Reasonable fermionic quantum information theories require relativity

TL;DR

This paper demonstrates that incorporating relativity via superselection rules is essential for a consistent fermionic quantum information theory, resolving ambiguities in entanglement definitions caused by anticommuting operators.

Contribution

It shows that the parity superselection rule derived from relativity is necessary to properly define entanglement in fermionic quantum theories.

Findings

Superselection rules rooted in relativity resolve entanglement ambiguities.

Unrestricted fermionic theories have non-matching marginal entropies.

Relativity enforces a fundamental link between quantum information and causal structure.

Abstract

We show that any quantum information theory based on anticommuting operators must be supplemented by a superselection rule deeply rooted in relativity to establish a reasonable notion of entanglement. While quantum information may be encoded in the fermionic Fock space, the unrestricted theory has a peculiar feature: The marginals of bipartite pure states need not have identical entropies, which leads to an ambiguous definition of entanglement. We solve this problem, by proving that it is removed by relativity, i.e., by the parity superselection rule that arises from Lorentz invariance via the spin-statistics connection. Our results hence unveil a fundamental conceptual inseparability of quantum information and the causal structure of relativistic field theory.