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Direct characteristic-function tomography of the quantum states of quantum fields

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Abstract

Herein, we propose a novel strategy for implementing a direct readout of the symmetric characteristic function of the quantum states of quantum fields without the involvement of idealized measurements, an aspect that has always been deemed ill-defined in quantum field theory. This proposed scheme relies on the quantum control and measurements of an auxiliary qubit locally coupled to the quantum fields. By mapping the expectation values of both the real and imaginary parts of the field displacement operator to the qubit states, the qubit’s readout provides complete information regarding the symmetric characteristic function. We characterize our technique by applying it to the Kubo-Martin-Schwinger (thermal) and squeezed states of a quantum scalar field. In addition, we have discussed general applications of this approach to analogue-gravity systems, such as Bose-Einstein condensates, within the scope of state-of-the-art experimental capabilities. This proposed strategy may serve as an essential in understanding and optimizing the control of quantum fields for relativistic quantum information applications, particularly in exploring the interplay between gravity and quantum, for example, the relation to locality, causality, and information.

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Authors and Affiliations

  1. CAS Key Laboratory of Microscale Magnetic Resonance, School of Physical Sciences, University of Science and Technology of China, Hefei, 230026, China

    Zehua Tian & Jiangfeng Du

  2. CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China

    Zehua Tian & Jiangfeng Du

  3. Department of Physics, Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha, 410081, China

    Jiliang Jing

  4. Hefei National Laboratory, University of Science and Technology of China, Hefei, 230088, China

    Jiangfeng Du

  5. School of Physics, Zhejiang University, Hangzhou, 310027, China

    Jiangfeng Du

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  1. Zehua Tian
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  2. Jiliang Jing
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Correspondence to Zehua Tian.

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The authors declare that they have no conflict of interest.

Additional information

This work was supported by the National Key Research and Development Program of China (Grant No. 2018YFA0306600), and Anhui Initiative in Quantum Information Technologies (Grant No. AHY050000). Zehua Tian was supported by the National Natural Science Foundation of China (Grant No. 11905218), and the CAS Key Laboratory for Research in Galaxies and Cosmology, Chinese Academy of Sciences (Grant No. 18010203)

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Tian, Z., Jing, J. & Du, J. Direct characteristic-function tomography of the quantum states of quantum fields. Sci. China Phys. Mech. Astron. 66, 110412 (2023). https://doi.org/10.1007/s11433-023-2196-9

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