> Or is this simply not seen as useful information in some specific definition?
You are adding another conditional but nested conditionals still all rely on the first.
We are getting 1 bit of data:0|1; from this entrangled pair.
Fleet1 has Strategy0 in case their measurement reads 0.
Strategy0 requires Fleet2 to act using Strategy2 for the highest probability of success.
Fleet1 also has Strategy1 in case their measurement reads 1.
If Strategy1 also requires Fleet2 to act using Strategy2 for highest probability of success then Fleet1's measurement is useless as Fleet2 can just use Strategy2 in both events.
If instead Strategy1 requires a new Strategy3, and even though you could communicate which of these strategies to choose faster than we know how to communicate that electromagnetically, our 1 bit of information is still useless because you would still have to prepare for both eventualities.
Both pairs: Strategies02 and Strategies13; would equally have to have the same probability of success because if one is favoured over another then using this technique to decide your fleet movements could result in your allowing the possibility for the measurement to order you in a strategy you know is less likely to be successful.
This is what I was trying to get at by using the word 'desirable'.
Fleet2 may appear to be waiting on Fleet1 for orders, but in fact both fleets are waiting on their orders from the first measurement.
I think an issue with communicating the lack of information transmission is that the statement usually fails to acknowledge two aspects:
1) We are unable to reliably force any one entangled particle to a specified state prior to measurement. ( You mention this more passively in a gp >"First of all, we don't know which color is in which envelope at the start." )
2) After measuring we have now entangled our particle to our measurement. So, if after our measurement we change the state of our particle the previously entangled particle fails to reliably correlate.
Information is transmitted; it's useful information that we are unable to communicate.
If I give you instructions saying if the envelope contains this then do this or if it contains that then do that, you can use the information from the particle's entanglement to make that decision, but because of 2) you can only use it to make that decision reliably once, and because of 1) those two outcomes will have to be equally desirable for this form of communication; making it useless. Just roll a dice.
You are adding another conditional but nested conditionals still all rely on the first.
We are getting 1 bit of data:0|1; from this entrangled pair.
Fleet1 has Strategy0 in case their measurement reads 0.
Strategy0 requires Fleet2 to act using Strategy2 for the highest probability of success.
Fleet1 also has Strategy1 in case their measurement reads 1.
If Strategy1 also requires Fleet2 to act using Strategy2 for highest probability of success then Fleet1's measurement is useless as Fleet2 can just use Strategy2 in both events.
If instead Strategy1 requires a new Strategy3, and even though you could communicate which of these strategies to choose faster than we know how to communicate that electromagnetically, our 1 bit of information is still useless because you would still have to prepare for both eventualities.
Both pairs: Strategies02 and Strategies13; would equally have to have the same probability of success because if one is favoured over another then using this technique to decide your fleet movements could result in your allowing the possibility for the measurement to order you in a strategy you know is less likely to be successful.
This is what I was trying to get at by using the word 'desirable'.
Fleet2 may appear to be waiting on Fleet1 for orders, but in fact both fleets are waiting on their orders from the first measurement.