Slightly off topic... I was excited to realize that this was by Nicole Yunger Halpern, who also wrote this interesting paper on quantum voting systems and a quantum analog of Arrow's impossibility theorem: https://arxiv.org/pdf/1501.00458
"The idea that quantum effects could have an important role in brain function is not new, but is routinely dismissed as wildly implausible. Matthew Fisher begs to differ. And those who read his paper (as I hope many will) are bound to conclude: This old guy’s not so crazy. He may be onto something. At least he’s raising some very interesting questions."
A lot of hypothesis and speculation in this, but nevertheless very intriguing. One thing that caught my attention is how the molecular structure of a lot of common psychedelics (Psilocybin, DMT) have pockets, where quantums are allowed to be in superposition, and during the process of metabolizing we are essentially collapsing them.
Can anyone with a background in quantum information theory tell me how QI models the distinction between a quantum system being measured or unitarily evolved? Nicole Yunger Halpern talks about these things as if the measurement process were a well-defined thing happening at a specific instant in time. How and what do quantum information theorists think about the measurement problem these days?
You treat them as separate things. Kinda. You have the measurement mechanism and you have the unitary evolution mechanism. There are varying degrees of sophistication for modeling the measurement mechanism, and there's ways to have unitary evolution with simultaneous measurement, as well as weak measurement, and there's systems where you can probe the dynamics of a measurement. For instance, you can "watch" a quantum jump or even stop and reverse it (Z. K. Minev et. al. 2018). Generally these things are all modeled using the Stochastic Master Equation. In the end though, the SME is just unitary evolution of a small system coupled to a large markovian bath, with a Bayesian update added. In other words, one could derive the SME by taking an infinitesimal evolution of the unitary system (coupled to the bath) followed by an infinitesimal bayesian update, followed by unitary, followed by Bayesian update, etc. These things are all well covered by Gardiner Zoller 97, and Dan Steck's quantum optics notes, available at http://atomoptics-nas.uoregon.edu/~dsteck/teaching/quantum-o... .
Some would say that the SME is the fundamental thing, the Maxwell's equations of quantum information with measurement, and that the instantaneous measurement you may be familiar with is just a limit of the SME's evolution. Some might also say that the SME is a thing you derive from weakly coupling a stream qubits to a system and then performing hard, instantaneous measurement on those qubits. The math makes no distinction.
Most QI professionals do not worry about the philosophical "measurement problem", because it does not matter in their daily work (the math just works). However, it is certainly interesting and it might end up being important for the foundations of quantum mechanics.
By the way, here is something you might want to look up: in the context of Lindbladian (non-unitary) evolution or in the context of weak quantum measurements, the measurement problem is not particularly obvious or disturbing. At the end it is still there, but these toolkits give you a way to reinterpret it as an uninteresting detail of the theory, not as a horrible stain.
> the distinction between a quantum system being measured or unitarily evolved
When you try to describe a part of an entangled quantum system, independently of the whole, you will be forced to use probabilities in your description. This is quantum measurement.
I don't think I would call this a "measurement". A measurement, in the Copenhagen interpretation, is a fundamentally non-unitary process.
What you're describing is simply tracing out the environment, so that we end up with a mixed state. The complete density matrix, however, is still being governed by the Von-Neumann equation and therefore evolving unitarily. So I assume what you're saying is that we don't need to model measurements separately since their results would be described by statistical ensembles and, at the level of a subsystem, you can't really tell the difference between a genuinely entangled state and a statistical ensemble, anyway?
This seems fascinating but most of it is way above my understanding. The main conclusion I got was that “entanglement between phosphorus nuclear spins in Posner molecules might stimulate coordinated neuron firing”, and that this could have implications in a wide array of other applications, but requires further research to be proven true.
Also can't really understand what this is, but I seem to have arrived at a conclusion of this being an answer to "what if we could store quantum information in the brain's cells and call it 'quantum cognition'". Is there something else going on?
Theoretically, it's not just limited to brains and neurons! Phosphates are extremely prevalent in living organisms, and Posner molecules are just a special arrangement of these common molecules which can prolong entangled quantum states. For example, from the blog post:
"Posners are believed to exist in us and might participate in bone formation."
And on a slightly different level, from the abstract: "This work opens the door for the QI-theoretic analysis of biological qubits and Posner molecules."
There are also a few interesting interactions with that stored QI:
* QI can be retrieved from Posners (into neurons via neurotransmitters).
* QI can be teleported between Posners, while suffering noise.
* Quantum error detection can be solved with Posners.
* Most importantly, Posners can participate in quantum computation. "Posner operations can prepare a state that fuels universal measurement-based quantum computation."
