Unbounded randomness from uncharacterized sources

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 its amount is bounded by the quantum system’s dimension. Here, we propose a Source-Device-Independent protocol, based on Positive Operator Valued Measurement (POVM), which can arbitrarily increase the number of certified bits for any fixed dimension. Additionally, the proposed protocol doesn’t require an initial seed and active basis switching, simplifying its experimental implementation and increasing the generation rates. 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 symmetric POVM on the Bloch sphere, we derive 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.

Semi-device-independent quantum random number generator with a broadband squeezed state of light

“…In these protocols, some devices for preparation or measurement are assumed to be trusted in some condition. For instance, the sourceindependent (SI) QRNG [18][19][20][21][22] and measurement-deviceindependent (MDI) QRNG [23][24][25] need complete characterizations of the measurement device and source respectively, which are commonly called semi-device-independent (SDI) QRNG, while there are also protocols based on other weak assumptions, such as the dimension of the produced quantum states 26,27 , their overlap 28,29 , their energy 30,31 , and so on. By contrast, SDI QRNG generates faster random bits with less stringent experimental requirements.…”

Informationally overcomplete measurements from generalized equiangular tight frames

“…Preserving the requirement of equal angles allows one to define equiangular measurements, which are closely related to other important mathematical objects: equiangular lines [28][29][30][31] and equiangular tight frames [32,33]. Equiangular measurements have been used in detection and quantification of quantum entanglement [34,35] with recent experimental applications in quantum key distribution [36] and quantum cryptography [37]. These measurements are projective but not informationally complete, which means that they do not allow for a full tomography of an arbitrary quantum state.…”