论文标题
使用经典代码的重量分布来描述使用擦除错误的量子计量学
Describing quantum metrology with erasure errors using weight distributions of classical codes
论文作者
论文摘要
量子传感器有望成为量子技术的突出用例，但实际上，噪声很容易降低其性能。例如，量子传感器可能会遭受擦除错误的折磨。在这里，我们考虑使用具有与经典$ [n，k，d] $最小距离$ d \ geq t+1 $的二进制块代码相对应的结构的量子探针状态。我们获得了这些探针状态可以给出的最终精度的界限，以估算量子探针状态的$ t $ Qubits之后的经典场的未知幅度。我们表明，量子Fisher信息与相应$ 2^t $缩短的代码的重量分布的方差成正比。如果固定代码与$ d \ geq t+1 $的缩短代码具有非平凡的权重分布，则通过将该代码与增加长度的重复代码相连获得的探针状态，启用了渐变的最佳现场感应，从而被动地可容忍$ t $擦除错误的错误。
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.
