Describing quantum metrology with erasure errors using weight distributions of classical codes

• URL: http://arxiv.org/abs/2007.02859v3
• Date: Tue, 21 Feb 2023 05:20:40 GMT
• Title: Describing quantum metrology with erasure errors using weight distributions of classical codes
• Authors: Yingkai Ouyang and Narayanan Rengaswamy
• Abstract summary: We consider using quantum probe states with a structure that corresponds to classical $[n,k,d]$ binary block codes of minimum distance. We obtain bounds on the ultimate precision that these probe states can give for estimating the unknown magnitude of a classical field.
• Score: 9.391375268580806
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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