Quantum Information Processing

, Volume 15, Issue 7, pp 2993–3004 | Cite as

Temporal correlations and device-independent randomness

  • Shiladitya Mal
  • Manik Banik
  • Sujit K. Choudhary


Leggett–Garg inequalities (LGI) are constraints on certain combinations of temporal correlations obtained by measuring one and the same system at two different instants of time. The usual derivations of LGI assume macroscopic realism per se and noninvasive measurability. We derive these inequalities under a different set of assumptions, namely the assumptions of predictability and no signaling in time (NSIT). As a novel implication of this derivation, we find application of LGI in randomness certification. It turns out that randomness can be certified from temporal correlations, even without knowing the details of the experimental devices, provided the observed correlations violate LGI but satisfy NSIT.


Temporal correlation Leggett–Garg inequality Device-independent randomness 



S.K.C. acknowledges fruitful discussions with Pankaj Agrawal. We also thank Guruprasad Kar for stimulating discussions. MB thankfully acknowledges comments from C. Brukner, C. Emary and A. J. Leggett. S.K.C. acknowledges support from the Council of Scientific and Industrial Research, Government of India (Scientists’ Pool Scheme). SM acknowledges support from the DST project SR/S2/PU-16/2007.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Shiladitya Mal
    • 1
  • Manik Banik
    • 2
    • 3
  • Sujit K. Choudhary
    • 4
  1. 1.S. N. Bose National Centre for Basic SciencesSalt Lake, KolkataIndia
  2. 2.Optics and Quantum Information GroupThe Institute of Mathematical SciencesChennaiIndia
  3. 3.Physics and Applied Mathematics UnitIndian Statistical InstituteKolkataIndia
  4. 4.Institute of PhysicsBhubaneswarIndia

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