Current memory hard key derivation techniques rely on functions that allow for serialisation on tiny memory, except for requiring a quadratic time penalty.
But, with Quantum's light-speed defying spooky entanglements comes the Question 1: is there currently any memory hard key derivation function that strictly requires all of the memory, without even allowing the slightest serialisation to being with? This might be thought as "infinite time penalty".
Question 2: Is there quantum hashing functions? I wonder if they can be also thought as memory hard key derivers.
My thoughts so far
Arrange $m$ kilograms of entangled quantum with high probability of being mostly in some specific distribution $D$.
Encode the password serially by altering the states of the quantum, 1 by 1, until all of password's $n$ bits are encoded in $n$ quantum states.
This step should instantly alter the states of all of the $m$ kilograms entangled quantum beyond the initial few that got the $n$ bits encoded in them.
Read the states of all of the $m$ kilobytes quantum, perform statistical analysis to account for errors based on the initial distribution $D$, then hash the filtered output into 32 bytes that serve as the "memory hard key".
Reading the quantum would alter their state, but if this alternation is statistically predictable, then this process would be reliable for hashing.
Here, I hope that, an adversary that uses $\ne m$ kilograms cannot possibly reach the same conclusion, because of quantum entanglement's nature that happens at the same instant time, hence eliminating the possibility of any serialisation (can't do it in batches with fewer entangled quantum).
