you cannot use the category of “quantum random” to actual coin flip, because an object to be truly so it must be in a superposition of at least two different pure states, a situation that with a coin at room temperature has yet to be achieved (and will continue to be so for a very long time).
Given the level of subtlety in the question, which gets at the relative nature of superposition, this claim doesn’t quite make sense. If I am entangled with a a state that you are not entangled with, it may “be superposed” from your perspective but not from either of my various perspectives.
For example: a projection of the universe can be in state
(you observe NULL)⊗(I observe UP)⊗(photon is spin UP) + (you observe NULL)⊗(I observe DOWN)⊗(photon is spin DOWN)
= (you observe NULL)⊗((I observe UP)⊗(photon is spin UP) + (I observe DOWN)⊗(photon is spin DOWN))
The fact that your state factors out means you are disentangled from the joint state of me and the particle, and so together the particle and I are “in a superimposed state” from “your perspective”. However, my state does not factor out here; there are (at least) two of me, each observing a different outcome and not a superimposed photon.
Anyway, having cleared that up, I’m not convinced that there is enough mutual information connecting my frontal lobe and the coin for the state of the coin to be entangled with me (i.e. not “in a superposed state”) before I observe it. I realize this is testable, e.g., if the state amplitudes of the coin can be forced to have complex arguments differing in a predictable way so as to produce an expected and measurable interference paterns. This is what we have failed to produce at a macroscopic level, and it is this failure that you are talking about when you say
a situation that with a coin at room temperature has yet to be achieved (and will continue to be so for a very long time).
I do not believe I have been shown a convincing empirical test ruling out the possibility that the state is not, from my brain’s perspective, in a superposition of vastly many states with amplitudes whose complex arguments are difficult to predict or control well enough to produce clear interference patterns, and half of which are “heads” state and half of which are “tails” states. But I am very ready to be corrected on this, so if anyone can help me out, please do!
Given the level of subtlety in the question, which gets at the relative nature of superposition, this claim doesn’t quite make sense. If I am entangled with a a state that you are not entangled with, it may “be superposed” from your perspective but not from either of my various perspectives.
For example: a projection of the universe can be in state
(you observe NULL)⊗(I observe UP)⊗(photon is spin UP) + (you observe NULL)⊗(I observe DOWN)⊗(photon is spin DOWN) = (you observe NULL)⊗((I observe UP)⊗(photon is spin UP) + (I observe DOWN)⊗(photon is spin DOWN))
The fact that your state factors out means you are disentangled from the joint state of me and the particle, and so together the particle and I are “in a superimposed state” from “your perspective”. However, my state does not factor out here; there are (at least) two of me, each observing a different outcome and not a superimposed photon.
Anyway, having cleared that up, I’m not convinced that there is enough mutual information connecting my frontal lobe and the coin for the state of the coin to be entangled with me (i.e. not “in a superposed state”) before I observe it. I realize this is testable, e.g., if the state amplitudes of the coin can be forced to have complex arguments differing in a predictable way so as to produce an expected and measurable interference paterns. This is what we have failed to produce at a macroscopic level, and it is this failure that you are talking about when you say
I do not believe I have been shown a convincing empirical test ruling out the possibility that the state is not, from my brain’s perspective, in a superposition of vastly many states with amplitudes whose complex arguments are difficult to predict or control well enough to produce clear interference patterns, and half of which are “heads” state and half of which are “tails” states. But I am very ready to be corrected on this, so if anyone can help me out, please do!