Quantum Information for Quantum Cats (9)

Up-Down Coding and Right-Left Coding

We are now equipt with sufficient quantum armaments, and are ready to do some information exchange.

Suppose Alice's basis set for quantum arrow preparation and Bob's basis set for observation are identical. Clearly, the direction of the arrow prepared by Alice is reproduced at Bob's detector fo 100% probability. So if Alice tells Bob that she used Up-Down mode of quantum stae preparation and send the arrow, Bob is able to find the arrow in exactly the same state all the time. We can view this as the exchange of information between Alice and Bob. Namely, Alice encode a bit, "0" or "1" into quantum states with

and send the quantum signal | up > or | down >, which Bob receives and decode using

to reproduce the original bit. Same information sharing can be achieved with alternative set

if they are taken up simultaneously by Alice and Bob.

Now suppose, however, that encoding mode and decoding mode are different. For example, Alice encode "0" in Up-Down mode, and send the quantum state | up >. If Bob sets up the detector in Right-Left mode, he will observe the state | right > in 50% chance which is to be interpreted as "0", and in another 50% chance, he will observe the state | left > that he interprete as '1". So the chance of correct information sharing is 50%, which is as bad as random guess.

In summary, if Up-Down mode and Right-Left mode are used in mixture for both encoding and decoding, the correct sharing of the informational bits is achived only when the same mode is used for Alice's encoding and Bob's decoding.