Post-quantum relativity

David Finkelstein

Christoph Striecks

This presentation shows how to securely combine quantum and post-quantum key establishment technologies and it was presented during the event "QCI Days Athens 2025" (28-29/04/2025). The related video is available here: The Hybrid State-of-Play: How to Securely Combine Quantum and Post-Quantum Technologies

Adam Teixidó-Bonfill, Joseph Schindler, Dominik Šafránek

Abstract We investigate four partial orderings on the space of quantum measurements (i.e. on POVMs or positive operator valued measures), describing four notions of coarse/fine-ness of measurement. These are the partial orderings induced by: (1) classical post-processing, (2) measured relative entropy, (3) observational entropy, and (4) linear relation of POVMs. The orderings form a hierarchy of implication, where e.g. post-processing relation implies all the others. We show that this hierarchy is strict for general POVMs, with examples showing that all four orderings are strictly inequivalent. Restricted to projective measurements, all are equivalent. Finally we show that observational entropy equality S M = S N (for all ρ) holds if and only if POVMs M ≡ N are post-processing equivalent, which shows that the first three orderings induce identical equivalence classes.

David Finkelstein

Noorolahi Siamak

Thomas van Himbeeck, Brask Bohr, Jonatan, Stefano Pironio +3 more

The causal structure of any experiment implies restrictions on the observable correlations between measurement outcomes, which are different for experiments exploiting classical, quantum, or post-quantum resources. In the study of Bell nonlocality, these differences have been explored in great detail for more and more involved causal structures. Here, we go in the opposite direction and identify the simplest causal structure which exhibits a separation between classical, quantum, and post-quantum correlations. It arises in the so-called Instrumental scenario, known from classical causal models. We derive inequalities for this scenario and show that they are closely related to well-known Bell inequalities, such as the Clauser-Horne-Shimony-Holt inequality, which enables us to easily identify their classical, quantum, and post-quantum bounds as well as strategies violating the first two. The relations that we uncover imply that the quantum or post-quantum advantages witnessed by the violation of our Instrumental inequalities are not fundamentally different from those witnessed by the violations of standard inequalities in the usual Bell scenario. However, non-classical tests in the Instrumental scenario require fewer input choices than their Bell scenario counterpart, which may have potential implications for device-independent protocols.