Quantum ciphertext authentication and key recycling with the trap code

We investigate quantum authentication schemes constructed from quantum error-correcting codes. We show that if the code has a property called purity testing, then the resulting authentication scheme guarantees the integrity of ciphertexts, not just plaintexts. On top of that, if the code is strong purity testing, the authentication scheme also allows the encryption key to be recycled, partially even if the authentication rejects. Such a strong notion of authentication is useful in a setting where multiple ciphertexts can be present simultaneously, such as in interactive or delegated quantum computation. With these settings in mind, we give an explicit code (based on the trap code) that is strong purity testing but, contrary to other known strong-purity-testing codes, allows for natural computation on ciphertexts

Catalytic space: Non-determinism and hierarchy

Catalytic computation, defined by Buhrman, Cleve, Koucký, Loff and Speelman (STOC 2014), is a space-bounded computation where in addition to our working memory we have an exponentially larger auxiliary memory which is full; the auxiliary memory may be used throughout the computation, but it must be restored to its initial content by the end of the computation. Motivated by the surprising power of this model, we set out to study the non-deterministic version of catalytic computation. We establish that non-deterministic catalytic log-space is contained in ZPP, which is the same bound known for its deterministic counterpart, and we prove that non-deterministic catalytic space is closed under complement (under a standard derandomization assumption). Furthermore, we establish hierarchy theorems for non-deterministic and deterministic catalytic computation

Nest defence behaviour is similar between pair members but only male behaviour predicts nest survival in barnacle geese

Behavioural patterns often differ consistently across individuals and are linked to fitness. In species with biparental care, the defence behaviour of both parents can affect reproductive success through offspring survival. In addition to the intensity of defence behaviour by both pair members, the similarity in this behaviour among parents may affect offspring survival. However, few studies have investigated the relative impact of both the intensity and similarity of defence behaviour. Here, we examined nest defence behaviour of males and females during the incubation stage in an Arctic population of barnacle geese Branta leucopsis. We calculated the repeatability of defence behaviour to test whether this behaviour is consistent within individuals and investigated how it is associated with age. In addition, we investigated how daily survival rate (DSR) of the nests until hatching is associated with nest defence behaviour and age of the parents, as well as the effect of parent similarity in nest defence behaviour as an emergent trait of the pair bond. Both male and female defence behaviour were highly repeatable. The ages of both partners within breeding pairs were positively related, but age was only significantly associated with defence behaviour in females. Further, we found high similarity in defence behaviour within breeding pairs, but the similarity and intensity of defence behaviour within breeding pairs did not predict DSR. Finally, male defence behaviour positively predicted DSR, but female defence behaviour and male and female age did not. Our results suggest that nest protection is adaptive in males but behavioural similarity of pair members does not enhance nest survival, indicating behavioural similarity itself is not adaptive but rather a by-product of different effects