1.5.1: An Advantage of Qubits

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Page ID: 50366

Paul Penfield, Jr.
Massachusetts Institute of Technology via MIT OpenCourseWare

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There are things that can be done in a quantum context but not classically. Some are advantageous. Here is one example:

Consider again Alice trying to send information to Bob using polarized photons. She prepares photons that have either horizontal or vertical polarization, and tells that to Bob, during the setup phase. Now let us suppose that a saboteur Sam wants to spoil this communication by processing the photons at some point in the path between Alice and Bob. He uses a machine that simply measures the polarization at an angle he selects. If he selects 45º, every photon ends up with a polarization at that angle or perpendicular to it, regardless of its original polarization. Then Bob, making a vertical measurement, will measure 0 half the time and 1 half the time, regardless of what Alice sent.

Alice learns about Sam’s scheme and wants to reestablish reliable communication with Bob. What can she do?

She tells Bob (using a path that Sam does not overhear) she will send photons at 45º and 135º, so he should measure at one of those angles. Sam’s machine then does not alter the photons. Of course if Sam discovers what Alice is doing, he can rotate his machine back to vertical. Or there are other measures and counter-measures that could be put into action.

This scenario relies on the quantum nature of the photons, and the fact that single photons cannot be measured by Sam except along particular angles of polarization. Thus Alice’s technique for thwarting Sam is not possible with classical bits.