Fig. 5: Experimental verification of topological resilience.
a QST results for the example state \(\left\vert \Psi \right\rangle=\frac{1}{\sqrt{2}}\left({\left\vert 3\right\rangle }_{A}{\left\vert H\right\rangle }_{B}+{\left\vert 0\right\rangle }_{A}{\left\vert V\right\rangle }_{B}\right)\) in the presence of varying noise levels from pure (point 1, γ = 0.80) to partially-mixed (point 2, γ = 0.45) and then maximally-mixed (point 3, γ = 0.25). b The experimental density matrices extracted from the QST of each state. c The quantum Stokes vector, \(\overrightarrow{S}(x,y)={({S}_{x},{S}_{y},{S}_{z})}^{T}\), derived from each density matrix corresponding to points 1 to 3 in part a. d Skyrmion number as a function of quantum contrast, with experiment (points) in excellent agreement with theory (dashed lines). The collapse of the topology when the maximally-mixed state limit (Qc = 1) is reached is shown in the zoomed-in inset. e While the Skyrmion number is stable to noise, typical entanglement witnesses such as concurrence, fidelity and purity are not, as shown experimentally (points) and theoretically (lines).
