Local orthogonality as a foundational principle

S. Aravinda, Amit Mukherjee, Manik Banik

The question concerning the physical realizability of a probability distribution is quite important in quantum foundations. Recent studies emphasized a principle which was first indicated by Specker. This principle, called Specker's principle, bounds physically realizable correlations. We study Specker's observation in the scenario that involves three inputs each with two outputs. Then using only linear constraints imposed on joint probabilities by this principle, we reveal the unphysical nature of Garg-Mermin (GM) correlation. Interestingly, GM correlation was proposed to falsify the following suggestion by Fine: if the inequalities of Clauser and Horne (CH) holds, then there exists a deterministic local hidden-variable model for a spin-1/2 correlation experiment of the Einstein-Podolsky-Rosen type, even when more than two observables are involved on each side. Our result establishes that, unlike in the CH scenario, the local orthogonality principle at single copy level is not equivalent to the no-signaling condition in the GM scenario.

Atanu Bhunia, Saronath Halder, Preeti Parashar +1 more

A set of orthogonal product states is said to exhibit "quantum nonlocality without entanglement" if it is locally indistinguishable, i.e. no sequence of local operations and classical communication (LOCC) can perfectly discriminate the states. Building on this foundational idea, recent studies have highlighted the phenomenon of "genuine activation of hidden nonlocality", where a set of initially distinguishable orthogonal states becomes locally indistinguishable through orthogonality-preserving LOCC transformations. In this letter, we establish that any complete orthogonal product basis that is initially locally distinguishable remains so under all orthogonality-preserving local projective measurements, thereby ruling out activation via orthogonality-preserving local projective measurements and classical communication. We further introduce and formalise the notions of "strongly local sets", namely locally distinguishable sets that remain non-activable under all bipartitions. Interestingly, the study of "local activability" of distinguishable sets is useful to characterise the boundary between LOCC distinguishability and its irreversible loss in multipartite systems. Our results provide a rigorous structural understanding of local-to-nonlocal transitions in quantum state discrimination.

John Harding, Remi Salinas Schmeis

Martin Gebert, Heinrich Küttler, Peter Müller

Steven K. Burger, Weitao Yang

An absolute energy minimum variational principle is used for carrying out linear scaling calculations with non-orthogonal localized orbitals. Compared with results based on orthogonal localized molecular orbitals, the method is shown to give significantly more accurate results when the localized molecular orbitals are allowed to be non-orthogonal. This is made possible by introducing a second minimization for approximating the inverse overlap matrix. We also show how an exact line search may be used efficiently with the conjugate gradient method for minimizing the energy functional.

Peter Bierhorst