Fully non-positive-partial-transpose genuinely entangled subspaces

Genuinely entangled subspaces are a class of subspaces in the multipartite Hilbert spaces that are composed of only genuinely entangled states. They are thus an interesting object of study in the context of multipartite entanglement. Here we provide a construction of multipartite subspaces that are not only genuinely entangled but also fully non-positive-partial-transpose (NPT) in the sense that any mixed state supported on them has non-positive partial transpose across any bipartition. Our construction originates from the stabilizer formalism known for its use in quantum error correction. To this end, we first introduce a couple of criteria allowing to assess whether any state from a given non-trivial stabilizer subspace is genuinely multipartite entangled. We then use these criteria to construct genuinely entangled stabilizer subspaces for any number of parties and arbitrary local dimension and conjecture them to be of maximal dimension achievable within the stabilizer formalism. At the same time, we prove that every genuinely entangled subspace is fully NPT in the above sense, which implies a quite surprising fact that no genuinely entangled stabilizer subspace can support PPT entangled states

Self-testing of any pure entangled state with minimal number of measurements and optimal randomness certification in one-sided device-independent scenario

Certification of quantum systems and their properties has become a field of intensive studies. Here, taking advantage of the one-sided device-independent scenario (known also as quantum steering scenario), we propose a self-testing scheme for all bipartite entangled states using a single family of steering inequalities with the minimal number of two measurements per party. Building on this scheme we then show how to certify all rank-one extremal measurements, including non-projective $d^2$-outcome measurements, which in turn can be used for certification of the maximal amount of randomness from every entangled bipartite state of local dimension $d$, that is, $2\log_2d$ bits. Finally, in a particular case of $d=3$, we extend our self-testing results to the fully device-independent setting.Comment: Corrected and improved version. Comments are welcome

High-dimensional monitoring and the emergence of realism via multiple observers

Quantum measurements are unitary evolutions followed by partial traces. Based on that, we address the problem of the emergence of physical reality from the quantum world by introducing a model that interpolates between weak and strong non-selective measurements for qudits. Our model, which is based on generalized observables and Heisenberg-Weyl operators, suggests that for high-dimensional qudits, full information about the system can only be obtained by making the system interact with not just one but several environmental qudits, following a Quantum Darwinism framework.Comment: 12 pages, 2 figure