Quantum sensors are expected to be a prominent use-case of quantum technologies, but in practice, noise easily degrades their performance. Quantum sensors can for instance be afflicted with erasure errors. Here, we consider using quantum probe states with a structure that corresponds to classical $[n,k,d]$ binary block codes of minimum distance $d \geq t+1$. We obtain bounds on the ultimate precision that these probe states can give for estimating the unknown magnitude of a classical field after at most $t$ qubits of the quantum probe state are erased. We show that the quantum Fisher information is proportional to the variances of the weight distributions of the corresponding $2^t$ shortened codes. If the shortened codes of a fixed code with $d \geq t+1$ have a non-trivial weight distribution, then the probe states obtained by concatenating this code with repetition codes of increasing length enable asymptotically optimal field-sensing that passively tolerates up to $t$ erasure errors.

翻译：量子传感器有望成为量子技术的突出应用场景，但在实践中噪声轻易会降低其性能。例如，量子传感器可能遭受擦除误差的影响。本文考虑使用具有与最小距离$d \geq t+1$的经典$[n,k,d]$二进制分组码相对应的结构的量子探针态。我们推导了这些探针态在量子探针态最多$t$个量子比特被擦除后，用于估计经典场未知大小的极限精度上限。研究表明，量子Fisher信息与对应的$2^t$个缩短码的权重分布的方差成正比。如果固定码（$d \geq t+1$）的缩短码具有非平凡权重分布，那么将该码与长度递增的重复码级联而获得的探针态能够实现渐近最优的场感测，并可被动容忍最多$t$个擦除误差。