Quantum entanglement might be responsible for arrow of time in subsystems through decoherence. However, the arrow of time for the wavefunction of the universe seems like a different question.
Before looking for the wave-function of the universe, try to write a wave-function for yourself, and see if it can be done.
What is your weight? Shall we say 70Kg? With which velocity you walk on the street? Shal we say you go slowly, at 1m/s? Then your wavelength is
λ = h/(mv) = 2π×10-27/(7×104×100)cm ≈ 10-33cm.
Now, what are the linear dimensions of your body? Shall we say that you are rather slim and you have a waist of 30cm? Compare that with your wavelength.
In order to become a quatum object, which has a wave-function, your wavelength has to be a good couple of orders of magnitude bigger that your linear dimensions, and not vice-versa.
So, do you still want to find a wave-function for the Universe?
It doesn't. Quantum entanglement doesn't have anything to do with any such asymmetry. It simply describes the fact that probability distributions don't factorize in non-relativistic quantum mechanics. Since they don't factorize, integrating out degrees of freedom leads to a non-local description for the degrees of freedom that haven't been integrated out.
What's, apparently, missing in their analysis is the distinction between thermal fluctuations and quantum fluctuations. What they seem to showi is that a quantum system is in equilibrium with its quantum fluctuations and that subsystems of such a systems are in equilibrium with each other in that sense. But one would have thought that to be known... The quantum fluctuations are controlled by Planck's constant-thermal fluctuations would be controlled by a temperature, however, that's a distinct parameter. And equilibrium with respect to the former is distinct from equilibrium with respect to the latter.
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