Semi-device-independent full randomness amplification based on energy bounds

TL;DR

This paper introduces a semi-device-independent protocol for full randomness amplification using energy bounds, which does not require entanglement or full device characterization, enhancing security and efficiency.

Contribution

It demonstrates that full randomness amplification is achievable in a semi-device-independent setting based on energy bounds, reducing resource requirements and assumptions.

Findings

Achieves full randomness amplification without entanglement.

Requires minimal inputs and outcomes for security.

Secure against quantum adversaries in a semi-device-independent framework.

Abstract

Quantum Bell nonlocality allows for the design of protocols that amplify the randomness of public and arbitrarily biased Santha-Vazirani sources, a classically impossible task. Information-theoretical security in these protocols is certified in a device-independent manner, i.e. solely from the observed nonlocal statistics and without any assumption about the inner-workings of the intervening devices. On the other hand, if one is willing to trust on a complete quantum-mechanical description of a protocol's devices, the elementary scheme in which a qubit is alternatively measured in a pair of mutually unbiased bases is, straightforwardly, a protocol for randomness amplification. In this work, we study the unexplored middle ground. We prove that full randomness amplification can be achieved without requiring entanglement or a complete characterization of the intervening quantum states and measurements. Based on the energy-bounded framework introduced in [Van Himbeeck et al., Quantum 1, 33 (2017)], our prepare-and-measure protocol is able to amplify the randomness of any public Santha-Vazirani source, requiring the smallest number of inputs and outcomes possible and being secure against quantum adversaries.