Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
140 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Multi-parameter quantum estimation of single- and two-mode pure Gaussian states (2403.03919v1)

Published 6 Mar 2024 in quant-ph

Abstract: We discuss the ultimate precision bounds on the multiparameter estimation of single- and two-mode pure Gaussian states. By leveraging on previous approaches that focused on the estimation of a complex displacement only, we derive the Holevo Cram\'er-Rao bound (HCRB) for both displacement and squeezing parameter characterizing single and two-mode squeezed states. In the single-mode scenario, we obtain an analytical bound and find that it degrades monotonically as the squeezing increases. Furthermore, we prove that heterodyne detection is nearly optimal in the large squeezing limit, but in general the optimal measurement must include non-Gaussian resources. On the other hand, in the two-mode setting, the HCRB improves as the squeezing parameter grows and we show that it can be attained using double-homodyne detection.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (53)
  1. Quantum-enhanced measurements: Beating the standard quantum limit. Science, 306(5700):1330–1336, 2004.
  2. Quantum Metrology. Phys. Rev. Lett., 96(1):010401, jan 2006.
  3. Advances in quantum metrology. Nat. Photonics, 5(4):222–229, apr 2011.
  4. Carlton M. Caves. Quantum-mechanical noise in an interferometer. Phys. Rev. D, 23:1693–1708, Apr 1981.
  5. Matteo G. A. Paris. Quantum estimation for quantum technology. Int. J. Quantum Inf., 07(supp01):125–137, jan 2009.
  6. Quantum Limits in Optical Interferometry. In Emil Wolf, editor, Prog. Opt. Vol. 60, chapter 4, pages 345–435. Elsevier, Amsterdam, 2015.
  7. Quantum sensing. Rev. Mod. Phys., 89(3):035002, jul 2017.
  8. Advances in photonic quantum sensing. Nat. Photonics, 12(12):724–733, dec 2018.
  9. Marco Barbieri. Optical quantum metrology. PRX Quantum, 3:010202, Jan 2022.
  10. A perspective on multiparameter quantum metrology: From theoretical tools to applications in quantum imaging. Physics Letters A, 384(12):126311, 2020.
  11. Multi-parameter quantum metrology. Adv. Phys. X, 1(4):621–639, jul 2016.
  12. Quantum fisher information matrix and multiparameter estimation. Journal of Physics A: Mathematical and Theoretical, 53(2):023001, dec 2019.
  13. Multi-parameter estimation beyond quantum fisher information. Journal of Physics A: Mathematical and Theoretical, 53(36):363001, aug 2020.
  14. Optimal estimation of joint parameters in phase space. Phys. Rev. A, 87(1):012107, jan 2013.
  15. Ultimate precision of joint quadrature parameter estimation with a Gaussian probe. Phys. Rev. A, 97(1):012106, jan 2018.
  16. A tight Cramér–Rao bound for joint parameter estimation with a pure two-mode squeezed probe. Phys. Lett. A, 381(32):2598–2607, aug 2017.
  17. Quantum Enhanced Multiple Phase Estimation. Phys. Rev. Lett., 111(7):070403, 2013.
  18. Gaussian systems for quantum-enhanced multiple phase estimation. Phys. Rev. A, 94(4):042342, oct 2016.
  19. Local versus global strategies in multiparameter estimation. Phys. Rev. A, 94(6):062312, dec 2016.
  20. Optimal Measurements for Simultaneous Quantum Estimation of Multiple Phases. Phys. Rev. Lett., 119(13):130504, sep 2017.
  21. Efficient computation of the Nagaoka–Hayashi bound for multiparameter estimation with separable measurements. npj Quantum Inf, 7(1):1–8, July 2021. Bandiera_abtest: a Cc_license_type: cc_by Cg_type: Nature Research Journals Number: 1 Primary_atype: Research Publisher: Nature Publishing Group Subject_term: Quantum information;Quantum metrology Subject_term_id: quantum-information;quantum-metrology.
