arXiv subjects

Gianluca Cuffaro

Publications and source records attributed to Gianluca Cuffaro.

6 recordsLinked to original sources

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

Clifford entropy

We introduce the Clifford entropy, a measure of how close an arbitrary unitary is to a Clifford unitary, which generalizes the stabilizer entropy for states. We show that this quantity vanishes if and only if a unitary is Clifford, is invariant under composition with Clifford unitaries, and is subadditive under tensor products. Rewriting the Clifford entropy in terms of the stabilizer entropy of the corresponding Choi state allows us to derive an upper bound: that this bound is not tight follows from considering the properties of symmetric informationally complete sets. Nevertheless we are able to numerically estimate the maximum in low dimensions, comparing it to the average over all unitaries, which we derive analytically. Finally, harnessing a concentration of measure result, we show that as the dimension grows large, with probability approaching unity, the ratio between the Clifford entropy of a Haar random unitary and that of a fixed magic gate gives a lower bound on the depth of a doped Clifford circuit which realizes the former in terms of the latter. In fact, numerical evidence suggests that this result holds reliably even in low dimensions. We conclude with several directions for future research.

quant-ph↗

arXiv2024

Quantum States with Maximal Magic

Finding ways to quantify magic is an important problem in quantum information theory. Recently Leone, Oliviero and Hamma introduced a class of magic measures for qubits, the stabilizer entropies of order $α$, to aid in studying nonstabilizer resource theory. This suggests a way to search for those states that are as distinct as possible from the stabilizer states. In this work we explore the problem in any finite dimension $d$ and characterize the states that saturate an upper bound on stabilizer entropies of order $α\geq2$. Particularly, we show that if a Weyl-Heisenberg (WH) covariant Symmetric Informationally Complete (SIC) quantum measurement exists, its states uniquely maximize the stabilizer entropies by saturating the bound. No other states can reach so high. This result is surprising, as the initial motivation for studying SICs was a purely quantum-foundational concern in QBism. Yet our result may have implications for quantum computation at a practical level, as it demonstrates that this notion of maximal magic inherits all the difficulties of the 25-year-old SIC existence problem, along with the deep questions in number theory associated with it.

quant-ph↗

arXiv2024

Stabilizer entropy of quantum tetrahedra

How complex is the structure of quantum geometry? In several approaches, the spacetime atoms are obtained by the SU(2) intertwiner called quantum tetrahedron. The complexity of this construction has a concrete consequence in recent efforts to simulate such models and toward experimental demonstrations of quantum gravity effects. There are, therefore, both a computational and an experimental complexity inherent to this class of models. In this paper, we study this complexity under the lens of stabilizer entropy (SE). We calculate the SE of the gauge-invariant basis states and its average in the SU(2) gauge invariant subspace. We find that the states of definite volume are singled out by the (near) maximal SE and give precise bounds to the verification protocols for experimental demonstrations on available quantum computers.

hep-th↗

arXiv2023

Curvature from multipartite entanglement in quantum gravity states

We investigate the multipartite entanglement of a uniformly curved quantum 3D space region with boundary, realised in terms of spin networks defined on a graph with non trivial SU(2) holonomies, in the framework of loop quantum gravity. The presence of intrinsic curvature in the region is encoded in closure (topological) defects associated with tag-spins attached to the vertices of the graph. For such states, we generalise the bulk-to-boundary mapping as to include the space of tags in an extended boundary space: bulk information is shared among generically entangled boundary surfaces and intrinsic curvature degrees of freedom. We model the quantum region on a tripartite system composed by two (complementary) boundary subregions and the set of bulk tags. Via replica techniques, we can compute the typical value of the logarithmic negativity of the reduced boundary, described as an open quantum system, in a large spin regime. We find three entanglement regimes, depending on the ratio between the number of tags (curvature) and the area of the dual surface at the boundary. These are well described by the generalised Page curve of a tripartite random state. In particular, we find area scaling behaviour for negativity in case of small curvature, while for large curvature the negativity vanishes, suggesting an effective thermalization of the boundary. Remarkably, the PPT character of the mixed boundary state corresponds to a change in the effective topology of the network, with the two boundary subregions becoming disconnected.

hep-th↗

arXiv2022

Entanglement Negativity on Random Spin Networks

We investigate multipartite entanglement for quantum states of 3d space geometry, described via generalised random spin networks with fixed areas, in the context of background independent approaches to quantum gravity. We focus on entanglement negativity as a well defined witness of quantum correlations for mixed states, in our setting describing generic subregions of the boundary of a quantum 3d region of space. In particular, we consider a generic tripartition of the boundary of an open spin network state and we compute the typical Rényi negativity of two boundary subregions A and B immersed in the environment C, explicitly for a set of simple open random spin network states. We use the random character of the spin network to exploit replica and random average techniques to derive the typical Rényi negativty via a classical generalised Ising model correspondence, generally used for random tensor networks in the large bond regime. For trivially correlated random spin network states, with only local entanglement between spins located on the network edges, we find that typical log negativity displays a holographic character, in agreement with the results for random tensor networks, in large spin limit. When non-local bulk entanglement between intertwiners at the vertices is considered the negativity increases, while at the same time the holographic scaling is generally perturbed by the bulk contribution.

hep-th↗