2007/10/20 by Sergio Boixo, Animesh Datta, Steven T. Flammia +4 · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Coupling constant #Geometry #Hamiltonian (control theory) #Mathematical optimization #Mathematical physics #Mathematics #Metrology #Physics #Product (mathematics) #Quadratic equation #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum decoherence #Quantum discord #Quantum entanglement #Quantum mechanics #Quantum metrology #Scaling #Statistical physics #cond-mat.other #quant-ph
paper · pdf · doi:10.1103/physreva.77.012317
published as Phys. Rev. A 77, 012317 (2007) · 15 pages, 6 figures
arxiv created 2007/10/20 · openalex publication_date 2008/01/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the performance of initial product states of n-body systems in generalized quantum metrology protocols that involve estimating an unknown coupling constant in a nonlinear k-body (k\ensuremath≪n) Hamiltonian. We obtain the theoretical lower bound on the uncertainty in the estimate of the parameter. For arbitrary initial states, the lower bound scales as 1/nk, and for initial product states, it scales as 1/n^k\ensuremath-1/2. We show that the latter scaling can be achieved using simple, separable measurements. We analyze in detail the case of a quadratic Hamiltonian (k=2), implementable with Bose-Einstein condensates. We formulate a simple model, based on the evolution of angular-momentum coherent states, which explains the O(n^\ensuremath-3/2) scaling for k=2; the model shows that the entanglement generated by the quadratic Hamiltonian does not play a role in the enhanced sensitivity scaling. We show that phase decoherence does not affect the O(n^\ensuremath-3/2) sensitivity scaling for initial product states.