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Symmetry-protected adiabatic quantum metrology

Takuya Hatomura, Atsuki Yoshinaga, Yuichiro Matsuzaki, Mamiko Tatsuta

Published Apr 7, 2021• 1 citation
OpenAlex

Abstract

The aim of quantum metrology is to estimate target parameters as precisely as possible. In this paper, we propose a protocol for quantum metrology based on symmetry-protected adiabatic transformation. We introduce a ferromagnetic Ising model with a transverse field as a probe and consider the estimation of a longitudinal field. Without the transverse field, the ground state of the probe is given by the Greenberger-Horne-Zeilinger state, and thus the Heisenberg limit estimation of the longitudinal field can be achieved through parity measurement. We find that full information of the longitudinal field encoded on parity can exactly be mapped to global magnetization by symmetry-protected adiabatic transformation, i.e., parity measurement can be replaced with global magnetization measurement. Our scheme requires neither accurate control of individual qubits nor that of interaction strength.

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The aim of quantum metrology is to estimate target parameters as precisely as possible. In this paper, we propose a protocol for quantum metrology based on symmetry-protected adiabatic transformation. We introduce a ferromagnetic Ising model with a transverse field as a probe and consider the estimation of a longitudinal field. Without the transverse field, the ground state of the probe is given by the Greenberger-Horne-Zeilinger state, and thus the Heisenberg limit estimation of the longitudinal field can be achieved through parity measurement. We find that full information of the longitudinal field encoded on parity can exactly be mapped to global magnetization by symmetry-protected adiabatic transformation, i.e., parity measurement can be replaced with global magnetization measurement. Our scheme requires neither accurate control of individual qubits nor that of interaction strength.
Abstract The aim of quantum metrology is to estimate target parameters as precisely as possible. In this paper, we consider quantum metrology based on symmetry-protected adiabatic transformation. We introduce a ferromagnetic Ising model with a transverse field as a probe and consider the estimation of a longitudinal field. Without the transverse field, the ground state of the probe is given by the Greenberger–Horne–Zeilinger state, and thus the Heisenberg limit estimation of the longitudinal field can be achieved through parity measurement. In our scheme, full information of the longitudinal field encoded on parity is exactly mapped to global magnetization by symmetry-protected adiabatic transformation, and thus the parity measurement can be replaced with global magnetization measurement. Moreover, this scheme requires neither accurate control of individual qubits nor that of interaction strength. We discuss the effects of the finite transverse field and nonadiabatic transitions as imperfection of adiabatic transformation. By taking into account finite time duration for state preparation, sensing, and readout, we also compare performance of the present scheme with a classical scheme in the absence and presence of dephasing.
Abstract Critical quantum metrology, which exploits quantum critical systems as probes to estimate a physical parameter, has gained increasing attention recently. However, the critical quantum metrology with a continuous quantum phase transition (QPT) is experimentally challenging since a continuous QPT only occurs at the thermodynamic limit. Here, we propose an adiabatic scheme on a perturbed Ising spin model with a first-order QPT. By introducing a small transverse magnetic field, we can not only encode an unknown parameter in the ground state but also tune the energy gap to control the evolution time of the adiabatic passage. Moreover, we experimentally implement the critical quantum metrology scheme using nuclear magnetic resonance techniques and show that at the critical point the precision achieves the Heisenberg scaling as 1/ T . As a theoretical proposal and experimental implementation of the adiabatic scheme of critical quantum metrology and its advantages of easy implementation, inherent robustness against decays and tunable energy gap, our adiabatic scheme is promising for exploring potential applications of critical quantum metrology on various physical systems.
