Can the use of the Leggett–Garg inequality enhance security of the BB84 protocol?

• Published in: Physics letters. A Vol. 381; no. 31; pp. 2478 - 2482
• Main Authors: Shenoy H., Akshata, Aravinda, S., Srikanth, R., Home, Dipankar
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 21.08.2017
• Subjects: Leggett–Garg inequality; Monogamy of correlations; Quantum cryptography; Quantum spatial correlations; Quantum temporal correlations; Quantum spatial correlations; Leggett–Garg inequality; Monogamy of correlations; Quantum cryptography; Quantum temporal correlations
• ISSN: 0375-9601; 1873-2429
• DOI: 10.1016/j.physleta.2017.05.053

Prima facie, there are good reasons to answer in the negative the question posed in the title: the Bennett–Brassard 1984 (BB84) protocol is provably secure subject to the assumption of trusted devices, while the Leggett–Garg-type inequality (LGI) does not seem to be readily adaptable to the device independent (DI) or semi-DI scenario. Nevertheless, interestingly, here we identify a specific device attack, which has been shown to render the standard BB84 protocol completely insecure, but against which our formulated LGI-assisted BB84 protocol (based on an appropriate form of LGI) is secure. •Quantum temporal correlations have limited usefulness in device-independent cryptography.•One reason is that they can violate “no-signaling in time.”•We point out another reason: they are less monogamous than spatial correlations, which are non-signaling.•Still, the Leggett–Garg inequality can protect quantum key distribution against a specific device attack.