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Quantum Processes Systems, and Information by Michael Westmoreland, Benjamin Schumacher

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20  Error correction

20.1  Undoing errors

image

Suppose the random variable X represents a message that Alice wishes to send to Bob. What Bob actually receives from the communication system is Y. It is not necessarily the case that X and Y are equal. Bob can, however, perform further data processing on Y to obtain image, his estimate of Alice’s message. The probability of error is

image

(20.1)

Under what circumstances can Bob reconstruct Alice’s message reliably, ...

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