Entanglement Energetics at Zero Temperature

We show how many-body ground state entanglement information may be extracted from subsystem energy measurements at zero temperature. Generically, the larger the measured energy fluctuations are, the larger the entanglement is. Examples are given with the two-state system and the harmonic oscillator. Comparisons made with recent qubit experiments show that this type of measurement provides another method to quantify entanglement with the environment.

Figure 1

Energy probabilities ${\rho }_{++}$ and ${\rho }_{--}$ for the spin-boson problem. With increasing coupling to the environment, it is more likely to measure the qubit in the excited state. For the symmetric case $(ϵ=0)$, we use the Bethe ansatz solution, while for the general case, we use a perturbative solution which is only valid for large $ϵ$ or large $\alpha$.

Figure 2

The probability to measure a harmonic oscillator in the ground and first three excited states as a function of $x$ and $y$ (see text). The line traces out the behavior of the Ohmic bath as a function of the coupling in the underdamped range.