arXiv subjects

Alioscia Hamma

Publications and source records attributed to Alioscia Hamma.

At least 19 recordsLinked to original sources

arXiv2026

Non-local Magic: closed-form solution and equivalence with magic of purification

Non-local magic quantifies the non-stabilizerness of a bipartite quantum state that cannot be removed by local unitary transformations. Despite its natural definition, its evaluation generally requires a difficult optimization over local unitaries. Here, we show that for the log-stabilizer fidelity this optimization admits an exact closed-form analytic solution depending only on the Schmidt spectrum. We then introduce the magic of purification, defined as the minimum pure-state magic over all purifications of a mixed state, and show that it naturally induces a resource theory whose free states are normalized stabilizer-code projectors. For the log-stabilizer fidelity, the magic of purification admits a distance-based formulation in terms of the Uhlmann fidelity. Remarkably, we prove that non-local magic coincides with the minimum magic of purification along the unitary orbit of the reduced density operator. Our results provide both an efficient analytical characterization and a mixed-state resource-theoretic interpretation of non-local magic.

quant-ph↗

arXiv2026

QTris: a pedagogical board game to teach Quantum Mechanics

In this paper we introduce the new version of QTris, a board game designed to teach and learn Quantum Mechanics within the framework of Quantum Information and Computation. The key idea behind the game is that every game sequence simulates a process on a system of qubits. Thus, QTris can be effectively integrated as a pedagogical tool to teach Quantum Mechanics at high-school level following a two-state approach. After arguing in support of this latter approach, we describe QTris' basic rules and some of its possible extensions, emphasizing how the game mechanics puts in clear light key quantum concepts such as incompatibility, probabilistic measurement and unitary transformation. Moreover, we report on the results of a QTris-based educational activity which involved about 150 high-school students and provided encouraging preliminary indications that QTris can be a useful pedagogical platform to promote an immediate understanding of some key concepts of Quantum Mechanics.

physics.ed-ph↗

arXiv2026

Quantum Chinese Remainder Clock

The Chinese remainder theorem is used in metrology for extending the range of quantum clocks/radar/interferometry, where the phase of a signal is known relative to a set of oscillators with different periods. This paper investigates the performance of a quantum-mechanical Chinese remainder clock, consisting of atoms/oscillators with pairwise coprime periods. We provide the optimal initial state and the optimal Heisenberg-limited quantum measurements for measuring time up to the product of the periods. We introduce a novel fault-tolerant post-processing protocol that allows reconstruction of the correct time even in the presence of errors in the remainders.

quant-ph↗

arXiv2026

Stabilizer entropy is trustworthy for mixed states

Quantifying non-stabilizerness in mixed states is provably intractable, as any strict monotone requires superexponential time. We propose a linear Stabilizer Entropy that acts as a proper non-stabilizerness monotone with overwhelming probability when restricted to non-adaptive Clifford channels acting on flat mixed stabilizer states. Analytical and numerical results for Haar-random states, Clifford orbits, and random matrix product states show that monotonicity violation probabilities decay as $\exp-\eta N$. We also prove the validity of Stabilizer Entropy in specific many-body systems undergoing partial measurements, where the amount of resource never increases for each measurement outcome as well as when averaged over outcome probabilities. Given the hardness of strict alternatives, Stabilizer Entropy emerges as a practical and theoretically justified resource measure.

quant-ph↗

arXiv2026

Induced Resource Theories and Harvesting via Quantum Probes

We consider scenarios in which a quantum system with a well-defined resource theory is used as a probe to interact with an environment, such as a quantum field, for which a resource-theoretic description is absent or incomplete. We clarify if and how the harvesting of a resource in the probe can tell us about the state of the environment. This is particularly ambiguous when the probe-environment interaction is not a free operation, or the concept of such free operations cannot be defined altogether. We propose a framework and precise conditions under which it becomes possible to interpret resource generation on the probe as evidence of resources in the environment, thereby introducing an effective notion of resources for the latter. Our results clarify in which sense resources can be said to be harvested from the environment and provide a systematic way to analyse such processes beyond fully controlled resource-theoretic settings. More generally, this work may provide a step towards a more general understanding of the interplay of different quantum resources.

quant-ph↗

arXiv2026

A journey through Flatland: What does the antiflatness of a spectrum teach us?

