Environment-assisted quantum sensing with entangled electronic spins in diamond

Intuitively, enlarging a quantum system by the addition of controllable qubits should only enhance—not decrease—its performance: in other words, any extra qubit should prove a resource. For quantum metrology, the transition from N=1 to N=2 qubits seems especially good for both promised improvement in sensitivity—via N-fold faster phase accumulation—and in readout—via quantum non-demolition measurements. This transition is further motivated in solid-state spin systems that inevitably host a decohering spin bath: its partial conversion into resources simultaneously reduces its size. Thus, utilizing a single nitrogen-vacancy (NV) center and a nearby electron spin (X) in diamond, we explore this question by comparing the performance of N=1 (NV) and N=2 (NV + X) register in ac magnetometry. We find experimentally the ostensible benefits of the resource can be overshadowed by its very cost: namely the increased complexity to perform the same task—resulting in decreased control fidelity and duty cycle—and sensitivity to noise—resulting in decreased dynamic range. We analytically confirm these results and find a parameter space in which the bath qubit will prove a resource. Extending this work for few-qubit algorithms should aid designs of small-scale registers with a quantum advantage.