Description
In this work we first propose a unification for quantum resource theories (QRTs) from the realization that beneath all QRTs lies an underlying algebraic structure that must be preserved. One of the most important consequences of this unifying framework is that we can now import tools from one QRT onto another, allowing us to gain general insights on what makes a free task "free". As a remarkable demonstration of this statement, we introduce a new set of operations which we denote as "complexified free operations" (CFOs). These are inspired by the QRT of standard entanglement where it is natural to transition from local unitaries to the set of resource non-increasing local operations and classical communication (SLOCC). Both operationally and mathematically, the CFOs capture the essence of this transition, and allow us to obtain previously unknown resource non-increasing operations in QRTs such as that of spin coherence and fermionic Gaussianity. We show the sanity of our novel framework through a set of rigorous theorems and numerical implementations of CFOs via weak measurements. While our results establish foundational insights into CFOs, they merely scratch the surface, leaving many exciting questions open for the community to explore.
