Unformatted text preview: on filter only allows horizontally polarized photons through. Turn that filter 90 degrees, and only vertically polarized photons can come through. Let’s say you have a pulse of horizontally polarized photons. If they try to pass through a horizontally polarized filter, they all get through. Slowly turn that filter 90 degrees; the number of photons getting through gets smaller and smaller, until none get through. This is counterintuitive. You’d think that turning the filter just a little will block all the photons, since the photons are horizontally polarized. But in quantum mechanics, each particle has a probability of suddenly switching its polarization to match the filter. If the angle is a little bit off, it has a high probability. If the angle is 90 degrees off, it has zero probability. And if the angle is 45 degrees off, it has a 50 percent probability of passing through the filter. Polarization can be measured in any basis: two directions at right angles. An example basis is rectilinear: horizontal and vertical. Another is diagonal: leftdiagonal and rightdiagonal. If a photon pulse is polarized in a given basis and you measure it in the same basis, you learn the polarization. If you measure it in the wrong basis, you get a random result. We’re going to use this property to generate a secret key: (1) Alice sends Bob a string of photon pulses. Each of the pulses is randomly polarized in one of four directions: horizontal, vertical, leftdiagonal, and rightdiagonal. For example, Alice sends Bob: /——\——/ (2) Bob has a polarization detector. He can set his detector to measure rectilinear polarization or he can set his detector to measure diagonal polarization. He can’t do both; quantum mechanics won’t let him. Measuring one destroys any possibility of measuring the other. So, he sets his detectors at random, for example: ×++×××+×++ Now, when Bob sets his detector correctly, he will record the correct polarization. If he sets his detector to measure rectilinear polarization and the pulse is polarized rectilinearly, he will lea...
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This note was uploaded on 10/18/2010 for the course MATH CS 301 taught by Professor Aliulger during the Fall '10 term at Koç University.
 Fall '10
 ALIULGER
 Cryptography

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