If you "measure" the bits per character in the base 45 alphanumeric encoding used in QR code, you'd get 5.5 bits per character as 11 bits is used for two characters.
How is it possible to have information less than a bit, a partial bit? What is that ".5" part? Isn't a bit indivisible?
Only in the context of a character doublet is all information expressed. To know the "half bit" part, you cannot "look" at just one character, you have to look at the total. The information is shared between the two characters. Measuring the bits-per-character is only useful when considering the whole system. The "partial bits" is information smeared across the system. Changing the middle bit may change one, or both, characters.
Here's a 11 bit example, where the middle bit is changed and it changes both characters:
(11101001010 vs 11101101010, or '/L' vs '%8' encoded)
The same principle applies to information theory and cryptography. Security can be measured in "partial bits" because it's measured across something larger.
5.5 bits is also the average information content of a single run of the GHZ experiment. In this setup three parties independently choose a binary detector setting and each observe a binary outcome. The first two parties observe an independent random bit regardless of their settings. If an odd number of the parties have their setting "on", then the third party also observes an independently random bit (6 bits total to record, 3 for the settings and 3 for the observations). But if an even number of of the three settings are "on", then the third party's observation is completely determined by the other 5 bits. When the settings are chosen randomly these two possibilities are equally likely so on average it takes 5.5 bits to record the results of the experiment.
How is it possible to have information less than a bit, a partial bit? What is that ".5" part? Isn't a bit indivisible?
Only in the context of a character doublet is all information expressed. To know the "half bit" part, you cannot "look" at just one character, you have to look at the total. The information is shared between the two characters. Measuring the bits-per-character is only useful when considering the whole system. The "partial bits" is information smeared across the system. Changing the middle bit may change one, or both, characters.
Here's a 11 bit example, where the middle bit is changed and it changes both characters: (11101001010 vs 11101101010, or '/L' vs '%8' encoded)
https://convert.zamicol.com/?in=11101001010&inAlpha=01&outAl...
https://convert.zamicol.com/?in=11101101010&inAlpha=01&outAl...
vs changing the last bit only changes the last character: (Using the preceding example, 11101101010 vs 11101101011, or '%8' vs '%9' encoded)
https://convert.zamicol.com/?in=11101101011&inAlpha=01&outAl...
The same principle applies to information theory and cryptography. Security can be measured in "partial bits" because it's measured across something larger.