Achieving metrological limits using ancilla-free quantum error-correcting codes

• URL: http://arxiv.org/abs/2303.00881v2
• Date: Sun, 14 Apr 2024 19:34:34 GMT
• Title: Achieving metrological limits using ancilla-free quantum error-correcting codes
• Authors: Sisi Zhou, Argyris Giannisis Manes, Liang Jiang,
• Abstract summary: Existing quantum error-correcting codes generally exploit entanglement between one probe and one noiseless ancilla of the same dimension. Here we construct two types of multi-probe quantum error-correcting codes, where the first one utilizes a negligible amount of ancillas and the second one is ancilla-free.
• Score: 1.9265037496741413
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum error correction (QEC) is theoretically capable of achieving the ultimate estimation limits in noisy quantum metrology. However, existing quantum error-correcting codes designed for noisy quantum metrology generally exploit entanglement between one probe and one noiseless ancilla of the same dimension, and the requirement of noiseless ancillas is one of the major obstacles to implementing the QEC metrological protocol in practice. Here we successfully lift this requirement by explicitly constructing two types of multi-probe quantum error-correcting codes, where the first one utilizes a negligible amount of ancillas and the second one is ancilla-free. Specifically, we consider Hamiltonian estimation under Markovian noise and show that (i)~when the Heisenberg limit (HL) is achievable, our new codes can achieve the HL and its optimal asymptotic coefficient; (ii)~when only the standard quantum limit (SQL) is achievable (even with arbitrary adaptive quantum strategies), the optimal asymptotic coefficient of the SQL is also achievable by our new codes under slight modifications.

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