Francesco Anna Mele

Huge thanks to Filippo Girardi and @ludovicolami.bsky.social for this very efficient collaboration, I’ve really learnt a lot!

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It seems that this random purification channel is such a simple yet conceptually beautiful textbook result! I bet it will have many other applications in quantum information theory.

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Uhlmann's theorem for relative entropies Uhlmann's theorem states that, for any two quantum states $ρ_{AB}$ and $σ_A$, there exists an extension $σ_{AB}$ of $σ_A$ such that the fidelity between $ρ_{AB}$ and $σ_{AB}$ equals the fidelity betwe...

We then use this result to obtain a one-line proof of the recently introduced Uhlmann’s theorem for quantum divergences (arxiv.org/abs/2502.01749).

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Uhlmann's theorem for relative entropies Uhlmann's theorem states that, for any two quantum states $ρ_{AB}$ and $σ_A$, there exists an extension $σ_{AB}$ of $σ_A$ such that the fidelity between $ρ_{AB}$ and $σ_{AB}$ equals the fidelity betwe...

In today’s paper, we give a very simple proof of this result, which makes new properties of this “random purification channel” immediately clear.

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Mixed state tomography reduces to pure state tomography A longstanding belief in quantum tomography is that estimating a mixed state is far harder than estimating a pure state. This is borne out in the mathematics, where mixed state algorithms have always ...

This result has already proved to be extremely useful in quantum learning theory (arxiv.org/abs/2511.15806). Their proof, however, is quite complicated, requiring many pages of hard-core representation theory.

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Recently, Ewin Tang, John Wright, and Mark Zhandry proved a beautiful result (arxiv.org/pdf/2510.07622): there exists a quantum channel that, given n copies of an arbitrary mixed state \rho, outputs n copies of a fixed random purification of \rho.

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Given a mixed state, one can always write down its purifications. However, the “purification operation” is unphysical, i.e. it cannot be realised via a quantum channel.

arxiv.org/pdf/2511.234...
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This is a publication I am extremely happy about. It is a bit rebellious, and yet it touches upon an old and important question: How can we learn an unknown continuous quantum state from data?

www.nature.com/articles/s41...

We prove that quantum state tomography is a lot harder than anticipated.

It’s been almost two years that I’ve been constantly thinking about these kinds of questions, and I’m very happy to continue this journey in the bosonic learning world!

I'm extremely happy about this paper, as it also opened many natural and promising research directions on "quantum learning theory with CV systems". Since its arXiv posting, we have been addressing several of these, but many others still remain unexplored.

Nature Physics has published our work!

nature.com/articles/s4156…

Thanks a lot to my amazing coauthors @antonioannamele.bsky.social , Lennart Bittel, @jenseisert.bsky.social, Vittorio Giovannetti, Ludovico Lami, Lorenzo Leone, @sfeoliviero.bsky.social !

Optimising quantum data hiding Quantum data hiding is the existence of pairs of bipartite quantum states that are (almost) perfectly distinguishable with global measurements, yet close to indistinguishable when only measurements im...

So excited that my coauthors and I have three papers accepted at QIP this year!

- Optimising quantum data hiding arxiv.org/abs/2510.03538

- Efficient learning of CV Gaussian unitaries arxiv.org/abs/2510.05531

- Is it Gaussian? Testing CV Gaussian states arxiv.org/pdf/2510.07305

The only thing that could possibly be hotter than Italian twins explaining entanglement in Italian is Italian triplets explaining the GHZ state.

YouTube video by TEDx Talks Quantum Computer: una possibile rivoluzione | Francesco Anna Mele & Antonio Anna Mele | TEDxPolicoro

Happy to share our TEDx talk where me and my twin @antonioannamele.bsky.social chat about quantum technologies!

(Italian only)

youtu.be/yzXUsDUPt8A?...

It consists of this cute trophy, $3,500, and a fully funded trip to the Chicago Quantum Summit, an event that brings together academics, companies, and even politicians interested in quantum technologies.

Honoured to have received the Boeing Quantum Creators Prize at the Chicago Quantum Exchange event today!

This prize recognises early-career researchers who advance quantum information in new directions

😂

A huge thanks to the great team: Filippo, Freek, Lennart, @sfeoliviero.bsky.social, David, and Michael. It was a wonderful collaboration!

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I’m very happy to see that the entire toolbox of CV trace-distance bounds we’ve developed over the past two years finds concrete applications in this fundamental task in CV quantum information.

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In this paper, we systematically investigate this problem, proving that testing Gaussianity can be done *efficiently* in the *pure-state* setting, but is fundamentally *inefficient* for general *mixed states*.

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Okay, last post on *quantum learning theory with CV systems* (for a few months🫣)

Today's new work tackles another natural and central question in this rapidly developing field: Given an unknown CV state, how to test whether is it Gaussian or not?

arxiv.org/pdf/2510.07305

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Many thanks to my amazing coauthors: Marco, @vishnu-psiyer.bsky.social, Junseo, @antonioannamele.bsky.social! It was fun meeting at odd hours to sync between Europe, Asia, and the US, with our WhatsApp research group constantly active 🤣

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This result is the symplectic analogue of the polar decomposition for nearly unitary matrices:

given a matrix X that is epsilon-close to an (unknown) unitary, the polar decomposition efficiently outputs an exact unitary matrix U that remains O(epsilon)-close to X.

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We also introduce a method that may be of independent interest:
Given as input a matrix X that is epsilon-close to an (unknown) symplectic matrix, our method efficiently outputs an (exact) symplectic matrix S that remains O(epsilon)-close to X.

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In our work, we carry out the first rigorous complexity analysis of learning Gaussian unitaries using a physically meaningful distance (the energy-constrained diamond norm), thereby proving that tomography of Gaussian unitary is efficient.

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Energy-constrained discrimination of unitaries, quantum speed limits and a Gaussian Solovay-Kitaev theorem We investigate the energy-constrained (EC) diamond norm distance between unitary channels acting on possibly infinite-dimensional quantum systems, and establish a number of results. Firstly, we prove ...

Useful bounds on the energy-constrained diamond distance between Gaussian unitaries were recently proved by Becker, Lami, Datta, and Rouzé (arxiv.org/abs/2006.06659).

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Energy-constrained diamond norms and their use in quantum information theory We consider the family of energy-constrained diamond norms on the set of Hermitian-preserving linear maps (superoperators) between Banach spaces of trace class operators. We prove that any norm from t...

To address this, Maksim Shirokov (arxiv.org/abs/1706.00361) and Andreas Winter (arxiv.org/pdf/1712.10267) introduced the *energy-constrained diamond norm*, a physically meaningful way to measure distances between CV quantum channels.

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This is so because the definition of diamond norm allows *infinite-energy* input states (which is, of course, unphysical!)

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However, the diamond norm loses its physical meaning for CV systems: e.g., the diamond distance between two different beam splitters is *always* maximal, even if their transmissivities differ by an infinitesimal amount.

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