By testing nonlocality, the security of entanglement-based quantum key distribution (QKD) can be enhanced to being ``device-independent.'' Here we ask whether such a strong form of security could also be established for one-way (prepare and measure) QKD. While fully device-independent security is impossible, we show that security can be guaranteed against individual attacks in a semi-device-independent scenario. In the latter, the devices used by the trusted parties are noncharacterized, but the dimensionality of the quantum systems used in the protocol is assumed to be bounded. Our security proof relies on the analogies between one-way QKD, dimension witnesses, and random-access codes.

We show that monogamy of Bell's inequality violations, which is strictly weaker condition than the no-signaling principle is enough to prove security of quantum key distribution. We derive our results for a whole class of monogamy constraints and generalize our results to any theory that communicating parties may have access to. Some of these theories do not respect the no-signaling principle yet still allow for secure communication. This proves that no signaling is only a sufficient condition for the possibility of secure communication, but not the necessary one. We also present some new qualitative results concerning the security of existing quantum key distribution protocols.

We study random-number-expansion protocols based on the n$\rightarrow${}1 quantum random access codes (QRACs). We consider them in the semi-device-independent scenario where the inner workings of the devices are unknown to us but we can certify the dimensions of the systems being communicated. This approach does not require the use of entanglement and makes the physical realization of these protocols much easier than in the standard device-independent scenario. In our work, we propose a protocol for randomness expansion, compute min-entropy for the semi-device-independent protocol, and investigate n$\rightarrow${}1 QRACs with a view to their use in randomness-expansion protocols. We also calculate the dependence of the effectiveness of the randomness generation on n and find it optimal for n=3, and provide the explanation for this fact.

An (n,m,p) random access code (RAC) makes it possible to encode n bits in an m-bit message in such a way that a receiver of the message can guess any of the original n bits with probability p greater than 12. In quantum RACs (QRACs), one transmits n qubits. The full set of primitive entanglement-assisted random access codes (EARACs) is introduced, in which parties are allowed to share a two-qubit singlet. It is shown that via a concatenation of these, one can build for any n an (n,1,p) EARAC. QRACs for n>3 exist only if parties also share classical randomness. We show that EARACs outperform the best of known QRACs not only in the success probabilities but also in the amount of communication needed in the preparatory stage of the protocol. Upper bounds on the performance of EARACs are given and shown to limit also QRACs.

We show that in device-independent quantum key distribution protocols the privacy of randomness is of crucial importance. For sublinear test sample sizes even the slightest guessing probability by an eavesdropper will completely compromise security. We show that a combined attack exploiting test sample and measurement choices compromises the security even with a linear-size test sample and otherwise device-independent security considerations. We explicitly derive the sample size needed to retrieve security as a function of the randomness quality. We demonstrate that exploiting features of genuinely higher-dimensional systems, one can reduce this weakness and provide device-independent security more robust against weak randomness sources.