Mutually unbiased bases (MUBs) are highly symmetric bases on complex Hilbert spaces, and the corresponding rank-1 projective measurements are ubiquitous in quantum information theory. In this work, we study a recently introduced generalisation of MUBs called mutually unbiased measurements (MUMs). These measurements inherit the essential property of complementarity from MUBs, but the Hilbert space dimension is no longer required to match the number of outcomes. This operational complementarity property renders MUMs highly useful for device-independent quantum information processing. It has been shown that MUMs are strictly more general than MUBs. In this work we provide a complete proof of the characterisation of MUMs that are direct sums of MUBs. We then construct new examples of MUMs that are not direct sums of MUBs. A crucial technical tool for this construction is a correspondence with quaternionic Hadamard matrices, which allows us to map known examples of such matrices to MUMs that are not direct sums of MUBs. Furthermore, we show that—in stark contrast with MUBs—the number of MUMs for a fixed outcome number is unbounded. Next, we focus on the use of MUMs in quantum communication. We demonstrate how any pair of MUMs with$d$outcomes defines a$d$-dimensional superdense coding protocol. Using MUMs that are not direct sums of MUBs, we disprove a recent conjecture due to Nayak and Yuen on the rigidity of superdense coding, for infinitely many dimensions. The superdense coding protocols arising in the refutation reveal how shared entanglement may be used in a manner heretofore unknown.

Antibodies are versatile molecular binders with an established and growing role as therapeutics. Computational approaches to developing and designing these molecules are being increasingly used to complement traditional lab-based processes. Nowadays, in silico methods fill multiple elements of the discovery stage, such as characterizing antibody-antigen interactions and identifying developability liabilities. Recently, computational methods tackling such problems have begun to follow machine learning paradigms, in many cases deep learning specifically. This paradigm shift offers improvements in established areas such as structure or binding prediction and opens up new possibilities such as language-based modeling of antibody repertoires or machine-learning-based generation of novel sequences. In this review, we critically examine the recent developments in (deep) machine learning approaches to therapeutic antibody design with implications for fully computational antibody design.

We investigate two-party cryptographic protocols that are secure under assumptions motivated by physics, namely special relativity and quantum mechanics. In particular, we discuss the security of bit commitment in the so-called split models, i.e., models in which at least one of the parties is not allowed to communicate during certain phases of the protocol. We find the minimal splits that are necessary to evade the Mayers-Lo-Chau no-go argument and present protocols that achieve security in these split models. Furthermore, we introduce the notion of local versus global command, a subtle issue that arises when the split committer is required to delegate noncommunicating agents to open the commitment. We argue that classical protocols are insecure under global command in the split model we consider. On the other hand, we provide a rigorous security proof in the global command model for Kent's quantum protocol. The proof employs two fundamental principles of modern physics, the no-signaling property of relativity and the uncertainty principle of quantum mechanics.