Applications and the Future - Codes: The Guide to Secrecy from Ancient to Modern Times - page 367

Now suppose that we use a polarizer axis that is horizontal, denoted by H .
Then no light gets past filter H , after havingpassed throuh filter V because
all of the photons are polarized , whose angle with H is α =90 ◦ , and the

probability of getting through is cos 2 90 ◦ = 0. This process is illustrated in
Diagram 9.11.

↑

Diagram 9.11 Polarization with Filters V and H

L

V H

polarized
−−−−−−−−−−→

↑

S
−−−−→

→ 0% of S

Suppose we now place a filter with polarizer axis 45 ◦ , denoted by F between
V and H . Then the 50% of those photons that get through V now have a 50%
chance of getting through F , and each of those will be polarized as ,sonow

25% of the original photons got through. Now we approach H and each of the

has a 50% chance of getting through H . Hence, once through all three filters,
12.5% of the original photons are emitted. Surprisingly, having put another
filter between two that allowed no photons through, now allows 12.5% through.

Diagram 9.12 Polarization with Filters V, F, and H

1 1

L

2 S 4 S

1

V F H

8 S
−−−−→
→

S
−−−−→

−−−−→
↑

−−−−→

This is the basic principle upon which Polaroid sunglasses work. One can
demonstrate this principle, usinga pair of Polaroid sunlasses, by takingone
lens out and placingit in front of the fixed lens. There will be an orientation
that is exactly the same for both lenses, so that the fixed lens has no effect
on the loose lens. If the loose lens is now rotated ninety degrees, the effect
will be complete blackness. This is because the polarization of the lenses are
now perpendicular, so that photons that get through the one lens are blocked
by the other. By rotating the loose lens forty-five degrees, one now gets an
intermediate stage between complete blackness and no effect. This is because
half of the photons that pass through the one lens succeed in getting through
the other. Placinga third lens in front of the loose lens with axis perpendicular
to the fixed lens, we get about half the light from the first two being filtered
through, which is Diagram 9.12 in action.

Quantum Key Generation
Now we turn back to cryptography and show how the above notion of po-
larization and its effects can be employed to generate cryptograms.