Information theory has its particles, bits and qubits, just as physics has electrons and photons. However, in physics we have a special category of objects with no clear counterparts in information theory: quasiparticles. They are introduced to simplify complex emergent phenomena making otherwise very difficult calculations possible and providing additional insight into the inner workings of the system. We show that we can adopt a similar approach in information theory. We introduce the hyperbits, information quasiparticles which we prove to be a resource equivalent to entanglement and classical communication, and we give examples of how they can be used to simplify calculations and get more insight into communication protocols.
Two sharp yes/no questions are mutually unbiased if and only if their involutions anticommute. A set of unbiased questions is therefore a Clifford algebra, whose maximal size is odd, meaning four anticommuting questions typically imply a fifth: the two-level systems of real, complex and quaternionic quantum theory allow two, three and five questions, while four is skipped. Without this operator product restriction, a two-level system with four unbiased questions exists as the four-dimensional Bloch ball, the hyperbit. The single-system postulates that pick out the Jordan state spaces allow such a model, and only energy observability rules it out. We show what it lacks, and realise it inside two qubits: its Kirkwood-Dirac imaginary parts are hidden
so(4) generators, its composites allow entanglement but no interaction, and its 24-cell of states stays Spekkens preparation contextual down to depolarising strength
2/3. In fermionic terms, the four questions are the Majorana operators of two modes while the fifth is parity: the four-question system is therefore the sector removed by parity superselection.
Paw\l{}owski and Winter's hyperbit theory, proposed in 2012, presented itself as an alternative to quantum theory, suggesting novel ways of redefining entanglement and classical communication paradigms. This research undertakes a meticulous reevaluation of hyperbit theory, uncovering significant operational constraints that question its equivalence with quantum mechanics. Crucially, the supposition that hyperbit theory and quantum theory are equivalent relies on the receiver having unattainable additional knowledge about the sender's laboratory, indicating that the work by Paw\l{}owski and Winter is incorrect. This study accentuates the constraints of hyperbits in information processing and sheds light on the superiority of quantum communication, thereby advancing the investigation at the intersection of classical and quantum communication.