By employing the Bloch-sphere formalism, I will present a novel class of unstable qubits, which are called Critical Unstable Qubits (CUQs). The characteristic property of CUQs is that the energy-level and decay-width Pauli vectors, E and Γ, are orthogonal to one another, and the key parameter r = |Γ|/(2|E|) is less than 1. A remarkable feature of CUQs is that they exhibit atypical behaviours like coherence-decoherence oscillations when analysed in an appropriately defined co-decaying frame of the system. In the same frame, I will show how a unit Bloch vector b describing a pure CUQ sweeps out unequal areas during equal intervals of time, while rotating about the vector E. These phenomena emerge beyond the usual oscillatory pattern due to the energy-level difference of a standard two-level quantum system. I will illustrate how these new features are relatively robust and persist even for quasi-CUQs, in which the vectors E and Γ are not perfectly orthogonal to each other. I discuss potential applications of our results to quantum information and to unstable meson-antimeson and other systems.

Neutrinos are the least known particles in the Standard Model. In particular, whether they are Dirac or Majorana particles is an important open question. Theoretically, it is also possible that they are pseudo-Dirac, which are fundamentally Majorana fermions, but essentially act like Dirac fermions in most experimental settings, due to extremely small active-sterile mass splitting. We will discuss how such tiny values of mass splitting can be accessed via oscillations over astrophysical baselines. We use the recent multi-messenger observations of high-energy neutrino sources to probe hitherto unexplored values of mass splitting, which improve the reach of terrestrial experiments by more than a billion. Finally, we will present an intriguing hint for nonzero active-sterile mass splitting in the recent IceCube data.

Currently, pulsed parametric down-conversion (PDC) in waveguides is one of the most promising platforms for non-classical light sources. PDC provides not only an efficient way to generate biphoton pairs and squeezed states but also can be used in more advanced circuits to prepare non-Gaussian states of light. However, waveguides typically possess surface imperfections that may cause significant scattering of the guided light, providing multimode mixed output states. In this talk, we discuss the properties of the multimode PDC in lossy waveguides and show how critical these losses are for the generation of biphoton, squeezed, and entangled states ([Quantum 9, 1621 (2025)] and [arXiv:2501.08917]).