Fermionic computation is non-local tomographic and violates monogamy of entanglement

TL;DR

This paper demonstrates that fermionic computation models violate local tomography and monogamy of entanglement due to parity superselection rules, revealing fundamental non-local features and their implications for quantum theory.

Contribution

It shows that fermionic models inherently violate key quantum properties like local tomography and monogamy, and generalizes superselection rules to probabilistic theories, linking them to holism.

Findings

Fermionic models violate local tomography.

Fermionic states can have maximal entanglement of formation.

Superselection rules relate to the holism of probabilistic theories.

Abstract

We show that the computational model based on local Fermionic modes in place of qubits does not satisfy local tomography and monogamy of entanglement, and has mixed states with maximal entanglement of formation. These features directly follow from the parity conservation corresponding to the parity superselection rule. We generalize quantum superselection rules to general probabilistic theories as sets of linear constraints on the convex set of states. We then provide a link between the cardinality of the superselection rule and the degree of holism of the resulting theory.