No payment, no waiving of fees, it's like getting a sticker on your CV I guess 🤷‍♂️

I got an invitation for this, but seems like a ton of work 😅

Thanks again to my wonderful co-authors Martin Larocca, @dgarciamartin.bsky.social, @nahuelldiaz.bsky.social, Paolo Braccia, Enrico Fontana, @quantummanuel.bsky.social, Pablo Bermejo, @aroosaijaz.bsky.social @supanut-thanasilp.bsky.social, Eric Anschuetz and @qzoeholmes.bsky.social

As always, the works is not meant to be a strict statement (only a Sith deals in absolutes), but we want to engage our community in an open discussions regarding the (many) limitations of variational methods and how to solve these issues!

forgot @nahuelldiaz.bsky.social on the list above #Shame

Hey Mark! Great question, we jump from local unitaries to SLOCC, as those are based on underlying Lie groups.

To be honest I have always found LOCC extremely confusion (separable a little less so), but making the leap of faith straight to SLOCC was the saving grace for us.

Huge propos to my co-authors Andy Deneris, Paolo Braccia, Pablo Bermejo and @antonioannamele.bsky.social !

We only scratched the surface of a cross-examination of a state’s resourcefulness, but our work revealed that resource is truly in the eye of the (QRT) beholder!

I can't really elaborate more than what the title already says, we take free states of one theory, we see how resourceful they are in another one.

Its a simple idea which leads to cool results, and the paper is packed with Haar integrals and numerics!

So What Do We Know QC To Be Good For?
- Simulating quantum physics and chemistry
- Breaking current public-key encryption (RSA, DH, ECC)
- Eventually, modest (square-root) speedups from Grover
- We’ll have to get lucky for most other applications!
(The world has been systemically lied to about this)

Huge thanks to my co-authors Pablo Bermejo, Paolo Braccia, @antonioannamele.bsky.social , @nahuelldiaz.bsky.social, Andrew E. Deneris and Martin Larocca

Bonus: certain small-irrep purities act as resourcefulness witnesses (they peak only for free states), and truncating high-irrep components leads to notions of state compressibility—think quantum data compression! 🗜️

Indeed, low resource state are VERY compressible!

We test universality across quantum resource theories: entanglement (bi- & multipartite), fermionic Gaussianity, spin coherence & Clifford stabilizerness—no resource theory left behind! 🌐

Across all of these we find:

Low/high resource = live in small/high dimensional irreps

Central to our framework are GFD purities—the norms of those projections. They reveal a spectrum: low-resource states live in small-dimensional irreps, while high-resource states spread into more & higher-dimensional irreps, mirroring classical harmonic analysis.

We introduce 👉group-Fourier decompositions (GFDs)👈 for quantum resource theories: projecting pure states onto the irreducible representations of the free-operation group to fingerprint resourcefulness & complexity.