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arXiv:2610.29146

Evaluation of the quantum Fisher information for large systems via an ancilla

Qi Liu, Xin-Yu Hao, Jing Liu

quant-phSubmitted Oct 21, 2026• Announced Oct 22, 2026• 0 citations
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Abstract

Quantum Fisher information (QFI) is a fundamental quantity in quantum information and quantum mechanics, and evaluating it in various physical systems has become an important research topic. However, its evaluation in large systems still faces many challenges. Hereby we propose an ancilla-based protocol for evaluating the QFI of large systems and establish the conditions under which this protocol can ``perfectly'' evaluate the QFI in theory. As a demonstration, the protocol is applied to quantum circuits to evaluate the QFI of the Greenberger-Horne-Zeilinger state.

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10 pages, 3 figures

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Quantum Fisher information (QFI) is a fundamental quantity in quantum information and quantum mechanics, and evaluating it in various physical systems has become an important research topic. However, its evaluation in large systems still faces many challenges. Hereby we propose an ancilla-based protocol for evaluating the QFI of large systems and establish the conditions under which this protocol can ``perfectly'' evaluate the QFI in theory. As a demonstration, the protocol is applied to quantum circuits to evaluate the QFI of the Greenberger-Horne-Zeilinger state.
Quantum Fisher information (QFI) plays a vital role in quantum precision measurement, quantum information, many-body physics, and other domains. Obtaining the QFI from experiment for a quantum state reveals insights such as the limits of estimation accuracy for a certain parameter, the degree of entanglement, and the geometric characteristics of the quantum state. Nonetheless, the measurement complexity of the QFI and its lower bound hinges on the dimension of the quantum state. Consequently, reducing the complexity of measurement is a significant challenge. This paper presents a methodology for evaluating the QFI of high-dimensional systems by transferring information to an auxiliary system and measuring its sub-QFI, while also offering conditions to diminish the dimension of auxiliary system to be measured without affecting the amount of information obtained by it.
We present the experimental measurement, on a quantum processor, of a series of polynomial lower bounds that to the quantum Fisher information (QFI), a fundamental quantity for certifying multipartite entanglement that is useful for metrological applications. We combine advanced methods of the randomized measurement toolbox to obtain estimators that are robust regarding drifting errors caused uniquely during the randomized measurement protocol. We estimate the QFI for Greenberger-Horne-Zeilinger states, observing genuine multipartite entanglement. Then we prepare the ground state of the transverse-field Ising model at the critical point using a variational circuit. We estimate its QFI and investigate the interplay between state optimization and noise induced by our increasing the circuit depth. Published by the American Physical Society 2024
We present the experimental measurement, on a quantum processor, of a series of polynomial lower bounds that converge to the quantum Fisher information (QFI), a fundamental quantity for certifying multipartite entanglement that is useful for metrological applications. We combine advanced methods of the randomized measurement toolbox to obtain estimators that are robust against drifting errors caused uniquely during the randomized measurement protocol. We estimate the QFI for Greenberg-Horne-Zeilinger states, observing genuine multipartite entanglement. Then, we prepare the ground state of the transverse field Ising model at the critical point using a variational circuit. We estimate its QFI and investigate the interplay between state optimization and noise induced by increasing the circuit depth.
The quantum Fisher information (QFI) is a fundamental quantity of interest in many areas from quantum metrology to quantum information theory. It can in particular be used as a witness to establish the degree of multiparticle entanglement in quantum many-body systems. In this work, we use polynomials of the density matrix to construct monotonically increasing lower bounds that converge to the QFI. Using randomized measurements we propose a protocol to accurately estimate these lower bounds in state-of-the-art quantum technological platforms. We estimate the number of measurements needed to achieve a given accuracy and confidence level in the bounds, and present two examples of applications of the method in quantum systems made of coupled qubits and collective spins.
The quantum Fisher information (QFI), as a function of quantum states, measures the amount of information that a quantum state carries about an unknown parameter.The (entanglement-assisted) QFI of a quantum channel is defined to be the maximum QFI of the output state assuming an entangled input state over a single probe and an ancilla.In quantum metrology, people are interested in calculating the QFI of N identical copies of a quantum channel when N → ∞, which is called the asymptotic QFI.Over the years, researchers found various types of upper bounds of the asymptotic QFI, but they were proven achievable only in several specific situations.It was known that the asymptotic QFI of an arbitrary quantum channel grows either linearly or quadratically with N .Here we show that a simple criterion can determine whether the scaling is linear or quadratic.In both cases, the asymptotic QFI and a quantum error correction protocol to achieve it are computable via a semidefinite program.When the scaling is quadratic, the Heisenberg limit, a feature of noiseless quantum channels, is recovered.When the scaling is linear, we show that the asymptotic QFI is still in general larger than N times the single-channel QFI and, furthermore, that sequential estimation strategies provide no advantage over parallel ones.