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<\/p>\n\n\n\nA famous 1936 paper by Einstein, Podolsky, and Rosen [31] brought the<\/p>\n\n\n\n
whole matter to a head. Popularly known as EPR, they examined a thought<\/p>\n\n\n\n
experiment with entangled particles<\/p>\n\n\n\n
1<\/p>\n\n\n\n
and concluded that the quantum me-<\/p>\n\n\n\n
chanical description of nature is incomplete, or else a paradox arises. Niels<\/p>\n\n\n\n
Bohr countered their claim in a paper of the same title with his pragmatic<\/p>\n\n\n\n
view that there is no more to nature than what quantum mechanics says about<\/p>\n\n\n\n
it.<\/p>\n\n\n\n
It is insightful to examine a simpli\ufb01ed version of the EPR thought exper-<\/p>\n\n\n\n
iment (due to Bohm [13], and sometimes referred to as \u201cEPRB\u201d) to see what<\/p>\n\n\n\n
they meant. This version of the experiment actually can be, and has been<\/p>\n\n\n\n
performed subsequently in the laboratory, so we have a concrete handle on<\/p>\n\n\n\n
the issue.<\/p>\n\n\n\n
Consider a source that produces pairs of qubits in the anticorrelated Bell<\/p>\n\n\n\n
state<\/p>\n\n\n\n
|\u03b2<\/p>\n\n\n\n
11<\/p>\n\n\n\n
i =<\/p>\n\n\n\n
1<\/p>\n\n\n\n
\u221a<\/p>\n\n\n\n
2<\/p>\n\n\n\n
(|0<\/p>\n\n\n\n
1<\/p>\n\n\n\n
1<\/p>\n\n\n\n
2<\/p>\n\n\n\n
i \u2212 |1<\/p>\n\n\n\n
1<\/p>\n\n\n\n
0<\/p>\n\n\n\n
2<\/p>\n\n\n\n
i). (4.13)<\/p>\n\n\n\n
Suppose these particles \ufb02y o\ufb00 in two di\ufb00erent directions and Alice captures<\/p>\n\n\n\n
one of them while Bob gets the other. Our two experimenters can measure<\/p>\n\n\n\n
the spin of their particle using SG machines oriented along any desired axis.<\/p>\n\n\n\n
The source emits many entangled pairs, and the measurements are repeated a<\/p>\n\n\n\n
large number of times, recorded, and then compared. Let\u2019s label the direction<\/p>\n\n\n\n
along which Alice\u2019s detector (SG<\/p>\n\n\n\n
a<\/p>\n\n\n\n
) is oriented as \u02c6a and that of Bob (SG<\/p>\n\n\n\n
b<\/p>\n\n\n\n
) as<\/p>\n\n\n\n
\u02c6<\/p>\n\n\n\n
b (Figure 4.2).<\/p>\n\n\n\n
Suppose Alice and Bob decided to align their detectors along the same<\/p>\n\n\n\n
direction, \u02c6a =<\/p>\n\n\n\n
\u02c6<\/p>\n\n\n\n
b = \u02c6z, and recorded their measurements. A selection is made<\/p>\n\n\n\n
of those pairs for which Alice measured +1. The entanglement in the state<\/p>\n\n\n\n
(Equation 4.13) implies that for each of those pairs, Bob must have measured<\/p>\n\n\n\n
1<\/p>\n\n\n\n
It is after this work that Bell states come to be known as EPR pairs.<\/p>\n\n\n\n
<\/p>\n\n\n\n
72 Introduction to Quantum Physics and Information Processing<\/p>\n\n\n\n
FIGURE 4.2: Spin measurement on an entangled pair of particles.<\/p>\n\n\n\n
\u22121. But this is true even if \u02c6a =<\/p>\n\n\n\n
\u02c6<\/p>\n\n\n\n
b = \u02c6x or \u02c6y. If we try to explain the correla-<\/p>\n\n\n\n
tions by saying that the values were pre-existing before measurement, then we<\/p>\n\n\n\n
run into problems with the indeterminacy principle! The spins of the individ-<\/p>\n\n\n\n
ual particles in the pair have \ufb01xed (anticorrelated) values in all directions in<\/p>\n\n\n\n
this scenario, contradicting the quantum mechanical fact that spins in three<\/p>\n\n\n\n
mutually perpendicular directions are incompatible observables.<\/p>\n\n\n\n
EPR has another objection to the quantum dictum that the particles do<\/p>\n\n\n\n
not have de\ufb01nite values of spin until a measurement is made. Assume at the<\/p>\n\n\n\n
beginning, a state in which neither qubit has a de\ufb01nite spin. When Alice<\/p>\n\n\n\n
