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

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 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.

The Feynman problem and fermionic entanglement: Fermionic theory versus qubit theory

“…24. Again, in the following we exploit the jwt to represent the states of the fqt and we will drop the J symbol for the sake of clarity.…”

“…22,23 In Section 2 we review the operational framework and present the recent results of Ref. 24, where the superselection rule has been formalized in the general context of opts.…”

“…24 allows for many other theories. Among them we will discuss briefly the case of rqt-which also lacks local tomography 23 and monogamy of entanglement 26 -and the theory with number superselectionwhich only admits superposition of states having the same particle occupation number.…”

Spectral properties of reduced fermionic density operators and parity superselection rule

“…One may expect that the transfer of quantum information through a fermionic channel would be different from that for bosons [39], as the fermionic theory differs from the qubit theory [40,41] in both tomography [42] and quantum computation [43].…”

Determinism without causality

“…The presented deterministic non-causal theory can also be built in a constructive way [10]. It is done in two steps.…”