Revisiting the Role of State Texture in Gate Identification and Fixed-Point Resource Theories

TL;DR

This paper revisits quantum gate identification protocols linked to state texture, generalizes the resource theory framework for various quantum resources, and introduces fixed-point resource theories with new monotonicity properties.

Contribution

It extends the state texture resource theory to broader settings, introduces fixed-point resource theories, and analyzes their monotonicity properties under free operations.

Findings

A more general fidelity-based gate identification protocol is effective for most laboratory bases.

A broader family of quantum resource theories is established for different reference states.

Fixed-point resource theories exhibit weak monotonicity and violations of strong monotonicity in certain measures.

Abstract

A protocol for identifying controlled-NOT (CNOT) gates versus single-qubit-only gates in universal quantum circuits using randomized input states was recently shown to be intimately connected to the quantum resource of state texture. Here we revisit this gate identification protocol and demonstrate that a more general fidelity-based formulation succeeds for nearly all laboratory bases. We then examine a broader family of quantum resource theories, where a distinct resource theory can be defined for each choice of reference pure state, establishing core resource-theoretic requirements without the computational shortcut offered by the "grand sum" employed in the original formulation of state texture. By extending from single "resourceless" states to convex sets via a convex-roof construction, we recover single-qubit measures of known resource theories such as imaginarity and coherence. Finally, we introduce a family of "fixed-point resource theories" that includes fixed-point instances of the theories of state texture, genuine coherence, purity, and athermality. For these fixed-point resource theories we show that, under free operations, the fidelity-based lower bound is weakly monotonic, while specific violations of strong monotonicity are found for the convex-roof logarithmic measure.