We establish operational limits on the broadcasting of genuine multipartite entanglement (GME) in quantum networks. Using a distributed protocol in which each of N parties locally implements optimal 1 $\to$ 2 cloning via beam-splitter interactions, we derive exact expressions for the broadcast fidelity of Greenberger-Horne-Zeilinger (GHZ), W states, and Cluster states in a limited setting. We show that the fidelity decays exponentially with system size as [c(R)]$^N$, providing a quantitative expression of multipartite entanglement monogamy in the broadcasting setting, and that both state families share a universal normalisation factor arising from independent post-selection probabilities. Most significantly, we prove a no-go result for simultaneous GME certification: for all reflectivities and all system sizes, the two broadcast copies cannot be simultaneously certified as genuinely multipartite entangled within the standard framework of fidelity-based witnesses. We further check this behaviour for three- and four-party cluster states, finding consistent results that support the generality of the no-go beyond the GHZ and W families. This obstruction arises from the redistribution of multipartite coherence, which both reduces the achievable fidelity and increases the corresponding certification threshold. Our results reveal a fundamental trade-off between the broadcastability of multipartite entanglement and its operational certifiability, and delineate intrinsic limits on entanglement distribution in quantum networks.
Entangled photons play a crucial role in quantum applications, and determining and characterising their entanglement is vital to using them effectively. High-dimensional entangled states offer richer possibilities, but their additional measurement degrees of freedom make them increasingly demanding to characterise. However, adaptive Bell-test methods based on complex simultaneous perturbation stochastic approximation (CSPSA) have so far focused mainly on qubits. Here we numerically investigate a Bell-inequality-violation-based method for detecting entanglement in unknown quantum states. We extend CSPSA to high-dimensional Bell testing by using the Collins-Gisin-Linden-Massar-Popescu (CGLMP) inequality for bipartite qudits. The resulting protocol can detect Bell-nonlocal correlations in unknown entangled states, whether pure or mixed, without first reconstructing their density matrix. Using 100 optimisation iterations in each of 100 independent finite-shot runs per number of dimensions d, we demonstrate certified CGLMP violations throughout d=2-8. For isotropic mixed states tested at a visibility of just 0.05 above the standard-Fourier violation threshold, we likewise observe confidence-certified CGLMP violations throughout the range of d studied. We compare this direct stochastic approach with quantum state tomography, the standard method for characterising an unknown state. In the matched benchmark, CSPSA uses fewer measurement configurations per attempt from d=6, whereas tomography requires fewer detected pairs per certified result through d=8. We also derive the phase dependence of the CGLMP parameter and clarify the features of its landscape that govern the adaptive search. Because the measurement-setting cost of each CSPSA iteration is independent of dimension, the method offers a particularly attractive route to the certification of high-dimensional entanglement.
Xu-Kang Tan, Jesvita Menezes, Sanjan D. Murthy et al.· 0 citations
We establish an exponential communication advantage enabled by multipartite quantum entanglement. Building on the bipartite Hidden Matching problem, we introduce a communication task involving multiple spatially separated senders and a single receiver. We show that a shared Greenberger-Horne-Zeilinger state enables completion of this task using only logarithmically many bits of classical communication from each sender. In contrast, without preshared entanglement, any protocol achieving high success probability requires polynomial communication from at least one sender, even when \emph{quantum} communication is allowed. Thus, classical communication assisted by multipartite entanglement can be exponentially more powerful than quantum communication without preshared entanglement. As a cryptographic application, we construct a seeded two-source randomness extractor and establish an exponential separation between entangled and unentangled quantum side-information. Specifically, compromising the extractor with two unentangled quantum states storing information about the two sources, respectively, requires polynomial-size memory, whereas exponentially smaller quantum memory suffices in the presence of a small amount of shared entanglement.
