Abstract
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 identical copies of a quantum channel when , 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 . 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 times the single-channel QFI and, furthermore, that sequential estimation strategies provide no advantage over parallel ones.
- Received 23 March 2020
- Revised 20 December 2020
- Accepted 26 February 2021
DOI:https://doi.org/10.1103/PRXQuantum.2.010343
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Among all novel quantum information technologies, quantum metrology is a rising field aiming to improve the sensitivity of physical quantities by employing the quantum features of physical systems. The widespread applications of quantum metrology include, but not limited to, frequency spectroscopy, magnetometry, clocks, and gravitational wave detection. Different protocols have been developed to enhance the sensitivity using quantum strategies to approach the fundamental sensing limit, but only on a case-by-case basis. Here we propose a universal metrological scheme achieving the ultimate sensitivity allowed by quantum mechanics for arbitrary quantum sensing channels.
We first find a criterion that classifies the sensitivity scaling for channels, which is either the Heisenberg scaling or the standard scaling, characterized by the quadratic or the linear scaling with respect to the number of probes. For different types of channels, the ultimate sensitivity is achievable using two different metrological protocols. They both involve first using a two-level encoding compatible with quantum error correction to suppress the undesired noises and then applying many-body entangled states at the logical level to achieve the ultimate sensitivity. Moreover, we develop an efficient numerical tool to calculate the ultimate sensitivity and the optimal encoding, revealing a promising path towards practical implementation of quantum sensors approaching the ultimate sensitivity.
Our work provides a general guideline on improving the sensitivity in general quantum systems. The results will stimulate future developments in sensing experiments and our techniques will also inspire more broadly further work in other realms in quantum information.
