Achieving quantum metrological performance and exact Heisenberg limit precision through superposition of $s$-spin coherent states

Abstract

In quantum phase estimation, the Heisenberg limit provides the ultimate accuracy over quasi-classical estimation procedures. However, realizing this limit hinges upon both the detection strategy employed for output measurements and the characteristics of the input states. This study delves into quantum phase estimation using $s$-spin coherent states superposition. Initially, we delve into the explicit formulation of spin coherent states for a spin $s=3/2$. Both the quantum Fisher information and the quantum Cramer-Rao bound are meticulously examined. We analytically show that the ultimate measurement precision of spin cat states approaches the Heisenberg limit, where uncertainty decreases inversely with the total particle number. Moreover, we investigate the phase sensitivity introduced through operators $e^{i\zeta S_z}$, $e^{i\zeta S_x}$ and $e^{i\zeta S_y}$, subsequently comparing the resultants findings. In closing, we provide a general analytical expression for the quantum Cramer-Rao boundary applied to these three parameter-generating operators, utilizing general $s$-spin coherent states. We remarked that attaining Heisenberg-limit precision requires the careful adjustment of insightful information about the geometry of $s$-spin cat states on the Bloch sphere. Additionally, as the number of $s$-spin increases, the Heisenberg limit decreases, and this reduction is inversely proportional to the $s$-spin number.

arXiv comment15 pages, 63 figures

References in corpus (34)

• Advances in Quantum Metrology
• Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat The Diffraction Limit
• Atom chip based generation of entanglement for quantum metrology
• Entanglement, Non-linear Dynamics, and the Heisenberg Limit
• Quantum metrology from a quantum information science perspective
• Quantum Optical Metrology -- The Lowdown on High-N00N States
• Super-resolving phase measurements with a multi-photon entangled state
• Beating the Standard Quantum Limit with Four Entangled Photons
• Quantum metrology with entangled coherent states
• Generalized Limits for Single-Parameter Quantum Estimation
• Quantum Metrology for Gravitational Wave Astronomy
• General optimality of the Heisenberg limit for quantum metrology
• Exponentially Enhanced Quantum Metrology
• Tutorial: Optical quantum metrology
• Quantum-limited metrology with product states
• Precision quantum metrology and nonclassicality in linear and nonlinear detection schemes
• Entangled SU(2) and SU(1,1) coherent states
• Flexible resources for quantum metrology
• A comparative study of local quantum Fisher information and local quantum uncertainty in Heisenberg $XY$ model
• Dissipative Quantum Metrology with Spin Cat States
• Quantum Metrology with Dicke Squeezed States
• Nonlinear interferometry beyond classical limit facilitated by cyclic dynamics
• Achieving Heisenberg-limited metrology with spin cat states via interaction-based readout
• Quantum metrology: Heisenberg limit with bound entanglement
• Quantum Fisher Information of Entangled Coherent States in a Lossy Mach-Zehnder Interferometer
• Maximal quantum Fisher information for phase estimation without initial parity
• Generating double NOON states of photons in circuit QED
• Bidirectional quantum teleportation of even and odd coherent states through the multipartite Glauber coherent state: Theory and implementation
• Estimating phase parameters of a three-level system interacting with two classical monochromatic fields in simultaneous and individual metrological strategies
• Connection between the N00N State and a superposition of SU(2) Coherent States
• Enhancing the estimation precision of an unknown phase shift in multipartite Glauber coherent states via skew information correlations and local quantum Fisher information
• A simple analytical expression of quantum Fisher and Skew information and their dynamics under decoherence channels
• Quantum phase estimations with spin coherent states superposition
• Quantum metrology with a non-linear kicked Mach-Zehnder interferometer

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