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Francesco Anna Mele @francescoannamele.bsky.social · 7d

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Francesco Anna Mele @francescoannamele.bsky.social · 7d

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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Francesco Anna Mele @francescoannamele.bsky.social · 7d

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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Francesco Anna Mele @francescoannamele.bsky.social · 7d

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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Francesco Anna Mele @francescoannamele.bsky.social · 7d

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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Francesco Anna Mele @francescoannamele.bsky.social · 8d

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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Francesco Anna Mele @francescoannamele.bsky.social · 8d

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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Francesco Anna Mele @francescoannamele.bsky.social · 8d

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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Francesco Anna Mele @francescoannamele.bsky.social · 8d

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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Francesco Anna Mele @francescoannamele.bsky.social · 8d

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 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 ...

arxiv.org

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Francesco Anna Mele @francescoannamele.bsky.social · 8d

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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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...

arxiv.org

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Francesco Anna Mele @francescoannamele.bsky.social · 8d

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

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Francesco Anna Mele @francescoannamele.bsky.social · 8d

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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Francesco Anna Mele @francescoannamele.bsky.social · 8d

The first non-trivial question is: how should we quantify the estimation error when learning a CV quantum channel? In DV systems, this is done using the *diamond norm*, a well-motivated metric for DV quantum channels.

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Francesco Anna Mele @francescoannamele.bsky.social · 8d

In our new paper, we answer this question, designing efficient learning algorithms with rigorous performance guarantees.

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Francesco Anna Mele @francescoannamele.bsky.social · 8d

The saga of *quantum learning theory with CV systems* never ends!

And indeed, when you look closely at this field, many natural and promising questions arise. For instance:
How to learn CV Gaussian unitaries?

arxiv.org/pdf/2510.05531

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Francesco Anna Mele @francescoannamele.bsky.social · 9d

While writing up this paper, we became aware of arxiv.org/abs/2502.18656, whose main result is similar to ours. The proof techniques in the two papers, however, are significantly different

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Quantum data-hiding scheme using orthogonal separable states

We consider bipartite quantum state discrimination and present a quantum data-hiding scheme utilizing an orthogonal separable state ensemble. Using a bound on local minimum-error discrimination, we pr...

arxiv.org

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Francesco Anna Mele @francescoannamele.bsky.social · 9d

Many thanks to Ludovico Lami for this collaboration that lasted two (very busy) years! And a big thanks also to @jenseisert.bsky.social for kindly hosting us in the Berlin group in 2023, where this project began.

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Francesco Anna Mele @francescoannamele.bsky.social · 9d

In this work, we find explicit examples of quantum data hiding states that are both separable and perfectly orthogonal, thereby exhibiting the phenomenon of nonlocality without entanglement to the utmost extent.

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Francesco Anna Mele @francescoannamele.bsky.social · 9d

Prior to this research, pairs of quantum data hiding states were known only in two cases: either separable or globally perfectly orthogonal, but not both — separability comes at the price of orthogonality being only approximate.

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Francesco Anna Mele @francescoannamele.bsky.social · 9d

Remarkably, quantum data hiding states can be separable, allowing secrets to be hidden without entanglement but nearly impossible to recover without it. This phenomenon is sometimes called `nonlocality without entanglement'.

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Francesco Anna Mele @francescoannamele.bsky.social · 9d

Quantum data hiding states are pairs of bipartite states that are (almost) perfectly distinguishable globally yet (almost) indistinguishable under LOCC. Hence, they can *hide* information that only entanglement can reveal.

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Francesco Anna Mele @francescoannamele.bsky.social · 9d

New work on *quantum data hiding*! If you have a quirk for semidefinite/linear programming as an analytical tool for quantum info, this paper might interest you

arxiv.org/pdf/2510.03538

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Francesco Anna Mele @francescoannamele.bsky.social · 17d

Congrats for the beautiful results!

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Francesco Anna Mele @francescoannamele.bsky.social · 20d

I'm looking forward to presenting my work and receiving the award at the Chicago Quantum Summit on November 3-4.

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