Sensitivity bounds for interferometry with Ising Hamiltonians

Year: 2019

Authors: Li Y., Pezzè L., Li WD., Smerzi A.

Autors Affiliation: Shanxi Univ, Collaborat Innovat Ctr Extreme Opt, Inst Theoret Phys, Taiyuan 030006, Shanxi, Peoples R China; Shanxi Univ, Collaborat Innovat Ctr Extreme Opt, Dept Phys, State Key Lab Quantum Opt & Quantum Opt Devices, Taiyuan 030006, Shanxi, Peoples R China; CNR, INO, QSTAR, Largo Enrico Fermi 2, I-50125 Florence, Italy; LENS, Largo Enrico Fermi 2, I-50125 Florence, Italy

Abstract: Sensitivity bounds for a generic interferometric phase estimation problem are the shot noise and the Heisenberg limits. The shot noise is the highest sensitivity that can be reached with separable states, while the Heisenberg limit is the ultimate bound in sensitivity which can be saturated with entangled states. The scaling of these bounds with the number of particles N entering the interferometer depends on the specific Hamiltonian governing the same interferometer. In typical cases, the Hamiltonian is linear, and the shot-noise and Heisenberg limits scale with N-1/2 and with N-1, respectively. With interferometers described by generic, nonlinear Hamiltonian, the scalings with the number of particles can be rather different. Here we study the shot-noise and Heisenberg limits of Ising-like Hamiltonians in the presence of longitudinal and transverse fields, both in the nearest-neighbor and in the fully connected spin interaction cases. We provide the explicit forms of the states saturating the shot-noise and Heisenberg limits. These results can be relevant not only for precision measurement purposes but also to characterize quantum phase transitions and, more generally, the witnessing of multipartite entanglement.

Journal/Review: PHYSICAL REVIEW A

Volume: 99 (2)      Pages from: 022324-1  to: 022324-11

More Information: This work was supported by the National Key R & D Program of China (No. 2017YFA0304500 and No. 2017YFA0304203), the National Natural Science Foundation of China (Grant No. 11874247), 111 project (Grant No. D18001), the innovative research team in the Hundred Talent Program of Shanxi Province, the Hundred Talent Program of the Shanxi Province (2018), PCSIRT (Grant No. IRT17R70), the Program of State Key Laboratory of Quantum Optics and Quantum Optics Devices (No. KF201703). We also acknowledge fundings by the European Union under the QuantERA project “Q-Clocks” and Empir project “USOQS”. Y. Li thanks Y.C. Yu and X.W. Guan for helpful discussions.
KeyWords: QUANTUM METROLOGY; LIMIT; ENTANGLEMENT
DOI: 10.1103/PhysRevA.99.022324

Citations: 8
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