General QSP framework for nonselective reflections

Develop a general quantum signal processing framework in which the signal reflection is implemented through a nonselective or imperfectly matched reflection operator, characterize the polynomial transformations achievable with restricted information about the target state, and determine which errors can be suppressed by increasing the polynomial degree versus which are fundamentally limited by the accessible projector.

Background

The paper introduces non-orthogonal amplitude amplification (NOAA) for hybrid continuous-variable–discrete-variable processors, where the accessible reflection is implemented through a projector that does not perfectly isolate the target state. The analysis establishes a fidelity ceiling imposed by the selectivity of that projector, independent of the amplification degree or phase optimization.

The authors identify as an open direction the formulation of NOAA within the broader quantum signal processing framework. Such a formulation would clarify the expressive power of polynomial transformations under imperfect target-state information and distinguish errors that can be reduced by increasing sequence degree from limitations intrinsic to the accessible reflection operator.