We explore the concept of antiflatness to characterize the structural fluctuations within the entanglement spectrum of a quantum state (i.e., the spectrum of its reduced density operator). As a measure of the interplay between entanglement and magic, two fundamental quantum resources, antiflatness provides second-order information about quantum correlations that standard average measures fail to capture. Recognizing that standard majorization theory fundamentally orders states by purity and is structurally blind to spectral fluctuations, we introduce a novel partial ordering known as antiflat majorization, based on the R\'enyi entropy spread. We define Flatness-Preserving Operations (FPOs), establishing new necessary conditions for state convertibility. Furthermore, we unify different measures of antiflatness-such as Capacity of Entanglement, Linear R\'enyi spread, and Logarithmic antiflatness-using the frameworks of escort distributions and Bregman divergences. We prove that the Capacity of Entanglement can be expressed as a second derivative of the Kullback-Leibler divergence along the escort trajectory, connecting it with the Quantum Fisher Information. Finally, we demonstrate that absolute maximal antiflatness is not achieved by a single universal state, but rather by a continuous Pareto frontier of extremal states with jump spectra, and we analyze the typicality of these spectral fluctuations using Haar, Bures-Hall and t-doped Clifford random state ensembles.

quant-ph↗

arXiv2026

Non-Local Magic Resources for Fermionic Gaussian States

Entanglement and magic are fundamental resources that capture the complexity of quantum many-body systems. Non-local magic isolates the irreducible nonstabilizerness intrinsically tied to entanglement. However, evaluating this quantity generally requires a prohibitive minimization over the full Hilbert space, making it computationally inaccessible beyond a few qubits. Here, we overcome this bottleneck by establishing a closed-form expression for the non-local stabilizer entropies of fermionic Gaussian states over local Gaussian unitaries, which we prove at R\'enyi index $\alpha=2$ for arbitrary subsystem size, and which can be evaluated in polynomial time directly from the eigenvalues of the reduced Majorana covariance matrix. We apply this framework to characterize fermionic non-local magic across diverse physical regimes: we derive an exact Page-like curve for typical random states, reveal logarithmic scaling at the quantum critical point of the XY model, and establish a quasiparticle picture for magic generation during out-of-equilibrium quantum quenches. Crucially, because our result relies solely on two-point correlation functions, it provides a scalable route for the experimental estimation of fermionic non-local magic in large-scale quantum processors via fermionic shadow tomography.

quant-ph↗

arXiv2026

Probes of chaos over the Clifford group and approach to Haar values

Chaotic behavior of quantum systems can be characterized by the adherence of the expectation values of given probes to moments of the Haar distribution. In this work, we analyze the behavior of several probes of chaos using a technique known as Isospectral Twirling [1]. This consists in fixing the spectrum of the Hamiltonian and picking its eigenvectors at random. Here, we study the transition from stabilizer bases to random bases according to the Haar measure by T-doped random quantum circuits. We then compute the average value of the probes over ensembles of random spectra from Random Matrix Theory, the Gaussian Diagonal Ensemble and the Gaussian Unitary Ensemble, associated with non-chaotic and chaotic behavior respectively. We also study the behavior of such probes over the Toric Code Hamiltonian.

quant-ph↗

arXiv2026

Non-stabilizerness and U(1) symmetry in chaotic many-body quantum systems

We present exact, closed-form results for the non-stabilizerness of random pure states subject to a U(1) symmetry constraint. Using stabilizer entropy as our non-stabilizerness monotone, we derive the average and the variance for U(1)-constrained Haar random states. We show that the presence of a conserved charge leads to a substantial suppression of non-stabilizerness (magic) compared to the unconstrained case, and identify a qualitative difference between entanglement and magic response. In the thermodynamic limit, stabilizer entropy exhibits a different leading-order scaling close to a vanishing relative charge density, implying that magic is more robust to charge density fluctuations than entanglement entropy. We test our analytical predictions against midspectrum eigenstates of two chaotic many-body systems with conserved U(1) charge: the complex-fermion Sachdev-Ye-Kitaev (cSYK) model and a Heisenberg XXZ chain with next-to-nearest-neighbour couplings and conserved magnetization. We find an excellent agreement for the non-local cSYK model and systematic deviations for the local XXZ chain, highlighting the role of interaction locality.

quant-ph↗

arXiv2026

Certifying ergotropy under partial information

Ergotropy, the maximum work extractable from a quantum system, is a central resource in quantum physics. Computing ergotropy is well established when the system state is fully known, but its estimation under partial information remains an open problem. Here we introduce a general certification framework that lower bounds ergotropy using only the expectation values of a limited set of arbitrary observables. The method naturally applies in the finite-statistics regime, yielding confidence-certified bounds that explicitly incorporate shot noise. We benchmark our approach on both synthetic data and experimental measurements from an IBM quantum processor. This establishes a robust and experimentally accessible tool for certifying extractable work in realistic quantum settings.

