Quantum-enhanced joint estimation of phase and phase diffusion
Abstract: Accurate phase estimation in the presence of unknown phase diffusive noise is a crucial yet challenging task in noisy quantum metrology. This problem is particularly interesting due to the detrimental impact of the associated noise. Here, we investigate the joint estimation of phase and phase diffusion using generalized Holland-Burnett states, known for their experimental accessibility. These states provide performance close to the optimal state in single-parameter phase estimation, even in the presence of photon losses. We adopt a twofold approach by analyzing the joint information extraction through the double homodyne measurement and the joint information availability across all probe states. Through our analysis, we find that the highest sensitivities are obtained by using states created by directing all input photons into one port of a balanced beam splitter. Furthermore, we infer that good levels of sensitivity persist even in the presence of moderate photon losses, illustrating the remarkable resilience of our probe states under lossy conditions.
- V. Giovannetti, S. Lloyd, and L. Maccone, Advances in quantum metrology, Nature photonics 5, 222 (2011).
- V. Giovannetti, S. Lloyd, and L. Maccone, Quantum-enhanced measurements: beating the standard quantum limit, Science 306, 1330 (2004).
- C. M. Caves, Quantum-mechanical noise in an interferometer, Physical Review D 23, 1693 (1981).
- S. L. Braunstein, Quantum limits on precision measurements of phase, Physical review letters 69, 3598 (1992).
- L. Pezzé and A. Smerzi, Mach-zehnder interferometry at the heisenberg limit with coherent and squeezed-vacuum light, Physical review letters 100, 073601 (2008).
- A gravitational wave observatory operating beyond the quantum shot-noise limit, Nature Physics 7, 962 (2011).
- S. M. Kay, Fundamentals of statistical signal processing: estimation theory (Prentice-Hall, Inc., 1993).
- E. L. Lehmann and G. Casella, Theory of point estimation (Springer Science & Business Media, 2006).
- C. W. Helstrom, Quantum detection and estimation theory, Journal of Statistical Physics 1, 231 (1969).
- A. S. Holevo, Probabilistic and statistical aspects of quantum theory, Vol. 1 (Springer Science & Business Media, 2011).
- L. Maccone and V. Giovannetti, Beauty and the noisy beast, Nature Physics 7, 376 (2011).
- K. Banaszek, R. Demkowicz-Dobrzański, and I. A. Walmsley, Quantum states made to measure, Nature Photonics 3, 673 (2009).
- H. Cable and G. A. Durkin, Parameter estimation with entangled photons produced by parametric down-conversion, Physical review letters 105, 013603 (2010).
- S. Knysh, V. N. Smelyanskiy, and G. A. Durkin, Scaling laws for precision in quantum interferometry and the bifurcation landscape of the optimal state, Physical Review A 83, 021804 (2011).
- B. Escher, R. L. de Matos Filho, and L. Davidovich, General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology, Nature Physics 7, 406 (2011).
- Y. Ouyang, N. Shettell, and D. Markham, Robust quantum metrology with explicit symmetric states, IEEE Transactions on Information Theory 68, 1809 (2021).
- M. Szczykulska, T. Baumgratz, and A. Datta, Multi-parameter quantum metrology, Advances in Physics: X 1, 621 (2016).
- R. Demkowicz-Dobrzański, W. Górecki, and M. Guţă, Multi-parameter estimation beyond quantum fisher information, Journal of Physics A: Mathematical and Theoretical 53, 363001 (2020).
- F. Albarelli, J. F. Friel, and A. Datta, Evaluating the holevo cramér-rao bound for multiparameter quantum metrology, Physical review letters 123, 200503 (2019).
- S. Ragy, M. Jarzyna, and R. Demkowicz-Dobrzański, Compatibility in multiparameter quantum metrology, Physical Review A 94, 052108 (2016).
- M. G. Genoni, S. Olivares, and M. G. Paris, Optical phase estimation in the presence of phase diffusion, Physical review letters 106, 153603 (2011).
- R. Demkowicz-Dobrzański, M. Jarzyna, and J. Kołodyński, Quantum limits in optical interferometry, Progress in Optics 60, 345 (2015).
- M. Szczykulska, T. Baumgratz, and A. Datta, Reaching for the quantum limits in the simultaneous estimation of phase and phase diffusion, Quantum Science and Technology 2, 044004 (2017).
- U. Leonhardt, Measuring the quantum state of light, Vol. 22 (Cambridge university press, 1997).
- M. Holland and K. Burnett, Interferometric detection of optical phase shifts at the heisenberg limit, Physical review letters 71, 1355 (1993).
- T. Heinosaari, T. Miyadera, and M. Ziman, An invitation to quantum incompatibility, Journal of Physics A: Mathematical and Theoretical 49, 123001 (2016).
- H. Zhu, Information complementarity: A new paradigm for decoding quantum incompatibility, Scientific reports 5, 14317 (2015).
- M. Hayashi, Asymptotic theory of quantum statistical inference: selected papers (World Scientific, 2005).
- K. Matsumoto, A new approach to the cramér-rao-type bound of the pure-state model, Journal of Physics A: Mathematical and General 35, 3111 (2002).
- C. Vaneph, T. Tufarelli, and M. G. Genoni, Quantum estimation of a two-phase spin rotation, Quantum Measurements and Quantum Metrology 1, 12 (2013).
- J. Suzuki, Explicit formula for the holevo bound for two-parameter qubit-state estimation problem, Journal of Mathematical Physics 57 (2016).
- R. Demkowicz-Dobrzański, J. Kołodyński, and M. Guţă, The elusive heisenberg limit in quantum-enhanced metrology, Nature communications 3, 1063 (2012).
- F. Albarelli and R. Demkowicz-Dobrzański, Probe incompatibility in multiparameter noisy quantum metrology, Physical Review X 12, 011039 (2022).
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