I am currently analyzing a system of coupled harmonic oscillators in a thermal state and have already asked a question related to this. I have calculated the entanglement entropy of a chain of two harmonic oscillators by taking the partial trace of the thermal state with respect to one harmonic oscillator and taking hte entropy of that and find that the entanglement entropy is finite. As expected as the inverse temperature vanishes the entanglement entropy vanishes as well. Is it possible to swap this entanglement between the coupled harmonic oscillators into two independent harmonic oscillators? How can one mathematically describe this and how would one experimentally realize this?
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