quant-ph↗

arXiv2026

Magic of discrete lattice gauge theories

Simulation of quantum field theories and fundamental interactions are one of the most challenging tasks in modern particle physics. Classical computers generally fail to reproduce accurate results when it comes to strongly coupled theories such as QCD. Recent developments in quantum technologies open up the possibility of simulating such physical regimes by using quantum computers. In this paper, we study the quantum resource related to the simulability of a quantum theory, i.e. non-stabilizerness for Lattice Gauge Theory (LGT) with discrete symmetry gauge groups. We show that enforcing gauge constraints for $\mathbb{Z}_l$ LGTs has no cost in terms of this resource and discuss the relation between non-abelianity of the gauge group with the average non-stabilizerness of the gauge invariant Hilbert space.

hep-lat↗

arXiv2025

Stabilizer Entropy of Subspaces

We consider the costs and benefits of embedding the states of one quantum system within those of another. Such embeddings are ubiquitous, e.g., in error correcting codes and in symmetry-constrained systems. In particular we investigate the impact of embeddings in terms of the resource theory of nonstabilizerness (also known as magic) quantified via the stabilizer entropy (SE). We analytically and numerically study the stabilizer entropy gap or magic gap: the average gap between the SE of a quantum state realized within a subspace of a larger system and the SE of the quantum state considered on its own. We find that while the stabilizer entropy gap is typically positive, requiring the injection of magic, both zero and negative magic gaps are achievable. This suggests that certain choices of embedding subspace provide strong resource advantages over others. We provide formulas for the average nonstabilizerness of a subspace given its corresponding projector and sufficient conditions for realizing zero or negative gaps: in particular, certain classes of stabilizer codes provide paradigmatic examples of the latter. Through numerical optimization, we find subspaces which achieve both minimal and maximal average SE for a variety of dimensions, and compute the magic gap for specific error-correcting codes and symmetry-induced subspaces. Our results suggest that a judicious choice of embedding can lead to greater efficiency in both classical and quantum simulations.

quant-ph↗

arXiv2025

Experimental demonstration of non-local magic in a superconducting quantum processor

Non-local magic is the non-stabilizerness that no local unitary operation can erase. It captures the joint action of entanglement and magic underlying quantum advantage, and it has never been measured on quantum hardware. Here we report its first experimental demonstration, on a superconducting quantum processing unit, through two independent routes: an optimal local-erasure protocol and a direct, state-agnostic measurement of subsystem purity. The two agree with each other and with theory. Exploiting direct access to the device, we construct a noise model with no free parameters that identifies readout error and a depolarizing controlled-Z channel as the dominant mechanisms, and we show that local and non-local magic can be addressed separately, erasing local magic in situ while preserving the non-local part. Non-local magic provides a hardware benchmark beyond standard gate-fidelity protocols and points toward more reliable pre-fault tolerant devices.The same tools underlie a purity-estimation protocol with exponential speedup and the decoding of Hawking radiation in a black-hole toy model.

quant-ph↗

arXiv2025

Van Hove singularities in stabilizer entropy densities

The probability distribution of a measure of non-stabilizerness, also known as magic, is investigated for Haar-random pure quantum states. Focusing on the stabilizer R\'enyi entropies, the associated probability density functions (PDFs) are found to display distinct non-analytic features analogous to Van Hove singularities in condensed matter systems. For a single qubit, the stabilizer purity exhibits a logarithmic divergence at a critical value corresponding to a saddle point on the Bloch sphere. This divergence occurs at the $|H\rangle$-magic states, which hence can be identified as states for which the density of non-stabilizerness in the Hilbert space is infinite. An exact expression for the PDF is derived for the case $\alpha = 2$, with analytical predictions confirmed by numerical simulations. The logarithmic divergence disappears for dimensions $d \ge 3$, in agreement with the behavior of ordinary Van Hove singularities on flat manifolds. In addition, it is shown that, for one qubit, the linear stabilizer entropy is directly related to the partial incompatibility of quantum measurements, one of the defining properties of quantum mechanics, at the basis of Stern-Gerlach experiments.