We consider quantum metrology for unitary evolutions generated by parameter-dependent Hamiltonians. We focus on the unitary evolutions generated by the Ising Hamiltonian that describes the dynamics of a one-dimensional chain of spins with nearest-neighbour interactions and in the presence of a global, transverse, magnetic field. We analytically solve the problem and show that the precision with which one can estimate the magnetic field (interaction strength) given one knows the interaction strength (magnetic field) scales at the Heisenberg limit, and can be achieved by a linear superposition of the vacuum and N free fermion states. In addition, we show that Greenberger–Horne–Zeilinger-type states exhibit Heisenberg scaling in precision throughout the entire regime of parameters. Moreover, we numerically observe that the optimal precision using a product input state scales at the standard quantum limit.
We study in this work the metrology precision of a probe system coupled to an ancillary qubit. Restricting the probe-qubit coupling along only one or two directions is found to be a sufficient criterion for the effective dynamical generator to achieve the Heisenberg limit in precision. Under the criterion, the quantum Fisher information (QFI) about the to-be-estimated parameter becomes the expectation value of mean square of the effective generator with respect to the initial state of the composite system. Our criterion is justified in two distinct systems. For a bosonic probe, QFI about the displacement estimation is found to be proportional to the mean excitation number of probe. It renders a counterintuitive result that quantum metrology sensitivity can be enhanced by increasing the temperature of the probe system. For a spin-ensemble probe, QFI about both rotation-phase and magnetic-field estimation exhibit a quadratic dependence on the probe-spin number. It is found that even when the spin-ensemble is prepared as a finite-temperature state, faraway from the so-called resource states, e.g., the squeezed state or the Greenberger-Horne-Zeilinger state, QFI can still manifest a Heisenberg scaling behavior.
In the scenario of the probe-ancilla interaction, we propose a quantum metrology protocol by the unconditional measurement on the ancillary qubit after an optimized period of joint evolution from a product state. Its key element is the construction of two parallel evolution paths by the measurement that can transform the probe system (a spin ensemble) from an eigenstate of a collective angular momentum operator $|j,m\ensuremath{\rangle}$ to a superposed state $(|j,m\ensuremath{\rangle}+|j,\ensuremath{-}m\ensuremath{\rangle})/\sqrt{2}$. With synchronous parametric encoding and qubit measurement, the quantum Fisher information about the phase encoded in the probe system with optimized initial states can exactly attain the Heisenberg scaling N2{N}^{2}N2 with respect to the probe size (spin number) NNN. The quadratic scaling behavior is not sensitive to the imprecise control over the joint evolution time, the time delay between encoding and measurement, and the coherence in the probe ensemble or the ancillary system that would be degraded by local dephasing. The classical Fisher information of the spin ensemble is found to saturate with its quantum counterpart, irrespective of the idle joint evolution after the parametric encoding. We suggest that both Greenberger-Horne-Zeilinger (GHZ)-like states and nonlinear Hamiltonian are not necessary resources for exceeding the standard quantum limit in metrology precision since in our protocol even thermal states can hold an asymptotic quadratic scaling.
We propose a measurement-based quantum metrology protocol in a composite model, where the probe system (a spin ensemble) is coupled to an ancillary two-level system (qubit) with a general Heisenberg XXZ interaction. With optimized probe-ancilla coupling strengths and duration of joint evolution, the two parallel evolution paths of the probe system induced by the unconditional measurement on qubit can transform an eigenstate of the collective angular momentum operator of spin ensemble into a two-component state with a large distance in eigenspace. The quantum Fisher information about the phase encoded in the probe system of polarized states or their superposition, that could be relaxed to mixed states, can therefore manifest an exact or asymptotic quadratic scaling with respect to the probe size (spin number) NNN. The quadratic scaling behavior is found to be insensitive to the imperfect encoding operator, polarized direction of probe, and coupling strength. The phase sensitivity can approach the Heisenberg limit by virtue of the parity detection on either ancillary qubit or probe system. This work justifies that the unconditional measurement on a weakly coupled qubit could be an efficient resource to replace Greenberger-Horne-Zeilinger-type states and squeezing Hamiltonian for exceeding the standard quantum limit in metrology precision.