The problem of device-independent randomness amplification against no-signaling adversaries has so far been studied under the assumption that the weak source of randomness is uncorrelated with the (quantum) devices used in the amplification procedure. In this work, we relax this assumption, and reconsider the original protocol of Colbeck and Renner using a Santha-Vazirani (SV) source. To do so, we introduce an SV-like condition for devices, namely that any string of SV source bits remains weakly random conditioned upon any other bit string from the same SV source and the outputs obtained when this further string is input into the devices. Assuming this condition, we show that a quantum device using a singlet state to violate the chained Bell inequalities leads to full randomness in the asymptotic scenario of a large number of settings, for a restricted set of SV sources (with 0 ≤ ε < (2 (1/12) − 1)/(2(2 (1/12) + 1)) ≈ 0.0144). We also study a device-independent protocol that allows for correlations between the sequence of boxes used in the protocol and the SV source bits used to choose the particular box from whose output the randomness is obtained. Assuming the SV-like condition for devices, we show that the honest parties can achieve amplification of the weak source, for the parameter range 0 ≤ ε < 0.0132, against a class of attacks given as a mixture of product box sequences, made of extremal nosignaling boxes, with additional symmetry conditions. Composable security proof against this class of attacks is provided.

The seminal idea of quantum money, not forgeable due to laws of Quantum Mechanics, proposed by Stephen Wiesner, has laid the foundations for the Quantum Information Theory in the early '70s.Recently, several other schemes for quantum currencies have been proposed, all, however, relying on the assumption that the quantum source device, acts according to its specification. This makes several known quantum money protocols vulnerable to the so-called hardware Trojan horse attacks. We, therefore, study the following problem: to what extent quantum money schemes can be made independent from the inner working of source and verification-devices used by the honest parties (bank and mint) in creating and processing the quantum money? Drawing inspirations from the semi-device-independent quantum key distribution protocol, we introduce the first scheme of quantum money with this assumption partially relaxed, along with the proof of its unforgeability. Finally, we formulate and discuss a quantum analog of the Oresme-Copernicus-Gresham's law of economy, that may hold in the future.

We investigate whether the heart rate can be treated as a semi-random source with the aim of amplification by quantum devices. We use a semi-random source model called ε-Santha–Vazirani source, which can be amplified via quantum protocols to obtain a fully private random sequence. We analyze time intervals between consecutive heartbeats obtained from Holter electrocardiogram (ECG) recordings of people of different sex and age. We propose several transformations of the original time series into binary sequences. We have performed different statistical randomness tests and estimated quality parameters. We find that the heart can be treated as a good enough, and private by its nature, source of randomness that every human possesses. As such, in principle, it can be used as input to quantum device-independent randomness amplification protocols. The properly interpreted ε parameter can potentially serve as a new characteristic of the human heart from the perspective of medicine.