photonic29
Is that a fair comparison? Yes, in either case, the experimenter is limited in his predictive capability by the information available to him. But in a chaotic system, your predictive power can be improved arbitrarily by surveying more information with greater precision. As I understand it-- and hopefully you can clarify if this is accurate-- decoherence forbids a measurement from receiving information from a branched outcome, so even if you take a measurement with arbitrary access to information now and repeat the same measurement in the future, there becomes a set of information that is fundamentally off limits to the observer in a given branch.
For what useful definition of deterministic? If a measurement comes with decoherence into multiple non-inteferring branches, then certainly the state evolves in a predictable way from "god's eye", but not from the perspective of the experiment occupying any given branch.
As I understood the description, they're not claiming that the process of entanglement encodes the information being transmitted, but rather that more information-carrying dimensions can now be entangled, so now those extra dimensions can also enjoy the proposed security benefits. For a system relying on those features, the throughput is effectively increased because more channels are eligible.
I should have distinguished better, but what you're more rigorously calling an eigenstate of a measurement operator, I'm calling an observable state. There is something lost in translation to an audience unfamiliar with terms like eigenstate, but that was my attempt. Would you suggest a better one?
>Note that this is only true on a collapse interpretation, like Copenhagen. On a no-collapse interpretation, like MWI, the "observation" is just an interaction that entangles the state of the measuring device with the state of the system being measured
The greater point being addressed is that MWI is no more deterministic than Copenhagen.
>Yes, it is; but it isn't observable by a simple method like looking to see if the coin is heads or tails. But according to QM, every state is an eigenstate of some operator
Some hermitian operator? But more to the point, if looking at the coin is the only operator at our disposal in the simple example, then its eigenstates are the ones we care about.
Now, you could definitely take issue with this example, because you could argue that the rotation of the coin is well described, so with initial conditions, you can predict its position at any given moment. But imagine a microscopic quantum system, and, for the sake of this simple explanation, believe that its "rotating through the air" state really does not have any precise heads or tails definition. Until something gets in the way of that system, creating an interaction that exchanges information about its observable state, it's not meaningful to say that it's in one of the observable states at all.
A superpositition of states, as such, is essentially the representation of a state in terms of a basis set of observables. In the case of the coin, heads and tails are the two observable states, they are orthogonal, and they fully represent the state space of the coin. You could flip the coin, and put its state vector into the form of sqrt(2)/2 * Heads + sqrt(2)/2 * Tails. This state isn't observable, but it can be described in terms of observable components, where the coefficients represent the probabilities that a given observable state will be measured upon observation.
Indeed it can. Roughly put, if information about the state left the undetermined system, a measurement has been made. One of the most frustrating interpretations of literature such as this is the idea that there is something spooky, special, and reality-making about a conscious mind. Lots to think about there philosophically, but the physics happens at lower levels of abstraction.
This study suggests some measurable effects, though not as simple and direct as the appearance of an EEG band at the target frequency: http://www.researchgate.net/publication/239803901_EEG_Cohere...
I think it's relatively clear that the tech works in a controlled setting. It even works surprisingly well in an uncontrolled setting. But as these devices become more mass marketed, sensitivity and selectivity become a much bigger concern. If you detect 99% of all true events, that looks great at first. But how useful is it if only 10% of all detected events are true? Selectivity must be tight before we can issue strong health warnings to masses of people. The challenge of real world noise can be bigger than getting the first principle tech to work.