Fermionic phase-preserving amplification

Develop a theory of fermionic phase-preserving amplification that generalizes the deterministic nonlinear phase-preserving bosonic amplification framework beyond bosonic modes and determines its fundamental quantum-noise limits.

Background

The paper characterizes deterministic nonlinear phase-preserving amplification for a single bosonic mode, showing that every such amplifier is equivalent to a unitary transformation of a linear phase-preserving amplifier. The authors then identify optimal schemes for amplifying Yurke–Stoler cat states and Kerr kitten states by sandwiching linear amplification between number-operator-commuting Kerr unitaries.

The corresponding problem for fermionic systems is not addressed. Fermionic modes have different anticommutation relations and symmetry structures from bosonic modes, so it remains unresolved how phase-preserving amplification should be defined for fermions, whether deterministic schemes with analogous properties exist, and what fundamental noise constraints govern them.