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The quantum description of reality is quite different from the classical one. Understanding this difference at a fundamental level is still an interesting topic. Recently, Dragan and Ekert [New J. Phys. 22 (2020) 033038] postulated that considering so-called superluminal observers can be useful in this context. In particular, they claim that the full mathematical structure of the generalized Lorentz transformation may imply the emergence of multiple quantum mechanical trajectories. On the contrary, here we show that the generalized Lorentz transformation, when used in a consistent way, does not provide any correspondence between the classical concept of a definite path and the multiple paths of quantum mechanics., Comment: 4 pages, new section added

The superposition principle is one of the landmarks of quantum mechanics. The importance of quantum superpositions provokes questions about the limitations that quantum mechanics itself imposes on the possibility of their generation. In this work we systematically study the problem of creation of superpositions of unknown quantum states. First, we prove a no-go theorem that forbids the existence of a universal probabilistic quantum protocol producing a superposition of two unknown quantum states. Secondly, we provide an explicit probabilistic protocol generating a superposition of two unknown states, each having a fixed overlap with the known referential pure state. The protocol is proven to be unique and optimal. Moreover, it can be implemented on arbitrary Hilbert spaces. In the context of quantum optics it can be used to efficiently generate highly nonclassical or nongaussian states., Comment: 4.5 pages + 4.5 pages of Appandix, 4 figures, updated discussion on the Alvarez-Rodriguez et. al. article arxiv:1411.4534, updated references, accepted for publication in PRL

We show that a one-dimensional discrete time quantum walk can be used to implement a generalized measurement in terms of positive operator value measure (POVM) on a single qubit. More precisely, we show that for a single qubit any set of rank 1 and rank 2 POVM elements can be generated by a properly engineered quantum walk. In such a scenario the measurement of particle at position x=i corresponds to a measurement of a POVM element E_i on a qubit. We explicitly construct quantum walks implementing unambiguous state discrimination and SIC-POVM., Comment: 6 pages, 1 figure