I am a PhD student in Scuola Normale Superiore (Pisa). I am working in quantum information theory. More specifically, so far I have been studying problems regarding
If you are interested in my research, feel free to reach out via email. Compatibly with my current commitments, I am happy to explore new topics in quantum information theory as well. If you have any idea for a project that you think might interest us both, please do not hesitate to reach out.
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FG, Nilanjana Datta, Giacomo De Palma, Ludovico Lami
arXiv:2605.18726
The asymptotic rates of information-theoretic protocols - including error exponents, data-compression rates, and channel capacities - are traditionally derived under the idealised assumption that the underlying resources are independent and identically distributed (i.i.d.). Somewhat surprisingly, even slight departures from the exact i.i.d. structure can drastically alter the asymptotic behaviour predicted by the i.i.d. theory. If the precise nature of the perturbation is known, for instance in the case of a pointwise defect, one can design a bespoke protocol that compensates for it, e.g. by discarding the corrupted subsystem. In realistic physical settings, however, exact i.i.d. behaviour cannot be guaranteed, and deviations from the ideal regime cannot generally be identified precisely. This raises a fundamental question: which notions of almost i.i.d. structure are sufficiently robust to preserve the asymptotic predictions of quantum Shannon theory? We investigate this question for three central information-theoretic tasks: asymmetric hypothesis testing, classical and quantum data compression, and classical communication through quantum channels. Rather than designing protocols tailored to specific defects, we seek robust protocols that remain asymptotically optimal and that are universal within a broad class of almost i.i.d. resources whose precise deviations from the ideal regime are unknown. To this end, we study three inequivalent notions of almost i.i.d. structure, and determine which of them preserve the asymptotic rates and error exponents predicted by the i.i.d. theory. Along the way, we introduce the notion of an almost i.i.d. process and a new distance measure between quantum channels - the club distance - designed to capture stability under local perturbations. These notions may be of independent interest.
FG, Francesco Anna Mele, Ludovico Lami
arXiv:2511.23451
The recently introduced random purification channel, which converts \(n\) i.i.d. copies of any mixed quantum state into a uniform convex combination of \(n\) i.i.d. copies of its purifications, has proved to be an extremely useful tool in quantum learning theory. Here we give a remarkably simple construction of this channel, making its known properties -- and several new ones -- immediately transparent. In particular, we show that the channel also purifies non-i.i.d. states: it transforms any permutationally symmetric state into a uniform convex combination of permutationally symmetric purifications, each differing only by a tensor-product unitary acting on the purifying system. We then apply the channel to give a one-line proof of (a stronger version of) the recently established Uhlmann's theorem for quantum divergences.
FG\(^\ast\), Freek Witteveen\(^\ast\), Francesco Anna Mele, Lennart Bittel, Salvatore F. E. Oliviero, David Gross, Michael Walter
arXiv:2510.07305
Gaussian states are widely regarded as one of the most relevant classes of continuous-variable (CV) quantum states, as they naturally arise in physical systems and play a key role in quantum technologies. This motivates a fundamental question: given copies of an unknown CV state, how can we efficiently test whether it is Gaussian? We address this problem from the perspective of representation theory and quantum learning theory, characterizing the sample complexity of Gaussianity testing as a function of the number of modes. For pure states, we prove that just a constant number of copies is sufficient to decide whether the state is exactly Gaussian. We then extend this to the tolerant setting, showing that a polynomial number of copies suffices to distinguish states that are close to Gaussian from those that are far. In contrast, we establish that testing Gaussianity of general mixed states necessarily requires exponentially many copies, thereby identifying a fundamental limitation in testing CV systems. Our approach relies on rotation-invariant symmetries of Gaussian states together with the recently introduced toolbox of CV trace-distance bounds.
FG, Giacomo De Palma
Communications in Mathematical Physics 406 (4), 1-146 (2025)
We study quantum neural networks made by parametric one-qubit gates and fixed two-qubit gates in the limit of infinite width, where the generated function is the expectation value of the sum of single-qubit observables over all the qubits. First, we prove that the probability distribution of the function generated by the untrained network with randomly initialized parameters converges in distribution to a Gaussian process whenever each measured qubit is correlated only with few other measured qubits. Then, we analytically characterize the training of the network via gradient descent with square loss on supervised learning problems. We prove that, as long as the network is not affected by barren plateaus, the trained network can perfectly fit the training set and that the probability distribution of the function generated after training still converges in distribution to a Gaussian process. Finally, we consider the statistical noise of the measurement at the output of the network and prove that a polynomial number of measurements is sufficient for all the previous results to hold and that the network can always be trained in polynomial time.
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