nowledge of the re-encoding transformation U, the recipient is then able to retrieve the original message state 1/>/ by performing the reverse operation, namely = This above notion of message re-encoding being understood, consider now that the originator has the option of implementing the following trick. Assume indeed that she or he performs a measurement on the third qubit of 14'): If the outcome of the fuzzy measurement is 0, then the message state (and its post- measurement) is of the form /xy0), a typical state; If the outcome of the fuzzy measurement is 1, then the message state (and its post- measurement) is of the form |zk1), an atypical state. Based on these two fuzzy measurement outcomes, the originator then takes the corre- sponding actions: If the outcome is 0, the remaining two qubits /xy), which we call 1/compl), are sent through the quantum channel; If the outcome is 1, a 2-qubit state 1/comp2) is sent through the quantum channel; such that U-1 (1Ycomp2)0))=2aaha), which is the most likely typical state. From the recipient's end, it is understood as a rule that the qubit |0) must be appended to the incoming message, which, thus, becomes either 1/comp1) x |0) or 1/comp2) x |0). The rule also has it that the inverse transform U-1 must be applied. From this "decompression" operation, the recipient, thus, obtains either one of the two states: (22.18) On decompression, the recipient is, thus, able to retrieve the original message state 1/typ), while occasionally getting a "junk" or "best-guess" message Ihahaha). This coding trick, along with the agreed rules, has, thus, made it possible for the originator to transmit the 3-qubit original message to the recipient in a compressed, 2-qubit message, and for the recipient to uncompress it into a 3-qubit message. But how faithful is this whole operation? To answer this question, we must express the density operator P of the uncompressed message, after reconstruction by the recipient. The original message, 1/s/, has density operator 1/s/ (V/. Its projection on