Enhancing sensitivity in quantum metrology by Hamiltonian extensions

Abstract

A well-studied scenario in quantum parameter estimation theory arises when the parameter to be estimated is imprinted on the initial state by a Hamiltonian of the form $\theta G$. For such "phase shift Hamiltonians" it has been shown that one cannot improve the channel quantum Fisher information by adding ancillas and letting the system interact with them. Here we investigate the general case, where the Hamiltonian is not necessarily a phase shift, and show that in this case in general it \emph{is} possible to increase the quantum channel information and to reach an upper bound. This can be done by adding a term proportional to the derivative of the Hamiltonian, or by subtracting a term to the original Hamiltonian. Both methods do not make use of any ancillas and show therefore that for quantum channel estimation with arbitrary parameter-dependent Hamiltonian, entanglement with an ancillary system is not necessary to reach the best possible sensitivity. By adding an operator to the Hamiltonian we can also modify the time scaling of the channel quantum Fisher information. We illustrate our techniques with NV-center magnetometry and the estimation of the direction of a magnetic field in a given plane using a single spin-1 as probe.

New references included

References in corpus (3)

• Generalized Limits for Single-Parameter Quantum Estimation
• Using entanglement against noise in quantum metrology
• Estimation of unitary quantum operations

Cited by in corpus (12)

• Quantum enhanced measurements without entanglement
• A Geometric Perspective on Quantum Parameter Estimation
• Generalizable control for quantum parameter estimation through reinforcement learning
• Symmetric Logarithmic Derivative of Fermionic Gaussian States
• Maximal Quantum Fisher Information for Mixed States
• Generalizable control for multiparameter quantum metrology
• The advantage of quantum control in many-body Hamiltonian learning
• Quantum parameter-estimation of frequency and damping of a harmonic-oscillator
• Estimation of general Hamiltonian parameters via controlled energy measurements
• Fluctuation-enhanced quantum metrology
• Many-body quantum metrology with scalar bosons in a single potential well
• Gaussian phase sensitivity of boson-sampling-inspired strategies