We prove that CFOs are genuine free operations mapping free states to free states. We also discuss CFOs channels and provide strong numerical evidence that these channels do not increase resources on average, just as in SLOCC!

CFOs are defined by a complexification of standard unitary free operations, and extends the intuition of SLOCC to Lie algebraic structures. The "phone call" in fermions for example!

An important consequence of our framework, is that we can now import tools from one QRT onto another. In the second part of the paper we showcase this by defining a new set of free operations: complexified free operations (CFOs).

In this work we show that QRTs can be defined in terms
of some preferred algebraic structure E that must be
preserved. The free operations follow as automorphisms of E, which in turn leads to natural notions of free states. This unifies so many different QRTs!

The very concept of "resource" depends on operational constraints. This makes it difficult to unify different QRTs under a common framework. E.g., while the concept of locality is very clear in a QRT of entanglement, what is the equivalent of phone calls in a QRT of fermions?

Quantum resource theories (QRTs) are a central tool of quantum information developed to acknowledge the fact that different quantum operations and states of a given system are more valuable than others.

We prove that CFOs are genuine free operations mapping free states to free states. We also discuss CFOs channels and provide strong numerical evidence that these channels do not increase resources on average, just as in SLOCC!

CFOs are defined by a complexification of standard unitary free operations, and extends the intuition of SLOCC to Lie algebraic structures. The "phone call" in fermions for example!

An important consequence of our framework, is that we can now import tools from one QRT onto another. In the second part of the paper we showcase this by defining a new set of free operations: complexified free operations (CFOs).

In this work we show that QRTs can be defined in terms
of some preferred algebraic structure E that must be
preserved. The free operations follow as automorphisms of E, which in turn leads to natural notions of free states. This unifies so many different QRTs!

The very concept of "resource" depends on operational constraints. This makes it difficult to unify different QRTs under a common framework. E.g., while the concept of locality is very clear in a QRT of entanglement, what is the equivalent of phone calls in a QRT of fermions?

Quantum resource theories (QRTs) are a central tool of quantum information developed to acknowledge the fact that different quantum operations and states of a given system are more valuable than others.