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Subquantum Information and Computation
Antony Valentini
(Submitted on 11 Mar 2002 (v1), last revised 12 Apr 2002 (this version, v2))
"It is argued that immense physical resources - for nonlocal communication, espionage, and exponentially-fast computation - are hidden from us by quantum noise, and that this noise is not fundamental but merely a property of an equilibrium state in which the universe happens to be at the present time. It is suggested that 'non-quantum' or nonequilibrium matter might exist today in the form of relic particles from the early universe. We describe how such matter could be detected and put to practical use. Nonequilibrium matter could be used to send instantaneous signals, to violate the uncertainty principle, to distinguish non-orthogonal quantum states without disturbing them, to eavesdrop on quantum key distribution, and to outpace quantum computation (solving NP-complete problems in polynomial time)."

Signal locality (aka nonlocal communication, passion at a distance, no cloning an arbitrary quantum state etc) follows from the linearity and unitarity of the Schrodinger equation for multi-particle entangled states psi(x1,x2, ... xN) in configuration space

-ihpsi,t = Hpsi

H is a linear Hermitian operator

U = e^iHt/hbar is unitary

UU* = U*U = 1

However, when there is spontaneous broken symmetry we get a time dependent Landau-Ginzburg (TDLG) equation that is nonlinear for a LOCAL order parameter  PSI(x) condensate in ordinary space and generally has a non-unitary dissipative time dependence.

(-iah + b)PSI,t = H'PSI

N = e^iH't/hbar

NN* =/= 1

Therefore, signal nonlocality should happen in such a case when b =/= 0.

There is a large literature in soft-condensed matter physics for models of a and b for different complex systems.

In 2nd quantized notation

PSI(operator) = PSI(c-number condensate) + PSI(q-number)

PSI(q-number) = Sum over modes k dependent on boundary conditions ak

ak|nk> = nk^1/2|nk-1>  in Fock space


Therefore the complete TDLG equation will be coupled to INCOHERENT RANDOM micro-quantum q-number noise that does obey the normal quantum rules in configuration space. The c-number ground state condensate COHERENT NON-RANDOM "signal" in ordinary space obeys a new set of rules "More is different." (P.W. Anderson).

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