Protocol for certifying entanglement in surface spin systems using a scanning tunneling microscope

Certifying quantum entanglement is a critical step toward realizing quantum-coherent applications. In this work, we show that entanglement of spins can be unambiguously evidenced in a scanning tunneling microscope with electron spin resonance by exploiting the fact that entangled states undergo a free time evolution with a distinct characteristic time constant that clearly distinguishes it from the time evolution of non-entangled states. By implementing a phase control scheme, the phase of this time evolution can be mapped back onto the population of one entangled spin, which can then be read out reliably using a weakly coupled sensor spin in the junction of the scanning tunneling microscope. We demonstrate through open quantum system simulations with currently available spin coherence times of T₂ ≈ 300 ns, that a signal directly correlated with the degree of entanglement can be measured at temperatures of 100–400 mK accessible in sub-Kelvin scanning tunneling microscopes.