[ExI] quantum brains

[scerir]

Damien:
And of course since I'm persuaded that some psi phenomena are real, *something* weird as
shit is needed to account for them, something that can either do stupendous simulations in
multiple worlds/superposed states, or can modify its state according to outcomes in the
future. If that's not QM, it's something equally hair-raising that electronic computers
aren't built to do.

#

But what is the quantum? J.Wheeler said there was just a "Merlin principle" (named after
the legendary magician who, when pursued, changed his form again and again). That is to
say: the more we pursue the quantum, the more it changes. Here below a short list of
changing, evolving concepts, rules, topics, problems.

Discreteness, indeterminism, probabilities, uncertainty relations, entropic uncertainty
relations, non-definiteness of values before measurements, no (in general) retrodiction,
essential randomness, incompressibile randomness and undecidability, a-causality,
contextuality, real/complex/quaternionic formalisms, Hilbert spaces or logical structures
representation, correspondence principle, complementarity, duality, smooth transitions,
quanta as carriers of limited information, second order complementarity, superpositions,
entanglements, conditional entropies can be negative, algebraic non-separability,
geometric non-locality, local hidden variables, non-local hidden variables, non-local
hidden variables plus time arrow assumption,  a-temporality, conspiracy theories, which
one: free will or space-time?, time (in general) is not an observable, quantum
interferences, Feynman rules, indistinguishability, erasure of indistinguishability,
second order interferences, quantum dips, quantum beats, interferences in time, fractal
revivals, ghost imaging, from potentiality to actuality via measurements, objective
reduction of wave-packet, subjective reduction of wave-packet, pre-measurements, weak
measurements, interaction-free measurements, two-time symmetric quantum theory, no-cloning
principle, no-deleting principle, no-signaling principle (relativistic causality), are
there negative probabilities?, de-coherence, sum-over-paths, beables, many-worlds,
many-and-consistent-histories, the transactional, and so on, and on, and on.

Is there also a "superquantum" domain? There is for sure since Sandu Popescu and Daniel
Rohrich wrote 'Quantum Nonlocality as an Axiom' (in Foundations of Physics, Vol. 24, No.
3, 1994). Essentially it is the domain of superquantum correlations, stronger than the
usual quantum correlations. As we all know John Bell Bell proved that quantum entanglement
enables two space-like separated parties to exhibit classically impossible correlations.
Even though these correlations are stronger than anything classically achievable, they
cannot be harnessed to make instantaneous (faster than light) communication possible. Yet,
Popescu and Rohrlich have shown that even stronger correlations can be defined, under
which instantaneous communication remains *impossible* (relativistic causality is safe).
This raises the question: Why are the correlations achievable by quantum mechanics not
maximal among those that preserve relativistic causality? There are no good answers to
this question. But it is possible to show that superquantum correlations would result in a
world in which the so called 'communication complexity' becomes 'trivial' [1] but 'magic'
[2] [3].

So, good news for the SF writers. Or it seems so.

s.


[1] Assume Alice and Bob wish to compute some Boolean function f(x, y) of input x, known
to Alice only, and input y, known to Bob only. Their concern is to minimize the amount of
(classical) communication required between them for Alice to learn the answer. It is clear
that this task cannot be accomplished without at least some communication (even if Alice
and Bob share prior entanglement), unless f(x, y) does not actually depend on y, because
otherwise instantaneous signalling would be possible. Thus, we say that the communication
complexity of f is 'trivial' if the problem can be solved with a single bit of
communication (a single bit of communication also protects relativistic causality).

[2] A nonlocal box is an imaginary device that has an input-output port at Alice's and
another one at Bob's, even though Alice and Bob can be space-like separated. Whenever
Alice feeds a bit x into her input port, she gets a uniformly distributed random output
bit a, locally uncorrelated with anything else, including her own input bit. The same
applies to Bob, whose input and output bits we call y and b, respectively. The "magic"
appears in the form of a correlation between the pair of outputs and the pair of inputs.
Much like the correlations that can be established by use of quantum entanglement. This
device (nonlocal box, also named PR box) is a-temporal. Alice gets her output as soon
as she feeds in her input, regardless of if and when Bob feeds in his input, and vice
versa. Also inspired by entanglement, this is a one-shot device. The correlation appears
only as a result of the first pair of inputs fed in by Alice and Bob, respectively.

[3] There is some literature, in example:
http://arxiv.org/abs/0907.3584
http://arxiv.org/abs/quant-ph/0501159