On the accuracy of twirled approximations in repeater chains

• URL: http://arxiv.org/abs/2509.16689v1
• Date: Sat, 20 Sep 2025 13:33:26 GMT
• Title: On the accuracy of twirled approximations in repeater chains
• Authors: Bethany Davies, Guus Avis, Stephanie Wehner,
• Abstract summary: In quantum networks, it is common to approximate bipartite entangled states as either being Bell-diagonal or Werner states.<n>We consider repeater chains where end-to-end entanglement is achieved by performing an entanglement swap at each repeater in the chain.<n>We show that, for non-postselected swapping, the Bell-diagonal approximation is exact for the computation of the Bell-diagonal elements of the end-to-end state.<n>We also find bounds on the difference in end-to-end fidelity from what is obtained with the twirled approximation, for initial states with a general noisy form
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In the performance analysis of quantum networks, it is common to approximate bipartite entangled states as either being Bell-diagonal or Werner states. We refer to these as twirled approximations because it is possible to bring any state to such a form with a twirling map. Although twirled approximations can simplify calculations, they can lead to an inaccuracy in performance estimates. The goal of this work is to quantify this inaccuracy. We consider repeater chains where end-to-end entanglement is achieved by performing an entanglement swap at each repeater in the chain. We consider two scenarios: postselected and non-postselected entanglement swapping, where postselection is performed based on the Bell-state measurement outcomes at the repeaters. We show that, for non-postselected swapping, the Bell-diagonal approximation is exact for the computation of the Bell-diagonal elements of the end-to-end state. We also find that the Werner approximation accurately approximates the end-to-end fidelity when the infidelity of each initial state is small with respect to the number of repeaters in the chain. For postselected swapping, we find bounds on the difference in end-to-end fidelity from what is obtained with the twirled approximation, for initial states with a general noisy form. Finally, for the example of performing quantum key distribution over a repeater chain, we demonstrate how our insights can be used to understand how twirled approximations affect the secret-key rate.

Related papers

• Nonlocality under Jaynes-Cummings evolution: beyond pseudospin operators [44.99833362998488]
  We re-visit the generation and evolution of (Bell) nonlocality in hybrid scenarios whose dynamics is determined by the Jaynes-Cummings Hamiltonian. Recent results on the optimal Bell violation in qubit-qudit systems show that the nonlocality is much greater than previously estimated.
  arXiv  Detail & Related papers  (2024-10-14T16:01:23Z)
• Quantum repeater protocol for deterministic distribution of macroscopic entanglement [0.0]
  We present a method to distribute a macroscopic amount of entanglement across long-distances using a number of operations that scales only linearly with the chain length. We show that there are particular magic'' interaction times that allow for distribution of entanglement with perfect fidelity, with no degradation with chain length.
  arXiv  Detail & Related papers  (2024-07-31T20:01:13Z)
• On the Analysis of Quantum Repeater Chains with Sequential Swaps [7.885533851646292]
  We evaluate the performance of two-way quantum repeater chains with sequential entanglement swapping. We consider memory decoherence, gate imperfections, and imperfect link-level entanglement generation.
  arXiv  Detail & Related papers  (2024-05-28T15:03:09Z)
• On noise in swap ASAP repeater chains: exact analytics, distributions and tight approximations [9.32782060570252]
  Losses are one of the main bottlenecks for the distribution of entanglement in quantum networks.<n>We analytically investigate the case of equally-spaced repeaters.<n>We find exact analytic formulae for all moments of the fidelity up to 25 segments.
  arXiv  Detail & Related papers  (2024-04-10T16:24:51Z)
• Optimal Entanglement Distillation Policies for Quantum Switches [0.64265933507484]
  In an entanglement distribution network, the function of a quantum switch is to generate elementary entanglement with its clients followed by entanglement swapping. We consider a discrete-time model for a quantum switch that attempts generation of fresh elementary entanglement with clients in each time step. We focus on establishing the value of entanglement distillation of the stored Bell pairs prior to entanglement swapping in presence of their inevitable aging.
  arXiv  Detail & Related papers  (2023-05-11T13:52:49Z)
• Sampled Transformer for Point Sets [80.66097006145999]
  sparse transformer can reduce the computational complexity of the self-attention layers to $O(n)$, whilst still being a universal approximator of continuous sequence-to-sequence functions. We propose an $O(n)$ complexity sampled transformer that can process point set elements directly without any additional inductive bias.
  arXiv  Detail & Related papers  (2023-02-28T06:38:05Z)
• Exact solution of a family of staggered Heisenberg chains with conclusive pretty good quantum state transfer [68.8204255655161]
  We work out the exact solutions in the one-excitation subspace. We present numerical evidence that pretty good transmission is achieved by chains whose length is not a power of two.
  arXiv  Detail & Related papers  (2022-06-28T18:31:09Z)
• Improved Quantum Algorithms for Fidelity Estimation [77.34726150561087]
  We develop new and efficient quantum algorithms for fidelity estimation with provable performance guarantees. Our algorithms use advanced quantum linear algebra techniques, such as the quantum singular value transformation. We prove that fidelity estimation to any non-trivial constant additive accuracy is hard in general.
  arXiv  Detail & Related papers  (2022-03-30T02:02:16Z)
• REGTR: End-to-end Point Cloud Correspondences with Transformers [79.52112840465558]
  We conjecture that attention mechanisms can replace the role of explicit feature matching and RANSAC. We propose an end-to-end framework to directly predict the final set of correspondences. Our approach achieves state-of-the-art performance on 3DMatch and ModelNet benchmarks.
  arXiv  Detail & Related papers  (2022-03-28T06:01:00Z)
• Exact rate analysis for quantum repeaters with imperfect memories and entanglement swapping as soon as possible [0.0]
  We present an exact rate analysis for a secret key that can be shared among two parties employing a linear quantum repeater chain. We consider additional tools and parameters such as memory cut-offs, multiplexing, initial state and swapping gate fidelities.
  arXiv  Detail & Related papers  (2022-03-19T12:55:56Z)
• Alleviate Exposure Bias in Sequence Prediction \\ with Recurrent Neural Networks [47.52214243454995]
  A popular strategy to train recurrent neural networks (RNNs) is to take the ground truth as input at each time step. We propose a fully differentiable training algorithm for RNNs to better capture long-term dependencies.
  arXiv  Detail & Related papers  (2021-03-22T06:15:22Z)
• Pretty good quantum state transfer on isotropic and anisotropic Heisenberg spin chains with tailored site dependent exchange couplings [68.8204255655161]
  We consider chains with isotropic and anisotropic Heisenberg Hamiltonian with up to 100 spins. We consider short transferred times, in particular shorter than those achievable with known time-dependent control schemes.
  arXiv  Detail & Related papers  (2021-01-08T19:32:10Z)
• Bayesian Bits: Unifying Quantization and Pruning [73.27732135853243]
  We introduce Bayesian Bits, a practical method for joint mixed precision quantization and pruning through gradient based optimization. We experimentally validate our proposed method on several benchmark datasets and show that we can learn pruned, mixed precision networks.
  arXiv  Detail & Related papers  (2020-05-14T16:00:34Z)

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.