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Detecting coherence with respect to general quantum measurements

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Abstract

Quantum coherence is crucial in quantum resource theory. Previous studies have mainly focused on standard coherence based on a complete orthogonal reference. Standard coherence has recently been extended to general positive-operator-valued measure (POVM)-based coherence, including block coherence as a special case. Therefore, it is necessary to construct block and POVM-based coherence witnesses to detect them. In this study, we present witnesses for block and POVM-based coherence and obtain the necessary and sufficient conditions for constructing these witnesses. We also discuss possible realizations of some block and POVM-based coherence witnesses in experiments and present examples of measuring block coherence witnesses based on real experimental data. Furthermore, we present an application of block coherence witnesses in a quantum-parameter estimation task with a degenerate Hamiltonian and estimate the unknown parameter by measuring the block coherence witnesses when the input state is block coherent. Finally, we prove that the quantum Fisher information of any block-incoherent state equals zero, which coincides with the result obtained from measuring block coherence witnesses.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11734015, 11704205, 12074206), Open Funding Program from State Key Laboratory of Precision Spectroscopy (East China Normal University), and K.C. Wong Magna Fund in Ningbo University.

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Authors and Affiliations

  1. School of Physical Science and Technology, Ningbo University, Ningbo, 315211, China

    Yu-Cheng Chen, Jiong Cheng, Wen-Zhao Zhang & Cheng-Jie Zhang

  2. State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai, 200241, China

    Cheng-Jie Zhang

Authors
  1. Yu-Cheng Chen
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  2. Jiong Cheng
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  3. Wen-Zhao Zhang
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  4. Cheng-Jie Zhang
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Correspondence to Wen-Zhao Zhang or Cheng-Jie Zhang.

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Chen, YC., Cheng, J., Zhang, WZ. et al. Detecting coherence with respect to general quantum measurements. Sci. China Inf. Sci. 66, 180504 (2023). https://doi.org/10.1007/s11432-022-3620-2

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  • DOI: https://doi.org/10.1007/s11432-022-3620-2

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