From Wikipedia, the free encyclopedia Photon entanglement
Photon entanglement
This brief explanation of photon entanglement is a sup- understanding one of the fundamental assumptions on
plement to the article Bohr-Einstein debates and is de- which the argument of Einstein, Podolsky and Rosen (or
signed to help clarify the discussion of the Ein- "EPR") is based:
stein-Podolsky-Rosen argument in quantum theory (R)If, without disturbing a system in any way, it is
which takes place in that article. possible to predict with certainty the result of the
measurement of an observable of the system, then there
Entanglement exists an element of reality associated with the
observable in question; the system "objectively
Let us recall, for purposes of exposition, that a quantum possesses" the relative property.
system is described, at every instant, by a vector state
which, according to the theory, represents the maximum
amount of information that it is possible to have with re-
spect to it. To simplify discussion, let’s take the example
of the state of polarization of a photon and associate with
it the vector state . What does this information tell
us about the properties of photons? The knowledge of
the vector state, in fact, provides us exclusively with in-
formation on the possible results of measurements which
we decide to carry out on the system. For example in the
case just referred to we know that if we were to apply a
test for vertical polarization to the photon whose state is
, it would have a probability of 1/2 of passing and
1/2 of failing. But the theory, which usually provides on-
ly probabilistic information on the results of hypotheti- The behaviour, during various processes of measurement, of
cal measurements, can, with reference to particular tests, two distant photons as discussed in the text
assign the value 1 or 0 to the probability of obtaining spe-
cific results. So, in the case we are considering, the theo- Now consider the following situation: two photons
ry tells us that the photon has a probability of 1 of pass- are emitted by a source S and are propagated in two op-
ing through a filter polarized at 45°, and a probability of posite directions. At a certain instant, one of them can be
0 of passing through a filter polarized at 135°. In this case, found in the region A, to the right of the source and the
and with precise and exclusive reference to the observ- other in the region B symmetric to A with respect to S
ables (polarization at 45° and 135°) for which we know a (figure G).
priori the results of measurement, we can assert that the We can call the photon at the right 1 and assume that
photon possesses the property in question: it is polarized it possesses a vertical polarization. This can be indicat-
at 45° or "possesses the property which guarantees that ed as the vector state . Analogously, suppose that
it will pass with certainty a test at 45°." This is an impor- the photon on the left, indicated as 2, has a horizontal
tant distinction with the situation in classical mechanics: polarization, so that it is described by the vector state
in classical physics, any system always possesses precise
. The entire system is described as the state
values for all of the observables that we can conceive,
but in quantum physics, a single system will indeed pos-
sess some property, but, with reference to other proper-
ties, we can do no better than make probabilistic predic- which corresponds to the single quantum state which as-
tion about the results of possible measurements, of and serts that "(one photon is in A with vertical polarization)
when they are actually executed. In a certain sense the and (one photon is in B with horizontal polarization)".
theory teaches us that a system must not have too many This state is called "factored" because it is, techni-
properties and that, in particular, some are incompatible cally, the product of the two photons. Its properties are
with others. So, for example, a photon that is "polarized rather obvious and are illustrated in Figure G. For exam-
at 45°" does not possess any definite property relative to ple if, given the state , we car-
vertical or horizontal polarization. This is important for ry out a test of vertical polarization on the photon on the
1
From Wikipedia, the free encyclopedia Photon entanglement
right and a test of horizontal polarization on the photon is also a possible state of the system of two photons. What
to the left, we know that both of them will pass with cer- are the properties of this system?
tainty. Similarly, if we carry out (center of figure) a test of It’s immediately clear that each of the two photons
horizontal polarization on both of the photons, the one does not possess the property of being polarized vertical-
on the right will certainly fail, while the one on the left ly or horizontally, since the probability of passing, for ex-
will certainly pass. Lastly, consider the more general case ample, a test of vertical polarization on the part of pho-
in which the photon to the right is passed through a fil- ton 1 is characterized by the coefficient of the state in
ter polarized at 45°. In this case, the photon 2 will pass which it has this polarization and the square of this co-
through 1/2 of the time and end up polarized at 45°, and efficient is one half. Therefore if one carries out this test,
it will fail to pass the other 1/2. The photon on the left photon 1 will pass about half of the time in an unpre-
has not been tested and therefore remains horizontally dictable manner. The same reasoning applies to the hori-
polarized. zontal test and for the other photon.
