5 ms·
For practitioners, a rough description of their argument is on pg 7 (note: separable=unentangled, β =1/kb T) of https://arxiv.org/pdf/2403.16850 https://arxiv.o
by gradschoolfail 2y ago
For practitioners, a rough description of their argument is on pg 7 (note: separable=unentangled, β =1/kb T) of https://arxiv.org/pdf/2403.16850 https://arxiv.org/pdf/2403.16850
This state [rho] is the Gibbs state at infinite temperature, and is in the interior of the convex hull of product states. So, as β tends to zero, ρ will eventually enter the interior of this convex hull, making it separable. This happens at a finite β which depends on system size.
- marginalia_nu 2y agoBeen a while since I've been working in the field, but wouldn't we expect this finding through the model of dissipation and decoherence? Seems like Caldeira & Leggett all over again.
- gradschoolfail 2y agoHmm, C&L argument involves taking a classical limit, does it not? This paper seems “fully quantum” (provided that you agree that the maximally mixed “Gibbs” state should not be considered a “classical” limit, only an infinite temp limit)
- marginalia_nu 2y agoYeah maybe that's what's bothering me, what is the high temperature limit if not the classical limit?
- gradschoolfail 2y agoHeh, you might be additionally bothered that for the C&L model, the strong coupling (to heat bath) limit can also be considered the (/a?) classical limit, e.g. https://arxiv.org/pdf/1603.07495 https://arxiv.org/pdf/1603.07495
- gautampk 2y agoI think the naive expectation would be that a hot state would be highly entangled and non-separable. The non-separability is what leads to decoherence when you do a partial trace. You can arbitrarily split any multi-part Hilbert space into a "system" and an "environment" and then trace out the environment. If they are highy entangled with one another then the resulting system-without-environment will be decohered.
- gradschoolfail 2y agoAlternatively formulated, this suggests that an entangled state, if weakly coupled to a bath at high temperature and allowed to thermalize, will become fully disentangled at a finite time. (p1) hinting that something different is happening here (from the C&L model mentioned below.) Indeed the CS guys are probably looking for a way to redefine entanglement (entropy, as you summarized above), to essentially “work” in the same way as what they have in their preprint, but also cover the prethermalized cases..