# Quantum error correction in multi-parameter quantum metrology

@article{Grecki2019QuantumEC, title={Quantum error correction in multi-parameter quantum metrology}, author={Wojciech G{\'o}recki and Sisi Zhou and Liang Jiang and Rafał Demkowicz-Dobrzański}, journal={arXiv: Quantum Physics}, year={2019} }

We derive a necessary and sufficient condition for the possibility of preserving the Heisenberg scaling in general adaptive multi-parameter estimation schemes in presence of Markovian noise. In situations where the Heiseneberg scaling can be preserved, we provide an efficient numerical algorithm to identify the optimal quantum error correcting (QEC) protocol that yields the best estimation precision. We provide examples of significant advantages offered by joint-parameter QEC protocols that…

## 8 Citations

### Optimal approximate quantum error correction for quantum metrology

- Computer SciencePhysical Review Research
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An optimal approximate quantum error correction (AQEC) strategy asymptotically saturating the precision lower bound in the most general adaptive parameter estimation scheme where arbitrary and frequent quantum controls are allowed is proposed.

### Weight Distribution of Classical Codes Influences Robust Quantum Metrology

- Computer ScienceArXiv
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It is shown that the resultant noisy probe can give an estimate of the magnetic field with a precision that scales inversely with the variances of the weight distributions of the corresponding $2^t$ shortened codes.

### Robust Quantum Metrology With Explicit Symmetric States

- Physics, Computer ScienceIEEE Transactions on Information Theory
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It is proved that, for a set of carefully chosen symmetric probe states that lie within certain quantum error correction codes, quantum metrology exhibits an advantage over classical metrology even after the probe states are corrupted by a constant number of erasure and dephasing errors.

### Continuous Symmetries and Approximate Quantum Error Correction

- Computer SciencePhysical Review X
- 2020

The approach provides insight into how time evolution in the bulk corresponds to time evolution on the boundary without violating the Eastin-Knill theorem, and the five-rotor code can be stacked to form a covariant holographic code.

### On the properties of the asymptotic incompatibility measure in multiparameter quantum estimation

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2021

We address the use of asymptotic incompatibility (AI) to assess the quantumness of a multiparameter quantum statistical model. AI is a recently introduced measure which quantifies the difference…

### Photonic quantum metrology

- PhysicsAVS Quantum Science
- 2020

This work discusses the current experimental and theoretical challenges, and the open questions towards implementation of photonic quantum sensors with quantum-enhanced performances in the presence of noise, in the research area of multiparameter quantum metrology, where multiple parameters have to be estimated at the same time.

### Time-local optimal control for parameter estimation in the Gaussian regime

- PhysicsPhysics Letters A
- 2020

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