Tripling is I think definitely a hard max since you can send 3 messages, action if true, action if false, + which is which—at least assuming you can reliably send a bit at all without the observation.
More tightly it’s doubling + number of bits required to send a single bit of information.
That sounds about right.
Tripling is I think definitely a hard max since you can send 3 messages, action if true, action if false, + which is which—at least assuming you can reliably send a bit at all without the observation.
More tightly it’s doubling + number of bits required to send a single bit of information.