  22. Multiparameter estimation with two-qubit probes in noisy channels. Entropy, 25(8), 2023.
  23. Parameter estimation in quantum optics. Phys. Rev. A, 62:023815, Jul 2000.
  24. Estimation of phase and diffusion: Combining quantum statistics and classical noise, 2013.
  25. Joint estimation of phase and phase diffusion for quantum metrology. Nature Communications, 5(1):3532, 2014.
  26. Weak measurements and the joint estimation of phase and phase diffusion. Phys. Rev. A, 92:032114, Sep 2015.
  27. Reaching for the quantum limits in the simultaneous estimation of phase and phase diffusion. Quantum Science and Technology, 2(4):044004, aug 2017.
  28. Entangling measurements for multiparameter estimation with two qubits. Quantum Science and Technology, 3(1):01LT01, oct 2017.
  29. Quantum theory of superresolution for two incoherent optical point sources. Phys. Rev. X, 6:031033, Aug 2016.
  30. On super-resolution imaging as a multiparameter estimation problem. International Journal of Quantum Information, 15(08):1740005, 2017.
  31. Optimal measurements for resolution beyond the rayleigh limit. Opt. Lett., 42(2):231–234, Jan 2017.
  32. Optimal measurements for quantum spatial superresolution. Phys. Rev. A, 98:012103, Jul 2018.
  33. Towards superresolution surface metrology: Quantum estimation of angular and axial separations. Phys. Rev. Lett., 122:140505, Apr 2019.
  34. General expressions for the quantum fisher information matrix with applications to discrete quantum imaging. PRX Quantum, 2:020308, Apr 2021.
  35. Achieving the ultimate quantum timing resolution. PRX Quantum, 2:010301, Jan 2021.
  36. Carl W. Helstrom. Quantum detection and estimation theory. Academic Press, New York, 1976.
  37. Alexander S. Holevo. Probabilistic and Statistical Aspects of Quantum Theory. Edizioni della Normale, Pisa, 2nd edition, 2011.
  38. On quantumness in multi-parameter quantum estimation. J. Stat. Mech. Theory Exp., 2019(9):094010, sep 2019.
  39. On the quantumness of multiparameter estimation problems for qubit systems. Entropy, 22(11), 2020.
  40. On the properties of the asymptotic incompatibility measure in multiparameter quantum estimation. Journal of Physics A: Mathematical and Theoretical, 54(48):485301, nov 2021.
  41. Quantum semiparametric estimation. Phys. Rev. X, 10:031023, Jul 2020.
  42. Hiroshi Nagaoka. A New Approach to Cramér-Rao Bounds for Quantum State Estimation, pages 100–112. 2005.
  43. Masahito Hayashi. A Linear Programming Approach to Attainable Cramésr-Rao Type Bounds, pages 150–161. 2005.
  44. K Matsumoto. A new approach to the cramér-rao-type bound of the pure-state model. Journal of Physics A: Mathematical and General, 35(13):3111–3123, mar 2002.
  45. Evaluating the holevo cramér-rao bound for multiparameter quantum metrology. Phys. Rev. Lett., 123:200503, Nov 2019.
  46. Optimal probes and error-correction schemes in multi-parameter quantum metrology. Quantum, 4:288, July 2020.
  47. Attainability of the holevo-cramér-rao bound for two-qubit 3d magnetometry, 2020.
  48. Jun Suzuki. Explicit formula for the Holevo bound for two-parameter qubit-state estimation problem. J. Math. Phys., 57(4):042201, apr 2016.
  49. Marcin Jarzyna. Quantum limits to polarization measurement of classical light, 2021.
  50. Conditional and unconditional Gaussian quantum dynamics. Contemp. Phys., 57(3):331–349, July 2016.
  51. Alessio Serafini. Quantum Continuous Variables : A Primer of Theoretical Methods. CRC Press, Boca Raton, 2017.
  52. Gaussian states in Quantum Information. Bibliopolis, Napoli, 2005.
  53. Optimal gaussian measurements for phase estimation in single-mode gaussian metrology. npj Quantum Information, 5(1):10, 2019.
Citations (2)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets