Unbounded Device-Independent Quantum Key Rates from Arbitrarily Small Nonlocality

Area of Science:

• Quantum Information Science
• Quantum Cryptography
• Foundations of Quantum Mechanics

Background:

• Device-independent quantum key distribution (DIQKD) offers provable security for cryptographic keys between distant parties using potentially untrusted devices.
• Security proofs in DIQKD rely on measurement outcome statistics from Bell experiments, guaranteed by quantum theory's fundamental laws.
• While Bell nonlocality is necessary for DIQKD security, it is not always sufficient, as recent findings indicate.

Purpose of the Study:

• To investigate the quantitative relationship between Bell nonlocality and key rates in device-independent quantum key distribution.
• To determine if a minimum level of nonlocality is required for secure DIQKD.
• To explore the possibility of extracting key rates from correlations exhibiting minimal nonlocality.

Main Methods:

• Rigorous connection established between self-testing protocols and device-independent quantum key distribution.
• Application of these techniques to a novel family of Bell inequalities featuring numerous measurement outcomes.
• Analysis of measurement outcome statistics and their implications for nonlocality and key generation.

Main Results:

• Demonstrated that there is no lower bound on the amount of Bell nonlocality required for device-independent quantum key distribution.
• Showcased that unbounded device-independent key rates can be extracted from correlations exhibiting arbitrarily small nonlocality.
• Established that a general quantitative relationship between DIQKD key rates and Bell nonlocality cannot be defined.

Conclusions:

• The security of device-independent quantum key distribution is not directly proportional to the degree of observed Bell nonlocality.
• Minimal nonlocality is sufficient for generating substantial secure key material in a device-independent manner.
• Future research in DIQKD security should consider alternative metrics beyond Bell nonlocality's quantitative measure.