Magic and entanglement are independent quantum resources, yet their exact relation in many-body dynamics has remained elusive. We uncover two structural principles. First, at any stabilizer state, the curvature of the second stabilizer R\'enyi entropy under an arbitrary Hermitian generator equals the quantum Fisher information up to a fixed normalization, creating a bidirectional bridge between computational and metrological resources. Second, for commuting Ising evolution on any forest graph, a Clifford pruning circuit yields the full stabilizer-R\'enyi family at arbitrary size and in any spatial embedding, thereby furnishing a graph-theoretic construction of families with finite magic density and vanishing entanglement density in the thermodynamic limit. We solve two paradigmatic one-dimensional realizations central to quantum simulation -- an Ising quench and a kicked Floquet chain -- exactly for arbitrary system size and directly in the thermodynamic limit, revealing finite magic density with vanishing entanglement density, distinct magic and entanglement revival periods, and Clifford points with zero magic but finite bipartite entanglement. The same tangent geometry fixes initial growth, perturbative revival lifting, and stability of thermodynamic magic minima. Large-scale Pauli-basis matrix-product-state calculations verify all predictions, and the tangent bridge yields a concrete protocol for detecting magic through established quantum-Fisher-information measurements.
Magic, or nonstabilizerness, is the resource that lifts Clifford circuits to universal quantum computation and has become a standard diagnostic of many-body states. For a state shared between two parties, however, a basic question has remained open: how much of the magic resides in the correlations between the parties rather than in their local bases? Isolating this nonlocal magic requires minimizing over all local bases, an optimization that has so far resisted exact solution. Here we solve it for the stabilizer fidelity: the nonlocal magic of every pure multiqubit state is the distance of its entanglement spectrum from the closest spectrum of Bell pairs. The same quantity governs an apparently unrelated task: a family of states universally embezzles entanglement under local operations and classical communication if and only if its nonlocal magic diverges. The deciding property is not the amount of entanglement but the way the entanglement spectrum spreads its weight across factor-of-two windows of rank, so that critical chains and random-singlet states, with identical logarithmic entanglement scaling, carry unbounded and vanishing nonlocal magic, respectively. Nonlocal magic thereby becomes an operationally meaningful property of quantum correlations, directly accessible to tensor-network simulations and, through entanglement spectroscopy, to experiments.
We develop a Clifford-orbit framework for studying magic-protected entanglement, which we refer to as magical entanglement: the part of bipartite entanglement that remains after optimal stabilizer simplification. This construction leverages residual entanglement under Clifford reduction as a state-level organizing principle for magic state space. It defines canonical representatives, spectra, and ranks that characterize the Clifford-irreducible structure of a state. We identify two regimes of the magic-entanglement interplay. In the $T$-magic regime, local nonstabilizer resources can coexist with entanglement, but the protected component remains weak and state-dependent. In the $W$-magic regime, by contrast, entanglement is Clifford-irreducibly tied to nonstabilizerness, producing typical, strongly self-averaging behavior. Analytical examples and random-circuit numerics support a crossover from broad $T$-magic fluctuations to concentrated, Haar-like $W$-magic behavior. These results identify magical entanglement as an orbit-level diagnostic of how nonstabilizerness protects quantum correlations against Clifford reduction.
Quantum entanglement and magic are complementary resources underlying quantum computational advantage, yet their dynamical relation in many-body systems remains poorly understood. In this Letter, we show that the mechanism of bipartite entanglement growth is encoded in the relative timescale between the entropy-growth-rate peak and the magic barrier, defined as the transient peak of the anti-flatness of the entanglement spectrum. When entanglement is locally built, the same microscopic process increases the entropy and reshapes the Schmidt spectrum, so the magic-barrier peak occurs in the time window of maximal entropy growth. When entanglement is mainly transported or redistributed, entropy can grow before appreciable spectral non-flatness is generated, naturally separating the two peak times. We demonstrate this distinction in the random-field XXZ chain: the two peaks remain strongly correlated in the thermal regime, while their separation grows systematically across the thermal--MBL crossover. We further validate this theoretical framework by employing Bell-pair initial states alongside a tunable SWAP--Haar random circuit. Our results reveal an intrinsic dynamical connection between entanglement and magic, establishing the magic barrier as a powerful spectral diagnostic of how quantum information is generated, transported, and reshaped.
Lv Zhang, Shi-Xin Zhang, Heng Fan et al.· 0 citations
Absolutely maximally entangled states represent a highly constrained form of multipartite entanglement and play an important role in quantum information theory. We investigate a weaker form of uniformity of entanglement for four-party systems of local dimension $d>2$ that requires the three balanced bipartitions to have equal but not necessarily maximal linear entropy. We introduce a linear map $\Xi$ that enforces exact equality of entropies under reshuffling and partial transposition. The transformation arises as the asymptotic limit of an iterative averaging procedure and admits a group-theoretic description in terms of permutations of tensor indices. For Haar-random unitary inputs, a leading-moment analysis supported by numerical simulations predicts highly entangled outputs whose common entropy approaches the maximal value as the local dimension grows. We characterize the algebraic structure, fixed points, and asymptotic behavior of this map and its relation to two-unitary matrices and orthogonal Latin squares.
Entanglement dynamics depend not only on how a quantum system is partitioned, but critically on how interactions across that partition are structured. For a spatial bipartition of a locally interacting system, entanglement is generated near the boundary and then propagates into the bulk. By contrast, when two extended quantum fields are coupled locally along their entire length, the interaction crosses the field-space partition everywhere, and this generates correlations throughout the system. Here, we study the entanglement dynamics between two gapless one-dimensional quantum many-body systems described by Luttinger liquid theory. The systems are initially decoupled and prepared at zero or finite temperature, after which a time-dependent tunneling interaction is activated uniformly along their length. Within a Gaussian approximation, we derive general analytical expressions for the logarithmic negativity, mutual information, and R\'enyi entropies under arbitrary coupling protocols. At zero temperature, entanglement displays an early-time power-law growth whose exponent is fixed solely by the first non-null derivative of the tunneling protocol. Once the coupling saturates, we obtain exact long-time averages of the information-theoretic quantities and characterise how the correlations scale with temperature and the final coupling strength. We also analyse how mutual information and logarithmic negativity approach the adiabatic limit for a very slow protocol with respect to intrinsic system timescale. This work extends the study of entanglement dynamics in nonequilibrium field theory to field-space partitions and mixed initial states.
L. Dupays, Taufiq Murtadho, Bi Hong Tiang et al.· 0 citations
Nonstabilizerness, or magic, is an archetypal \emph{quantum} resource that is necessary for quantum computational advantage. Here we uncover a phenomenon seemingly at odds with the quantum nature of magic: entirely nonlocal magic (ENM)---magic present only in correlations and absent from each party's marginal---can live without entanglement. We systematically study this separation and show it is universal and operationally reversible: every magical state or channel can be encoded into and recovered from a separable ENM realization using only local stabilizer processing and classical communication. We leverage this mechanism to devise an activation key protocol in which a classical key controls access to non-Clifford operations. We further formulate magic secret sharing, in which computational power inaccessible to any party alone becomes accessible through cooperation. On a superconducting quantum processor, we experimentally demonstrate activation key and network computing primitives, together with separable ENM state preparation and extraction protocols. Together, our results establish that magic can be classically activated, localized, and secret-shared without entanglement, providing new resource-control primitives for distributed quantum computation.
Fuchuan Wei, Rui-Xia Wang, Yujia Zhang et al.· 0 citations
