Unbounded randomness from uncharacterized sources

TL;DR

This paper introduces a novel Source-Device-Independent protocol utilizing POVMs to certify an unbounded amount of randomness from fixed-dimensional quantum systems, supported by theoretical bounds and experimental validation.

Contribution

It proposes a new POVM-based protocol that can arbitrarily increase certified randomness regardless of system dimension, with analytical bounds and experimental demonstration.

Findings

Derived tight lower bounds on quantum conditional min-entropy using POVM structure.

Experimental validation with a photonic setup employing polarization-encoded qubits and POVMs.

Achieved certification of randomness with POVMs up to 6 outcomes.

Abstract

Randomness is a central feature of quantum mechanics and an invaluable resource for both classical and quantum technologies. Commonly, in Device-Independent and Semi-Device-Independent scenarios, randomness is certified using projective measurements and the amount of certified randomness is bounded by the dimension of the measured quantum system. In this work, we propose a new Source-Device-Independent protocol, based on Positive Operator Valued Measurement (POVM), which can arbitrarily increase the number of certified bits for any fixed dimension. A tight lower-bound on the quantum conditional min-entropy is derived using only the POVM structure and the experimental expectation values, taking into account the quantum side-information. For symmetrical POVM measurements on the Bloch sphere we have derived closed-form analytical bounds. Finally, we experimentally demonstrate our method with a compact and simple photonic setup that employs polarization-encoded qubits and POVM up to 6 outcomes.