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.
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.
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.
In distributed fault-tolerant quantum computing, entanglement and magic are essential resources for quantum communication and universal fault-tolerant computation, respectively. Although they are usually treated as distinct resource currencies, whether they admit a unified resource-theoretic description remains an open question. Here, we introduce the distributed resource theory of entanglement and magic (DREAM). In this framework, the free states are convex mixtures of product local stabilizer states, and the free operations are local stabilizer circuits assisted by classical communication (LSCC). We show that DREAM contains nontrivial resource states that are neither entanglement nor magic, so it is strictly richer than treating the two resources independently. Surprisingly, such resources can enable the teleportation of magic states between distant parties without consuming entanglement, revealing a counterintuitive form of resource teleportation mediated entirely by separable states. We further generalize this result to quantum networks and investigate general quantum-state teleportation under LSCC. We show that the shared resource under DREAM is closely related to the teleportation capability, quantified by the magic of the teleported state. Our work establish a systematic framework for studying distributed quantum resources and uncover intrinsic relations among distinct resources within a unified resource theory.
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.
We introduce Magic Secret Sharing (MSS), a quantum cryptographic primitive in which the secret is the computational capability of a quantum state rather than its classical description. In the resource theory of magic, non-stabilizer states fuel universal quantum computation via non-Clifford gates; MSS distributes this resource with an (n-1,n) threshold structure using a pre-shared GHZ state and a single local phase gate P(phi) = diag(1, exp(i*phi)). Any individual party holds the maximally mixed state I/2, with Wigner distance C(I/2) = 0, so no local operation can yield non-Clifford computational advantage regardless of what operations are applied or what noise acts on the device. The authorised coalition reconstructs magic content C(phi) = (|sin(phi)| + |cos(phi)| - 1)/2 exactly, enabling a logical T gate via gate teleportation in multi-server blind quantum computation (BQC). Among diagonal parametric gates, phase gates are the unique class satisfying the security condition, characterised via an exact column-sum condition. The protocol is elevated to a one-sided device-independent (1SDI) setting via a steering inequality: the assemblage produced on the recipient's side certifies magic delivery without trusting the coalition's devices. We demonstrate the (2,3) instance on ibm_marrakesh (156-qubit IBM Heron): security (C(rho_Bob) < 10^-6, the linear-programming solver tolerance) holds in every run and is independently reproduced on a second qubit assignment, and state fidelity reaches 0.959-0.973 for the authorised party, with faithfulness confirmed for all four test values of phi to within 0.025 in magic content, a residual that depolarising noise alone accounts for.
The stabilizer formalism plays a central role in quantum information processing and quantum computing. Since stabilizer states and operations can be efficiently simulated classically and fault-tolerantly implemented in quantum error-correcting codes, quantum states and operations beyond the stabilizer framework, characterized by nonstabilizerness or magic, naturally emerge as resources for quantum computation. Here, we demonstrate that a quantum-information task involving only stabilizer states can reveal a fundamental limitation of stabilizer operations. Specifically, we construct a set of mutually orthogonal stabilizer states that cannot be perfectly distinguished using stabilizer operations and extend this construction to an arbitrary number of qubits. Our results provide an efficient test of nonstabilizerness without requiring the direct use of resourceful states or operations nor relying on computational-hardness assumptions. This nonstabilizerness test could serve as a resource-efficient benchmark for fault-tolerant quantum computers powered by magic-state injection, by providing quantitative bounds on the robustness of magic. More fundamentally, the resulting asymmetry between the preparation and discrimination of free states parallels "nonlocality without entanglement" in entanglement theory, revealing an unexpected connection between these two distinct quantum resource theories.
Quantum state purification aims to recover higher-fidelity quantum states from multiple noisy copies and is a fundamental primitive for quantum information processing. Magic resources enable operations beyond classically simulable dynamics and are central to universal fault-tolerant quantum computation. Recent no-go results show that classically simulable operations cannot achieve a nontrivial universal fidelity gain. This motivates a quantitative theory of the magic required for purification at prescribed success probability and target fidelity. For universal purification with two input copies, we prove an exact linear mana law in odd dimensions and a two-sided linear robustness law for multi-qubit systems, which becomes exact for a single qubit. We also identify an explicit successful purification map that makes the tradeoff transparent. These results establish universal purification as a task obeying a quantitative magic-fidelity law and link magic resources to error mitigation and fault-tolerant quantum information processing.