Adiabatic critical quantum metrology cannot reach the Heisenberg limit even when shortcuts to adiabaticity are applied

Karol Gietka, Friederike Metz, Tim Keller, and Jing Li

Quantum Systems Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904-0495, Japan

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We show that the quantum Fisher information attained in an adiabatic approach to critical quantum metrology cannot lead to the Heisenberg limit of precision and therefore $regular$ quantum metrology under optimal settings is always superior. Furthermore, we argue that even though shortcuts to adiabaticity can arbitrarily decrease the time of preparing critical ground states, they cannot be used to achieve or overcome the Heisenberg limit for quantum parameter estimation in adiabatic critical quantum metrology. As case studies, we explore the application of counter-diabatic driving to the Landau-Zener model and the quantum Rabi model.

Critical metrology, which relies on the extreme sensitivity of critical ground states to small changes of Hamiltonian parameters, is believed to give rise to an enhanced precision compared to regular quantum metrology. However, the required time resources for preparing the critical ground state are usually not considered and will result in critical quantum metrology protocols which will inevitably operate on time scales beyond the decoherence times of an experiment. In order to decrease the time of an adiabatic protocol one could harness shortcuts-to-adiabaticity and, in principle, overcome the Heisenberg limit of precision. However, in our article we show that not only the adiabatic approach to critical quantum metrology cannot lead to the Heisenberg limit of precision but also argue that even though shortcuts-to-adiabaticity can arbitrarily decrease the time of preparing critical ground states, they cannot be used to achieve or overcome the Heisenberg limit for quantum parameter estimation in adiabatic critical quantum metrology.

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