  What is the energy cost of extracting entanglement from complex quantum
systems? In other words, given a state of a quantum system, how much energy
does it cost to extract m EPR pairs? This is an important question,
particularly for quantum field theories where the vacuum is generally highly
entangled. Here we build a theory to understand the energy cost of entanglement
extraction. First, we apply it to a toy model, and then we define the
entanglement temperature, which relates the energy cost to the amount of
extracted entanglement. Next, we give a physical argument to find the energy
cost of entanglement extraction in some condensed matter and quantum field
systems. The energy cost for those quantum field theories depends on the
spatial dimension, and in one dimension, for example, it grows exponentially
with the number of EPR pairs extracted. Next, we outline some approaches for
bounding the energy cost of extracting entanglement in general quantum systems.
Finally, we look at the antiferromagnetic Heisenberg and transverse field Ising
models numerically to calculate the entanglement temperature using matrix
product states.
