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Scheme for reading and writing digits in a photon, a single particle of light which obeys the strange laws of quantum mechanics.

A sender, whom we shall call Alice, wants to send a string of digits to a receiver (Bob) by using single photons. Because it carries light, a photon contains vibrating electric and magnetic fields. To represent a 0, Alice can simply create a photon whose electric field vibrates in a horizontal plane. As a result, the photon is said to have horizontal polarization (a). To represent a 1, Alice creates a photon whose electric field vibrates in a vertical plane. This photon has vertical polarization (b).

Bob reads Alice's message by using a polarizer (oval with lines), a sheet of film which blocks certain types of polarized light. Let's assume that he orients his polarizer vertically, so that it will allow all vertically polarized light to go through but will block all the horizontally polarized light. Therefore, when a photon passes through the polarizer, Bob knows that it is a vertically polarized photon and records a 1.

Problems crop up when Alice tries to convey additional digits with her photon. For example, Alice can try to represent a 2 by creating a polarization state which is tilted at an angle of 45 degrees relative to the horizontally and vertically polarized states (c).

There's something unfortunate about the 45-degrees-polarized state: it can be thought of as being composed of half the vertical polarization and half the horizontal polarization. When such a photon reaches the polarizer, you might think that half the light might pass through the polarizer while another half would be blocked.

But the photon is a single object and it must do one thing or the other. As a result, there is a 50 percent chance that the photon will pass through the polarizer, and a 50 percent chance that the photon will be blocked by it.

If Alice now attempts to send a 2, it will either look identical to a 0 (if the photon gets blocked) or identical to a 1 (if the photon passes through). So if Bob detected a blocked photon, he wouldn't really know if Alice intended to transmit a 0 or a 2. Similarly, if Bob detected a photon that passed through, he wouldn't really know if Alice intended to transmit a 1 or a 2. In sum, the 45-degrees-polarized state is not perfectly distinguishible from the other polarization states.

Physicists who study how to send information using the quantum states of single photons and other quantum particles are realizing something very important: it is crucial to make the different states as distinguishible as possible. Now, all hope is not lost in the above example. There are many strategies that Alice can employ to successfully transmit the 2. For example, Alice can choose to send 100 photons per digit she wants to transmit. When Bob sees that half of the photons get blocked and the other half pass through, he deduces that Alice wanted to send a 2.