Optimal GHZ-State Distribution in LOSR Quantum Networks via Local Decoding from Information Sets

• URL: http://arxiv.org/abs/2606.21500v1
• Date: Fri, 19 Jun 2026 14:53:28 GMT
• Title: Optimal GHZ-State Distribution in LOSR Quantum Networks via Local Decoding from Information Sets
• Abstract summary: We prove the conjecture for regular and uniform networks of arbitrary size.<n>By identifying the hyperedges of the network with the coordinates of a linear code, we show that whenever the edges incident to each node form an information set, a fixed collection of local unitaries transforms the source state into an (N)-party GHZ state with fidelity (dm-M)<n>These results demonstrate that multipartite sources, together with shared randomness, can replace real-time classical communication for entanglement distribution.
• Score: 40.76168869865134
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: Distributing multipartite entanglement is a prerequisite for scalable quantum networks. Networks restricted to local operations and shared randomness (LOSR) avoid the quantum-memory and latency costs associated with the real-time classical communication required by LOCC-based networks. However, when only bipartite sources are available, LOSR networks cannot prepare useful GHZ states. In earlier work, we conjectured that multipartite sources overcome this limitation and supported this claim with a single numerical example. In this work, we prove the conjecture for regular and uniform networks of arbitrary size. By identifying the hyperedges of the network with the coordinates of a linear code, we show that whenever the edges incident to each node form an information set, a fixed collection of local unitaries, namely the local decoders of the code, transforms the source state into an (N)-party GHZ state with fidelity (d^{m-M}), without requiring any classical communication. Here, (m) denotes the number of edges incident to each node and (M) the total number of edges in the network. For the complete ((N-1))-uniform hypergraph (K_N^{(N-1)}), this fidelity reduces to (1/d). We further prove that this value is optimal among all local-unitary strategies and exceeds the best fidelity achievable using only bipartite sources. For example, in the four-node case, the optimal fidelity is (1/2), compared with the bipartite bound of (1/8). These results demonstrate that multipartite sources, together with shared randomness, can replace real-time classical communication for entanglement distribution.

Related papers

• Asymptotic Limits of Entanglement Distribution [43.748379918040854]
  We investigate the limits of entanglement distribution across quantum networks utilizing intermediate stations and local operations.<n>We establish a strict dichotomy: the preservation of entanglement over arbitrarily long distances is possible if the underlying quantum channel admits a correctable subspace.<n>We derive a fundamental lower bound on the physical resource requirements, proving that for channels without a correctable subspace, the number of parallel channels per link must scale at least logarithmically with the number of intermediate stations to sustain a non-zero amount of entanglement.
  arXiv  Detail & Related papers  (2026-05-22T09:56:38Z)
• Entanglement percolation in random quantum networks [39.146761527401424]
  Entanglement percolation aims at generating maximal entanglement between any two nodes of a quantum network.<n>In a network of identically partially entangled states, the network topology determines the minimum entanglement needed for percolation.
  arXiv  Detail & Related papers  (2026-02-10T19:00:01Z)
• Continuously Distributing Entanglement in Quantum Networks with Regular Topologies [0.0]
  Small interconnected quantum processors can collaborate to tackle quantum computational problems. We analyze a protocol where entanglement is continuously distributed among nodes. We investigate how nodes can optimize the frequency of attempting entanglement swaps.
  arXiv  Detail & Related papers  (2024-02-02T16:14:50Z)
• Differentially Private Non-convex Learning for Multi-layer Neural Networks [35.24835396398768]
  This paper focuses on the problem of Differentially Private Tangent Optimization for (multi-layer) fully connected neural networks with a single output node. By utilizing recent advances in Neural Kernel theory, we provide the first excess population risk when both the sample size and the width of the network are sufficiently large.
  arXiv  Detail & Related papers  (2023-10-12T15:48:14Z)
• On the Bipartite Entanglement Capacity of Quantum Networks [9.377912974064227]
  We consider multi-path entanglement distribution to a pair of nodes in a quantum network consisting of devices with non-deterministic entanglement swapping capabilities. We propose a mixed-integer quadratically constrained program (MIQCP) to solve this flow problem. We then compute the overall network capacity, defined as the maximum number of EPR states distributed to users per time unit.
  arXiv  Detail & Related papers  (2023-07-10T10:58:02Z)
• Multiparty Entanglement Routing in Quantum Networks [0.0]
  A protocol is proposed for extracting maximally entangled (GHZn) states for any number of parties in quantum networks. The protocol only requires local measurements at the network nodes and just a single qubit memory per user.
  arXiv  Detail & Related papers  (2022-11-12T15:40:34Z)
• On the Effective Number of Linear Regions in Shallow Univariate ReLU Networks: Convergence Guarantees and Implicit Bias [50.84569563188485]
  We show that gradient flow converges in direction when labels are determined by the sign of a target network with $r$ neurons. Our result may already hold for mild over- parameterization, where the width is $tildemathcalO(r)$ and independent of the sample size.
  arXiv  Detail & Related papers  (2022-05-18T16:57:10Z)
• Analysis of Multipartite Entanglement Distribution using a Central Quantum-Network Node [0.0]
  We study the performance of distributing multipartite entangled states in a quantum network through the use of a central node. Specifically, we consider the scenario where the multipartite entangled state is first prepared locally at a central node, and then transmitted to the end nodes of the network through quantum teleportation.
  arXiv  Detail & Related papers  (2022-03-10T18:14:40Z)
• The Separation Capacity of Random Neural Networks [78.25060223808936]
  We show that a sufficiently large two-layer ReLU-network with standard Gaussian weights and uniformly distributed biases can solve this problem with high probability. We quantify the relevant structure of the data in terms of a novel notion of mutual complexity.
  arXiv  Detail & Related papers  (2021-07-31T10:25:26Z)
• Optimized Quantum Networks [68.8204255655161]
  Quantum networks offer the possibility to generate different kinds of entanglement prior to network requests. We utilize this to design entanglement-based quantum networks tailored to their desired functionality.
  arXiv  Detail & Related papers  (2021-07-21T18:00:07Z)
• Accelerating variational quantum algorithms with multiple quantum processors [78.36566711543476]
  Variational quantum algorithms (VQAs) have the potential of utilizing near-term quantum machines to gain certain computational advantages. Modern VQAs suffer from cumbersome computational overhead, hampered by the tradition of employing a solitary quantum processor to handle large data. Here we devise an efficient distributed optimization scheme, called QUDIO, to address this issue.
  arXiv  Detail & Related papers  (2021-06-24T08:18:42Z)
• Computation-aided classical-quantum multiple access to boost network communication speeds [61.12008553173672]
  We quantify achievable quantum communication rates of codes with computation property for a two-sender cq-MAC. We show that it achieves the maximum possible communication rate (the single-user capacity), which cannot be achieved with conventional design.
  arXiv  Detail & Related papers  (2021-05-30T11:19:47Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.