Fig. 2: Two-spin entanglement scheme using sensor spin read-out.

a Two relatively long-lived spins (A, B) are entangled while a third, short-lived sensor spin (R) is used for the read-out. Each pair of titanium and iron (Fe) atom serves as a qubit in the ESR-STM experiment. b Energy level diagram showing CNOT (red), Hadamard (blue) spin control and read-out (purple). c Actual pulse scheme as implemented in the simulations as well as expectation values along x, y, z for each spin involved in case of ϕ = π. The top panel shows the implemented pulse scheme where X and Y represent the rotation axes and the subscript indicates the rotation angle. The next two panels show the time-evolution of spins A and B under driving, followed by the concurrence \(\mathcal{C}\) which serves as direct measure of entanglement in the simulation. The last panel shows the time evolution of the sensor spin when reading out spin A as well as the corresponding time-averaged entanglement witness \({{\mathcal{W}}}_{R}({t}_{{\rm{meas}}})\). The entanglement witness reaches the steady state within the first ≈ 40 ns of the measurement time. Idealized parameters were used for clarity: T = 10 mK, Ω = 0.04 GHz, \({T}_{1}^{R}\) = 20 ns, no relaxation for A and B, and Larmor frequencies and exchange couplings are in GHz as indicated in (a).