 0 0 0 0 1 1 1 1 2<br />
n 1 0 0 0 1 1 1 -1 -1 2<br />
n 2 0 0 1 0 -1 -1 1 1 -2<br />
n 3 0 0 1 1 -1 -1 -1 -1 -2<br />
n 4 0 1 0 0 1 -1 1 -1 -2<br />
n 5 0 1 0 1 1 -1 -1 1 2<br />
n 6 0 1 1 0 -1 1 1 -1 -2<br />
n 7 0 1 1 1 -1 1 -1 1 2<br />
n 8 1 0 0 0 -1 1 -1 1 2<br />
n 9 1 0 0 1 -1 1 1 -1 -2<br />
n 10 1 0 1 0 1 -1 -1 1 2<br />
n 11 1 0 1 1 1 -1 1 -1 -2<br />
n 12 1 1 0 0 -1 -1 -1 -1 -2<br />
n 13 1 1 0 1 -1 -1 1 1 -2<br />
n 14 1 1 1 0 1 1 -1 -1 2<br />
n 15 1 1 1 1 1 1 1 1 2<br />
229
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