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Quantum violation of trivial and non-trivial preparation contextuality: nonlocality and steering

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Abstract

This paper illustrates a direct connection between quantum steering and non-trivial preparation contextuality. In two party–two measurement per party–two outcomes per measurement \((2-2-2)\) Bell scenario, any argument of Bell nonlocality is a proof of trivial preparation contextuality; however, the converse may not hold. If one of the parties (say, Alice) performs the measurements of more than two dichotomic observables, then it is possible to find a set of non-trivial functional relations between Alice’s observables. We argue that the existence of a suitable set of such non-trivial relations between Alice’s observables may warrant the unsteerability of quantum states at the end of another spatially separated party (say, Bob). Interestingly, such constraints can be read as non-trivial preparation non-contextuality assumptions in an ontological model. We further demonstrate two types of Bell inequalities that can be converted into linear steering inequalities using the aforementioned non-trivial conditions on Alice’s observables. Such steering inequalities can also be considered as non-trivial preparation noncontextual inequalities. Since the local bound of the family of Bell expression gets reduced under the additional non-trivial conditions, it provides a test of quantum steering and nonlocality from the same family of Bell expressions depending upon its violation of the non-trivial preparation non-contextual or the local bound, thereby establishing a direct connection between quantum steering and non-trivial preparation contextuality.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.]

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Acknowledgements

PR acknowledges the support from the research grant DST/ICPS/QuEST/2019/4. AKP acknowledges the support from the research grant MTR/2021/000908.

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Authors and Affiliations

  1. National Institute of Technology Patna, Ashok Rajpath, Patna, Bihar, 800005, India

    Prabuddha Roy & A. K. Pan

  2. Department of Physics, Indian Institute of Technology, Hyderabad, Telengana, 502284, India

    A. K. Pan

Authors
  1. Prabuddha Roy
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  2. A. K. Pan
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Contributions

AKP conceived the idea and supervised the work. Both authors contributed to the calculations, and preparation of the manuscript.

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Correspondence to A. K. Pan.

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Roy, P., Pan, A.K. Quantum violation of trivial and non-trivial preparation contextuality: nonlocality and steering. Eur. Phys. J. D 76, 204 (2022). https://doi.org/10.1140/epjd/s10053-022-00538-9

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