Ananya Chakraborty, Manik Banik, Ronald de Wolf· 1 citation
Practical robust self-testing of multipartite entanglement has so far been restricted to small-scale systems due to error bounds that degrade severely with system size. In this work, we establish multipartite self-testing with robustness independent of the size of the quantum network. We derive a fully analytic, device-independent self-testing bound for $n$-qubit Greenberger-Horne-Zeilinger (GHZ) states. The bound scales linearly with the observed violation error and lies universally within a constant factor of two from a theoretical upper bound. Furthermore, the operator-inequality framework reduces the verification of the conjectured optimal bound to a highly efficient numerical check, which we perform up to $n=100$. Consequently, GHZ entanglement can be certified under a fixed noise level in arbitrarily large systems, enabling scalable device-independent verification.
Shen Cao, Xing-Jian Zhang, Fei Shi et al.· 0 citations
Quantum locally recoverable codes (qLRCs) allow a single qudit erasure to be corrected by accessing only a small number of other qudits. Standard CSS and Hermitian constructions, however, impose dual-containing or self-orthogonal constraints on the underlying classical codes, thereby restricting the well-structured classical LRCs (cLRCs) that can be used to construct qLRCs. To relax these constraints, we introduce entanglement-assisted quantum locally recoverable codes (EAQLRCs) by assuming that halves of the pre-shared maximally entangled pairs are noiseless. We characterize sufficient support conditions on extended stabilizers under which entanglement-assisted stabilizer codes have locality $r$ and derive a CSS-like construction from two classical codes without imposing the ordinary dual-containing condition. We further establish an upper bound on locality and a Singleton-like bound for arbitrary CSS-like EAQLRCs, and characterize the pure codes attaining equality in the latter bound. These results yield a general framework for constructing optimal pure EAQLRCs from pairs of cLRCs. Applying this framework to $\ell$-intersection pairs of MDS codes and block parity-check matrices, we obtain two families of optimal pure CSS-like EAQLRCs with flexible parameters and nontrivial localities. To the best of our knowledge, these represent the first explicit families of EAQLRCs.
Yang Li, San Ling, Zhenliang Lu et al.· arXiv.org· 2 citations· ⚡1
This work achieves information-theoretically secure QSS both within and across subnetworks, providing a solid technical foundation for the development of scalable and multifunctional quantum networks.
Qijun Zhang, Yuehan Xu, Tao Wang et al.· PhotoniX· 0 citations
The device-independent (DI) certification of high-dimensional entanglement and complex measurement structures is central to scalable quantum information processing. While existing approaches to high-dimensional self-testing have largely relied on Bell tests with multi-outcome measurements, achieving such certification using only binary-outcome Bell tests remains an open challenge. Here, we put forth a simultaneous self-testing framework for maximally entangled two-qudit state of local dimension m∗=2⌊n/2⌋ (equivalently, ⌊n/2⌋ copies of maximally entangled two-qubit pairs), together with n mutually anticommuting observables on one side. To this end, we employ a family of n-settings Bell inequalities comprising two spatially separated observers, Alice and Bob, with 2n−1 and n binary-outcome measurement settings, respectively. We first derive the optimal local and quantum bounds of these inequalities without presupposing the dimension of the underlying state or observables. We then prove that any physical realisation achieving the maximal quantum violation must, up to local isometries and complex conjugation, correspond to a maximally entangled state of local dimension of at least 2⌊n/2⌋, together with local observables forming an irreducible representation of the Clifford algebra. Consequently, the maximal violation self-tests the minimal-dimension quantum realisation compatible with n mutually anticommuting observables. Finally, we establish robustness by proving that if the observed Bell violation deviates from the optimal quantum value by δ, then the realised state and measurements are Oδ-close to the ideal strategy. Our results thus provide a unified DI route for the certification of high-dimensional entanglement and Clifford measurements using only binary-outcome Bell tests.
S. Sasmal, Ritesh K. Singh, Prabuddha Roy et al.· 0 citations
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