makes an SG<\/p>\n\n\n\n
a<\/p>\n\n\n\n
measurement, then the combined state collapses to one that is<\/p>\n\n\n\n
an eigenstate of \u03c3<\/p>\n\n\n\n
a<\/p>\n\n\n\n
\u2297 . The collapsed state is also an eigenstate of \u2297 \u03c3<\/p>\n\n\n\n
a<\/p>\n\n\n\n
with the opposite eigenvalue. This conveying of information about the collapse<\/p>\n\n\n\n
from one qubit to the other is mystifying, particularly if we recall that the two<\/p>\n\n\n\n
detections are taking place at spatially separated points, and could be really<\/p>\n\n\n\n
really far from each other! Is this even compatible with Einstein\u2019s special<\/p>\n\n\n\n
relativity, which claims that information cannot travel faster than the speed<\/p>\n\n\n\n
of light? In such a scenario, it wouldn\u2019t even make sense to decide which<\/p>\n\n\n\n
measurement was made \ufb01rst!<\/p>\n\n\n\n
Einstein, Podolsky and Rosen summarized their conclusions as follows: The<\/p>\n\n\n\n
assumption that the quantum system possesses certain properties, viz. spin,<\/p>\n\n\n\n
independent of whether it is measured or not, is known as realism. Also, the<\/p>\n\n\n\n
value of this property cannot be altered by measurements made at spatially<\/p>\n\n\n\n
separate locations. This tenet is known as locality. The EPR experiment<\/p>\n\n\n\n
shows that quantum mechanics violates local realism. In order to sort out<\/p>\n\n\n\n
the paradox, they concluded that<\/p>\n\n\n\n
I. There is some instantaneous mechanism by which the measurement re-<\/p>\n\n\n\n
sult of the particle at A is conveyed to the experiment at B, meaning<\/p>\n\n\n\n
that quantum mechanics is non-local<\/p>\n\n\n\n
OR<\/p>\n\n\n\n
II. The quantum mechanical description of the initial entangled state by the<\/p>\n\n\n\n
vector |\u03b2<\/p>\n\n\n\n
11<\/p>\n\n\n\n
i is incomplete, since it does not provide a full speci\ufb01cation<\/p>\n\n\n\n
of the actual system, i.e., it is not realistic.<\/p>\n\n\n\n
Since non-locality was counter to relativity, EPR were inclined to choose<\/p>\n\n\n\n
the latter option in claiming that quantum mechanics was incomplete,<\/p>\n","protected":false},"excerpt":{"rendered":"
A famous 1936 paper by Einstein, Podolsky, and Rosen [31] brought the whole matter to a head. Popularly known as EPR, they examined a thought experiment with entangled particles 1 and concluded that the quantum me- chanical description of nature is incomplete, or else a paradox arises. Niels Bohr countered their claim in a paper […]<\/p>\n","protected":false},"author":1,"featured_media":4002,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[490],"tags":[],"class_list":["post-4015","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-5-interpreting-quantum-physics"],"jetpack_featured_media_url":"https:\/\/workhouse.sweetdishy.com\/wp-content\/uploads\/2024\/09\/atom-1.png","_links":{"self":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/4015","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/comments?post=4015"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/4015\/revisions"}],"predecessor-version":[{"id":4016,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/4015\/revisions\/4016"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media\/4002"}],"wp:attachment":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media?parent=4015"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=4015"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=4015"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}