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arXiv:2605.15029

A Resource-Driven Framework for Configurable Entanglement in Quantum Networks

Francesco Mazza, Claudio Pellitteri, Angela Sara Cacciapuoti, Marcello Caleffi

quant-phcs.NISubmitted May 14, 2026• Announced May 15, 2026• 0 citations
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Abstract

Shared multipartite entanglement defines a ``whatever channel'', i.e., a latent communication substrate that does not determine a priori which end-to-end entangled links are activated, but can be configured to support different entanglement-connectivity graphs through Local Operations and Classical Communication (LOCC). Building on this, we propose a resource-driven framework in which multipartite entanglement is treated as a programmable resource that induces a space of admissible entanglement-graph configurations. Within this framework, connectivity provisioning emerges as a particular instance of a more general resource reconfiguration process. To support this paradigm, we introduce a set of structural design parameters that characterize the operational degrees of freedom of the resource and define the admissible transformations independently of the specific mechanism used to realize them. We then formalize Entanglement Rolling as a measurement-based protocol that operates over the induced configuration space, enabling the systematic reconfiguration of the shared resource across a family of multipartite states. Finally, we analyze the proposed framework under realistic noise conditions. Leveraging the Noisy Stabilizer Formalism (NSF), we derive closed-form noise maps that characterize the effect of noise on the resource transformations and show that the proposed approach maintains reliable performance under relevant noise processes.

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This work has been funded by the European Union under the ERC grant QNattyNet, n. 101169850

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Shared multipartite entanglement defines a ``whatever channel'', i.e., a latent communication substrate that does not determine a priori which end-to-end entangled links are activated, but can be configured to support different entanglement-connectivity graphs through Local Operations and Classical Communication (LOCC). Building on this, we propose a resource-driven framework in which multipartite entanglement is treated as a programmable resource that induces a space of admissible entanglement-graph configurations. Within this framework, connectivity provisioning emerges as a particular instance of a more general resource reconfiguration process. To support this paradigm, we introduce a set of structural design parameters that characterize the operational degrees of freedom of the resource and define the admissible transformations independently of the specific mechanism used to realize them. We then formalize Entanglement Rolling as a measurement-based protocol that operates over the induced configuration space, enabling the systematic reconfiguration of the shared resource across a family of multipartite states. Finally, we analyze the proposed framework under realistic noise conditions. Leveraging the Noisy Stabilizer Formalism (NSF), we derive closed-form noise maps that characterize the effect of noise on the resource transformations and show that the proposed approach maintains reliable performance under relevant noise processes.
Measurement-based quantum computation (MBQC) performs quantum algorithms by local, adaptive measurements on an initially entangled many-body "resource" state. This thesis investigates MBQC through two tightly coupled lenses: (i) which physical states and phases of matter constitute universal resources, and (ii) how the temporal order induced by measurement adaptivity constrains and, in turn, is constrained by those resources. Resources from valence-bond constructions. We develop hybrid AKLT-type (valence-bond) resources on two-dimensional lattices and show how a generalized POVM reduces higher-spin degrees of freedom to effective qubits while preserving computational viability. We analyze worst-case and frustrated geometries (e.g., kagome and decorated lattices), identify planarity-restoring local operations, and use percolation-style diagnostics on the induced graph states to certify universality beyond idealized cluster-state settings. A two-parameter phase with noisy POVMs. Extending ground states across a phase connected to the AKLT point, we introduce a measurement-noise–aware framework with probabilistic restoration and closed-form weight formulae derived via a graphical (g-)calculus. Large-scale numerics that account for correlations map a two-parameter phase diagram and delineate regimes of universal vs. non-universal post-measurement graphs. These results exhibit a robust universal region that persists away from ideal measurements and clarify how noise and Hamiltonian deformation jointly control computational power. Temporal order and determinism. We develop a stabilizer-and-influence-matrix formalism that places temporal dependencies on the same footing as resource structure. Four theorems establish a two-way determination between (a) the classical processing relations (including the influence matrix that generates the partial order of measurements) and (b) the resource stabilizer in a normal form, up to local equivalence. This links gauge freedoms, byproduct handling, and flow/gflow–style constraints into a unified picture of when adaptive measurement schedules yield deterministic computation. Together, these contributions clarify when physically motivated ground states serve as universal MBQC resources under realistic measurement noise, and how temporal constraints fundamentally shape the space of admissible computations in MBQC.
The topology of classical networks is determined by physical links between nodes, and after a network request the links are used to establish the desired connections. Quantum networks offer the possibility to generate different kinds of entanglement prior to network requests, which can substitute links and allow one to fulfill multiple network requests with the same resource state. We utilize this to design entanglement-based quantum networks tailored to their desired functionality, independent of the underlying physical structure. The kind of entanglement to be stored is chosen to fulfill all desired network requests (i.e. parallel bipartite or multipartite communications between specific nodes chosen from some finite set), but in such a way that the storage requirement is minimized. This can be accomplished by using multipartite entangled states shared between network nodes that can be transformed by local operations to different target states. We introduce a clustering algorithm to identify connected clusters in the network for a given desired functionality, i.e. the required network topology of the entanglement-based network, and a merging algorithm that constructs multipartite entangled resource states with reduced memory requirement to fulfill all desired network requests. This leads to a significant reduction in required time and resources, and provides a powerful tool to design quantum networks that is unique to entanglement-based networks.
Cluster states and graph states in general offer a useful model of the stabilizer formalism and a path toward the development of measurement-based quantum computation. Their defining structure – the stabilizer group – encodes all possible correlations that can be observed during measurement. The measurement outcomes which are consistent with the stabilizer structure make error correction possible. Here, we leverage both properties to design feasible families of states that can be used as robust building blocks of quantum computation. This procedure reduces the effect of experimentally relevant noise models on the extraction of smaller entangled states from the larger noisy graph state. In particular, we study the extraction of Bell pairs from linearly extended graph states – this has the immediate consequence for state teleportation across the graph. We show that robust entanglement can be extracted by proper design of the linear graph with only a minimal overhead of the physical qubits. This scenario is relevant to systems in which the entanglement can be created between neighboring sites. The results shown in this work provide a mathematical framework for noise reduction in measurement-based quantum computation. With proper connectivity structures, the effect of noise can be minimized for a large class of realistic noise processes.
Quantum network states are multipartite states built from distributing pairwise entanglement among parties and underpin the paradigm of quantum networks for quantum information processing. In this work we introduce the problem of partial distillability in noisy quantum networks. This corresponds to the possibility of distilling by local operations and classical communication an arbitrary pure state for an arbitrary subset of parties starting from a single copy of a quantum network state of an increasing number of parties that share noisy (i.e. mixed) bipartite entangled states. Here, distillation means that the target state is obtained with fidelity as close to 1 as desired as the size of the network increases when the pairwise entangled links support a constant amount of noise. While we prove an obstruction to multipartite distillation protocols after teleportation with channels with constant noise, we show that partial distillability is indeed possible if certain well-established graph-theoretic parameters that measure the connectivity in the network grow fast enough with its size. We give necessary as well as sufficient conditions for partial distillability in terms of these parameters and we moreover provide explicit constructions of networks with partial distillability and a relatively slow connectivity growth.
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