Suppose we are now interested in measuring the po-
The state is actually a superposition of states,
larizations at 45° and 135°. We must express the state of
however, and must be rewritten as follows:
vertical and horizontal polarizations as the superposi-
tions of states of polarization at 45° and 135°. Substituting
the appropriate expressions into the preceding formula
and carrying out the explicit calculations, we have:
Substituting this into the expression for the state ,
we have:
The result is the superposition of the states of two pho-
tons polarized at 45° and of two polarized at 135°. The
According to this formula, a measure of polarization at two new orthogonal directions have taken the place of
45° in A can result, with equal probability, in the photon the vertical and horizontal of the preceding expressions.
1 passing the test, in which case the system will be repre- This implies, of course, that every photon has a probabil-
sented, according to wave packet reduction, as follows: ity of 1/2 to pass a test of this type exactly as it has to
pass the tests for vertical and horizontal polarization. If
one were to continue and calculate the results for other
possible measures of polarizations along arbitrary direc-
tions in the plane, it would eventually be noted that this
result is generalizable as follows:
An important case is the one in which the photons have
the same initial polarization:
In words, this means that the state always has the
same form regardless of the directions chosen: it is the
or
superposition of two states, in the first of which both of
the photons are polarized in the chosen direction n, and
in the second of which both of the photons are polarized
In order to understand entanglement, consider again the
on the orthogonal direction .
two photons discussed above and observe that that states
Now, suppose that an observer decides to carry out a
and are both possible states of the system. But, measurement of the polarization of photon 1 along an ar-
if this is the case, then it follows that the superposition of bitrarily chosen direction n. If the photon passes the test,
the two states: then according to the principle of wave packet reduction,
we have:
2
From Wikipedia, the free encyclopedia Photon entanglement
and the final state is factored. Spontaneously, photon 2, Photon entanglement may soon be used as a Covert
which had no property of polarization before the mea- channel if not already. This is due to it being impossible
surement, has acquired a precise property as a result of to eavesdrop on the channel, at least for now. Although it
the measurement of photon 1! This is entanglement. may be possible to entangle additional photons and thus
observe the communication or tamper with it in the fu-
Applications ture, this would most likely require physical access to the
photons. See the No cloning theorem for additional infor-
One important area where entanglement can be applied mation.
is in computer microchips. Normally, the size of a mi- It may soon be possible to mass produce entangled
crochip is restricted by the wavelength of the photon photons since scientists have discovered a way to pro-
carving the chip, being able to carve at one-half of the duce these photons using a simple semi-conductor. This
wavelength in accordance with the Rayleigh criterion. approach is not only simpler then the previous nonlinear
However, entangled photons can be separated and then optical crystals such as beta barium borate (BBO) or Po-
rejoined together, and since they have exactly the same tassium titanyl phosphate (KTP), but also produces them
position the constructive interference doubles the ener- on demand as opposed to the one in ten billion being
gy so that it can carve as low as 1/4 of the original wave- downconverted into entangled photons within the crys-
length and thus make microelectronic devices half the tal. The semiconductor is made from gallium arsenide
size of what was previously possible. Entangling more used in optoelectronics, and dots made from indium ar-
than one photon can lead to even greater energies, hit- senide mere nanometers in size; this compound is con-
ting 1/6 and theoretically even 1/8 the original wave- venient since it self organizes into dots. Currently it has
length. to be produced at low temperatures to produce infrared
Instantaneous communication by means of quantum light, but some companies predict that it can be produced
entanglement is actually impossible because neither side at room temperature soon.
can manipulate the state of the entangled particles, they
can only measure it (see No-communication theorem).
This fact means that if you measure one particle you can-
External links
not infer anything meaningful about the observers mea- • AdvR - Photon entanglement in KTP Waveguides
suring the other particle, except you know what state • LED entangles light at the flick of a switch
they will measure, or have already measured. Thus causal-
ity is preserved.
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Categories:
• Quantum measurement
• Albert Einstein
• Philosophy of physics
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