quant-ph↗

arXiv2025

Non-Clifford Cost of Random Unitaries

Recent years have enjoyed a strong interest in exploring properties and applications of random quantum circuits. In this work, we explore the ensemble of $t$-doped Clifford circuits on $n$ qubits, consisting of Clifford circuits interspersed with $t$ single-qubit non-Clifford gates. We establish rigorous convergence bounds towards unitary $k$-designs, revealing the intrinsic cost in terms of non-Clifford resources in various flavors. First, we analyze the $k$-th order frame potential, which quantifies how well the ensemble of doped Clifford circuits is spread within the unitary group. We prove that a quadratic doping level, $t = \tilde{\Theta}(k^2)$, is both necessary and sufficient to approximate the frame potential of the full unitary group. As a consequence, we refine existing upper bounds on the convergence of the ensemble towards state $k$-designs. Second, we derive tight bounds on the convergence of $t$-doped Clifford circuits towards relative-error $k$-designs, showing that $t = \tilde{\Theta}(nk)$ is both necessary and sufficient for the ensemble to form a relative $\varepsilon$-approximate $k$-design. Similarly, $t = \tilde{\Theta}(n)$ is required to generate pseudo-random unitaries. All these results highlight that generating random unitaries is extremely costly in terms of non-Clifford resources, and that such ensembles fundamentally lie beyond the classical simulability barrier. Additionally, we introduce doped-Clifford Weingarten functions to derive analytic expressions for the twirling operator over the ensemble of random doped Clifford circuits, and we establish their asymptotic behavior in relevant regimes.

quant-ph↗

arXiv2025

Integrability and Chaos via fractal analysis of Spectral Form Factors: Gaussian approximations and exact results

It is well known that the spectral form factor (SFF) of a possibly degenerate many-body Hamiltonian can be identified with a planar random walk taking steps of unequal length. In this paper we push this identification further and propose to study the chaotic content of a Hamiltonian $H$ via its associated random walk seen as a fractal, using the tools of fractal geometry. In particular we conjecture that for chaotic Hamiltonians the Hausdorff dimension of the frontier of the corresponding random walk approaches the universal value $d_F=4/3$ -- the same value obtained when the random walk describes a Wiener process. Our numerical simulations for non-integrable models confirm this expectation while for quasi-free integrable models we obtain a value $d_F = 1$. Additionally, we numerically show that ``Bethe Ansatz walkers'' fall into a category similar to the non-integrable walkers. To motivate this conjecture we consider many-body Hamiltonians with degenerate but rationally independent eigenvalues. We prove that if the degeneracies satisfy certain Lyapunov conditions, the random walk becomes a Wiener process, $d_F=4/3$, and the distribution of the SFF becomes Gaussian. This is the familiar Gaussian approximation for the SFF which we show to be violated at very low temperature. We also compute the moments of the SFF exactly under milder hypotheses thus solving the classical problem of determining the moments of a random walker taking steps of unequal lengths. Finally, we consider quasi-free Fermionic models with possibly degenerate but rationally independent one-particle spectra. We show that in this case the distribution of the SFF becomes log-Normal and also give the exact form of the moments under milder hypotheses.

quant-ph↗

arXiv2025

Non-stabilizerness and violations of CHSH inequalities

We study quantitatively the interplay between entanglement and non-stabilizer resources in violating the CHSH inequalities. We show that, while non-stabilizer resources are necessary, they must have a specific structure, namely they need to be both asymmetric and (surprisingly) {\it local}. We employ stabilizer entropy (SE) to quantify the non-stabilizer resources involved and the probability of violation given the resources. We show how spectral quantities related to the flatness of entanglement spectrum and its relationship with non-local SE affect the CHSH inequality. Finally, we utilize these results - together with tools from representation theory - to construct a systematic way of building ensembles of states with higher probability of violation.

quant-ph↗

arXiv2025

Interplay of entanglement structures and stabilizer entropy in spin models

Understanding the interplay between nonstabilizerness and entanglement is crucial for uncovering the fundamental origins of quantum complexity. Recent studies have proposed entanglement spectral quantities, such as antiflatness of the entanglement spectrum and entanglement capacity, as effective complexity measures, establishing direct connections to stabilizer R\'enyi entropies. In this work, we systematically investigate quantum complexity across a diverse range of spin models, analyzing how entanglement structure and nonstabilizerness serve as distinctive signatures of quantum phases. By studying entanglement spectra and stabilizer entropy measures, we demonstrate that these quantities consistently differentiate between distinct phases of matter. Specifically, we provide a detailed analysis of spin chains including the XXZ model, the transverse-field XY model, its extension with Dzyaloshinskii-Moriya interactions, as well as the Cluster Ising and Cluster XY models. Our findings reveal that entanglement spectral properties and magic-based measures serve as intertwined, robust indicators of quantum phase transitions, highlighting their significance in characterizing quantum complexity in many-body systems.

quant-ph↗