[Physics] Classical/Quantum Coin Toss

classical-mechanicsprobabilityquantum mechanics

I am having a brainfreeze moment and have confused myself, help appreciated!

Classical Coin: Heads OR tails.

Quantum Coin: Superposition Heads AND Tails.

Classical Mechanics: Deterministic (in principle, if not in practice) if I repeat the same experiment I get the same result.

Quantum Mechanics: Non-deterministic no way that I can predict if I get heads or tails.

Now think of some physical implementation of a quantum coin perhaps I send some electron to mirror, afterwards it is on a superposition on both sides of the mirror. Perhaps reflected (heads) with probability 0.9 and transmitted (tails) with probability 0.1.

My question is does a classical analogy exist here? It can't be both deterministic and agree with the probabilities predicted by quantum mechanics right? Is the problem just that I should not be applying classical physics at all here? Does this question even make any sense?

Best Answer

1) Classical is not equivalent to determinism. You could use probabilities in classical problems (Statistical mechanics, for instance)

2) It makes more sense, in fact, to consider the difference between a classical probabilistical problem, and a quantum probabilistical problem.

3) Quantum correlations are stronger than classical correlations, this is because, in quantum mechanics, we work with probabilites complex amplitudes $\psi$, instead of working directly with probabilites $p$ (The relation is $p = |\psi|^2$). Some experiment results cannot be explained by classical correlations.

4) If you consider, for instance, a superposition 1-spin quantum state like $\psi = |+_z>$ + $|-_z>$, a measurement of the spin on the $z$ axis will gives you always $+1$ OR $-1$. So, from the point of view of the measurement, it is an OR, it is not a AND. You will have 50% probability to measure +1, and 50% probability to measure -1.

Related Question