When I say quantum state, I am referring to what a quantum state is in general physics literature. In the case of “n” qubits that would be a norm 1 vector in the space $\bigotimes_{k=1}^n\mathbb{C}^2$ or if you prefer, a density matrix in the space of operators on said space.
Discussion
Working on a response as I blend this in the what I am currently working on.
On first glance; I think this seems self evident by simple observation.
In any Block you know the total number of UTXOs = n qubits. Only what is in a block is spent (1); all other UTXOs are 0 by deduction; all states are known and measured each block. Each block is a unique tensor product for all UTXOs/qubits in relation to the previous mined block. I’m not sure it’s possible to quantify the probability for each UTXO, you also need to know who will mine the next block as only their mempool is what actually matters.
Qubit/UTXO quantity of each computation state (Block) dynamically changes depending on how the network uses their UTXOs.
Hope this helps somewhat for now.
I also do not believe you can quantify the probabilities. But this leaves my original question: what decoherence is solved? If it is not possible to even describe the state then what is the use?
Just because you cannot quantify the probabilities does not mean they are not real. The state is described in every single block, you have a full history of every UTXO/qubit state from Genesis. Your UTXOs remain spendable and preserved to the rightful private key regardless of time; that’s the decoherence solved. What is the value in computing the probabilities of the next future state; anyone pretending to know the future is lying.
I’m not here making the claim that quantum computing can do anything physics/comp scientists claim it can do. It’s entirely a fiat theory that remains unproven backed by fiat & academic science. All I know is that bitcoin has been here for 16 years and all UTXOs/qubits remain coherent; I’m still waiting for a second best quantum computer. I doubt it will compete with bitcoin if it can only be operated by authority of a singular centralized laboratory.
However, it just so happens these qubits or UTXOs serve as what we call “perfect money”. Maybe it’s the perception and possibilities of what a quantum computer is or can be is what is actually wrong.
Bitcoin is not claiming to reduce all uncertainty, break encryption, ect. It flourishes on uncertainty. Computing an energy backed free market with 1:1 money is a much better solution to quantum computing than physicists pretending to be god; implying they can remove the veil on all uncertainty, they haven’t a clue. It’s all fiat science.
All I know is Bitcoin exists and “centralized quantum computers” continue to fail for good reason, centralization.