Figure 1

EAEE for the open RBC, with local jump operators $c_j={\sigma }_j^z$. (a) EAEE profile in the long time limit for various unravellings. Solid lines denote homodyne unravellings with changing phase from ${\phi }_j=0$ (red) to ${\phi }_j=\pi /2$ (grey) in increments of $\pi /20$; dashed blue and green lines correspond to the number and EOQT measurements. The insets show time evolution of EAEE for various unravellings and measurement choices of the EOQT. Here $m=n=16$, $\chi =128$. (b) Half-chain EAEE for larger systems (with $\chi =512$). Depending on the homodyne phase, the ensembles display an area law at small ${\phi }_j$ and a volume law at ${\phi }_j\approx \pi /2$. The EOQT method results in an area-law EAEE close to the homodyne unravelling with ${\phi }_j=0$, whereas the number unravelling leads to a volume law EAEE. The phase diagram is shown in the inset. For all data in this figure we used $\alpha /\gamma =0.4$ ($\alpha =1$) and $N=200$. The statistical error bars lie within the lines’ thickness.