Multiparameter Estimation with Two-Qubit Probes in Noisy Channels
Abstract
1. Introduction
2. Preliminaries
2.1. Parameter Estimation and Quantum Fisher Information
2.2. Holevo and Nagaoka–Hayashi Bounds
2.3. Quantum Channels
3. Results
3.1. Decoherence Channel
3.1.1. Single-Qubit Probe
3.1.2. Two-Qubit Probe
3.1.3. Decoherence of Both Qubits
3.1.4. Collective Measurements on Multiple Copies of the State
3.2. Amplitude Damping Channel
3.2.1. Single-Qubit Probe
3.2.2. Two-Qubit Probe
3.2.3. Decoherence of Both Qubits
3.2.4. Collective Measurements on Multiple Copies of the State
3.3. Phase Damping Channel
3.3.1. Single-Qubit Probe
3.3.2. Two-Qubit Probe
3.3.3. Decoherence of Both Qubits
3.3.4. Collective Measurements on Many Copies of the State
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Conflicts of Interest
Appendix A. Computing the SLD Bound for Single Parameter Estimation in the Decoherence Channel
Appendix B. Explicit Construction of Xx Matrix for Single Parameter Estimation in the Decoherence Channel
Appendix C. Measurement Scheme Attaining the Nagaoka Bound for Single Qubit Probes Subject to the Decoherence Channel
Appendix D. Measurement Saturating the Nagaoka Bound for Estimating Two Parameters with a Two-Qubit Probe Subject to the Decoherence Channel
Appendix E. Measurement Scheme Required to Saturate the NHB for Estimating Three Parameters with the Optimal Two-Qubit Probe in the Decoherence Channel
Appendix F. Measurement Saturating the Nagaoka Bound for Estimating Two Parameters with Two Copies of a Single Qubit Probe Subject to the Decoherence Channel
Appendix G. POVM’s Attaining the Nagaoka Bound for Single Qubit Probes Subject to the Amplitude Damping Channel
Appendix H. Optimal Estimator for Estimating Two Parameters in the Amplitude Damping Channel with Two Copies of the Single-Qubit Probe
Appendix I. Explicit Construction of the Optimal Estimator for Estimating a Single Parameter in the Phase Damping Channel with a Single Qubit Probe
Appendix J. Explicit Construction of the Optimal Estimator for Estimating Two Parameters in the Phase Damping Channel with a Single Qubit Probe
Appendix K. Measurement Scheme Which Saturates the NHB for Estimating Three Parameters in the Phase Damping Channel with a Two-Qubit Probe
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Conlon, L.O.; Lam, P.K.; Assad, S.M. Multiparameter Estimation with Two-Qubit Probes in Noisy Channels. Entropy 2023, 25, 1122. https://doi.org/10.3390/e25081122
Conlon LO, Lam PK, Assad SM. Multiparameter Estimation with Two-Qubit Probes in Noisy Channels. Entropy. 2023; 25(8):1122. https://doi.org/10.3390/e25081122
Chicago/Turabian StyleConlon, Lorcán O., Ping Koy Lam, and Syed M. Assad. 2023. "Multiparameter Estimation with Two-Qubit Probes in Noisy Channels" Entropy 25, no. 8: 1122. https://doi.org/10.3390/e25081122
APA StyleConlon, L. O., Lam, P. K., & Assad, S. M. (2023). Multiparameter Estimation with Two-Qubit Probes in Noisy Channels. Entropy, 25(8), 1122. https://doi.org/10.3390/e25081122