Bounds on semi-device-independent quantum random number expansion capabilities

Abstract

The randomness expansion capabilities of semi-device-independent (SDI) prepare and measure protocols are analyzed under the sole assumption that the Hilbert state dimension is known. It's explicitly proved that the maximum certifiable entropy that can be obtained through this set of protocols is $-{\log }_2\left[\frac{1}{2}\left(1+\frac{1}{\sqrt{3}}\right)\right]$ and the same is independent of the dimension witnesses used to certify the protocol. The minimum number of preparation and measurement settings required to achieve this entropy is also proven. An SDI protocol that generates the maximum output entropy with the least amount of input setting is provided. An analytical relationship between the entropy generated and the witness value is obtained. It's also established that certifiable entropy can be generated as soon as dimension witness crosses the classical bound, making the protocol noise-robust and useful in practical applications.

Bound on the maximum certifiable entropy that can be obtained through semi-device-independent (SDI) prepare and measure protocols is obtained explicitly using geometrical arguments

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Cited by in corpus (3)

• A Comprehensive Review of Quantum Random Number Generators: Concepts, Classification and the Origin of Randomness
• Certification of qubits in the prepare-and-measure scenario with large input alphabet and connections with the Grothendieck constant
• Sequential Semi-Device-Independent Quantum Randomness Certification