Leggett-Garg inequalities: distinguishing quantum and classical dynamics

(when the Leggett–Garg inequality is violated, the time evolution of a system cannot be classical, in the macrorealist sense)


  1. N. Lambert, C. Emary, Y.N. Chen, F. Nori
    Distinguishing quantum and classical transport through nanostructures
    Phys. Rev. Lett. 105, 176801 (2010). [PDF][Link][arXiv]

  2. N. Lambert, Y.N.Chen, F. Nori
    Unified single-photon and single-electron counting statistics: From cavity QED to electron transport
    Phys. Rev. A 82, 063840 (2010). [PDF][Link][arXiv]

  3. N. Lambert, J.R. Johansson, F. Nori
    Macrorealism inequality for optoelectromechanical systems
    Phys. Rev. B 84, 245421 (2011). [PDF][Link][arXiv]

  4. G.Y. Chen, N. Lambert, C.M. Li, Y.N. Chen, F. Nori
    Delocalized single-photon Dicke states and the Leggett-Garg inequality in solid state systems
    Scientific Reports 2, 869 (2012). [PDF][Link][arXiv][Errata]

  5. C.M. Li, N. Lambert, Y.N. Chen, G.Y. Chen, F. Nori
    Witnessing Quantum Coherence: from solid-state to biological systems
    Scientific Reports 2, 885 (2012). [PDF][Link][arXiv]

  6. C. Emary, N. Lambert, F. Nori
    Leggett-Garg inequality in electron interferometers
    Phys. Rev. B 86, 235447 (2012). [PDF][Link][arXiv]

  7. C. Emary, N. Lambert, F. Nori
    Leggett-Garg Inequalities
    Reports on Progress in Physics 77, 016001 (2014). [PDF][Link][arXiv][Errata]

  8. N. Lambert, K. Debnath, A.F. Kockum, G.C. Knee, W.J. Munro, F. Nori
    Leggett-Garg inequality violations with a large ensemble of qubits
    Phys. Rev. A 94, 012105 (2016). [PDF][Link][arXiv]

  9. K.D. Wu, Z. Hou, G.Y. Xiang, C.F. Li, G.C. Guo, D. Dong, F. Nori
    Detecting non-Markovianity via quantified coherence: theory and experiments
    npj Quantum Information 6, 55 (2020). [PDF][Link_1][Link_2][arXiv][Suppl. Info.]

  10. H.Y. Ku, N. Lambert, F.J. Chan, C. Emary, Y.N. Chen, F. Nori
    Experimental test of non-macrorealistic cat states in the cloud
    npj Quantum Information 6, 98 (2020). [PDF][Link_1][Link_2][arXiv]

  11. H.Y. Ku, H.C. Weng, Y.A. Shih, P.C. Kuo, N. Lambert, F. Nori, C.S. Chuu, Y.N. Chen
    Hidden nonmacrorealism: Reviving the Leggett-Garg inequality with stochastic operations
    Phys. Rev. Research 3, 043083 (2021). [PDF][Link][arXiv]

  12. H.Y. Ku, J. Kadlec, A. Cernoch, M.T. Quintino, W. Zhou, K. Lemr, N. Lambert, A. Miranowicz, S.L. Chen, F. Nori, Y.N. Chen
    Quantifying Quantumness of Channels Without Entanglement
    PRX Quantum 3, 020338 (2022). [PDF][Link][arXiv]

Quantum Steering (spatial and temporal)

(Quantum steering refers to the ability to perform a measurement on one side of an entangled system with different outcomes leading to different sets of states for another part of the entangled system arbitrarily far away. This purely quantum phenomena has no classical analogue. It is closely related to entanglement and Bell nonlocality. Temporal steering refers to steering a single system in time, and is partly inspired by the Leggett-Garg inequality, and its relationship to the Bell Inequality)


  1. Y.N. Chen, C.M. Li, N. Lambert, S.L. Chen, Y. Ota, G.Y. Chen, F. Nori
    Temporal steering inequality
    Phys. Rev. A 89, 032112 (2014). [PDF][Link][arXiv]

  2. C.M. Li, Y.N. Chen, N. Lambert, C.Y. Chiu, F. Nori
    Certifying single-system steering for quantum-information processing
    Phys. Rev. A 92, 062310 (2015). [PDF][Link][arXiv]

  3. S.L. Chen, N. Lambert, C.M. Li, A. Miranowicz, Y.N. Chen, F. Nori
    Quantifying Non-Markovianity with Temporal Steering
    Phys. Rev. Lett. 116, 020503 (2016). [PDF][Link][arXiv][Suppl. Info.]

  4. C.Y. Chiu, N. Lambert, T.L. Liao, F. Nori, C.M. Li
    No-cloning of quantum steering
    npj Quantum Information 2, 16020 (2016). [PDF][Link][Link][arXiv]

  5. K. Bartkiewicz, A. Černoch, K. Lemr, A. Miranowicz, F. Nori
    Temporal steering and security of quantum key distribution with mutually unbiased bases against individual attacks
    Phys. Rev. A 93, 062345 (2016). [PDF][Link][arXiv]

  6. K. Bartkiewicz, A. Černoch, K. Lemr, A. Miranowicz, F. Nori
    Experimental temporal quantum steering
    Scientific Reports 6, 38076 (2016). [PDF][Link][arXiv]

  7. H.Y. Ku, S.L. Chen, H.B. Chen, N. Lambert, Y.N. Chen, F. Nori
    Temporal steering in four dimensions with applications to coupled qubits and magnetoreception
    Phys. Rev. A 94, 062126 (2016). [PDF][Link][arXiv]

  8. S.L. Chen, N. Lambert, C.M. Li, G.Y. Chen, Y.N. Chen, A. Miranowicz, F. Nori
    Spatio-Temporal Steering for Testing Nonclassical Correlations in Quantum Networks
    Scientific Reports 7, 3728 (2017). [PDF][Link][arXiv]

  9. H.Y. Ku, S.L. Chen, N. Lambert, Y.N. Chen, F. Nori
    Hierarchy in temporal quantum correlations
    Phys. Rev. A 98, 022104 (2018). [PDF][Link][arXiv]

  10. C.Y. Huang, N. Lambert, C.M. Li, Y.T. Lu, F. Nori
    Securing quantum networking tasks with multipartite Einstein-Podolsky-Rosen steering
    Phys. Rev. A 99, 012302 (2019). [PDF][Link][arXiv]

  11. J.D. Lin, W.Y. Lin, H.Y. Ku, N. Lambert, Y.N. Chen, F. Nori
    Quantum steering as a witness of quantum scrambling
    Phys. Rev. A 104, 022614 (2021). [PDF][Link][arXiv]

  12. K.Y. Lee, J.D. Lin, A. Miranowicz, F. Nori, H.Y. Ku, Y.N. Chen
    Steering-enhanced quantum metrology using superpositions of noisy phase shifts
    Phys. Rev. Research 5, 013103 (2023). [PDF][Link][arXiv]