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Temporal Framework for Causality-Preserving Scheduling of Measurements in Quantum Networks

Jakob Kaltoft Søndergaard, René Bødker Christensen, Petar Popovski

TL;DR

This paper tackles causality ambiguity in measurement-based quantum networks caused by heterogeneous hardware timing by introducing a time-division coordination framework with quantum slots of duration $T_q$ and classical slots of duration $T_c$. It formalizes feedforward and adjacency constraints to ensure a unique, interpretable causal order of measurements and demonstrates scheduling strategies on 1D cluster states, including sequential and parallel regimes. The main contributions include a precise temporal model, analytic bounds and algorithms for slot assignment, and simulations illustrating the transition from sequential to parallel operation as $T_q$ grows, with streaming reliability benefits. The framework provides a practical coordination layer that links classical timing with quantum measurement processing, enabling more robust and scalable MBQNs, while outlining directions for tighter optimality results and fault-tolerant extensions.

Abstract

Distributed quantum protocols rely on classical feedforward information to process measurement outcomes, but heterogeneous hardware and uncertain local timing can make the causal order of measurements ambiguous when inferred solely from arrival times. Even in simple line networks with only Pauli measurements, end nodes cannot distinguish whether a missing outcome is caused by slow measurement or by delayed classical propagation. To resolve this ambiguity, we propose a time-division architecture for quantum networks in which nodes perform measurements in pre-assigned slots, ensuring a unique causal interpretation of outcomes. We formalize this temporal framework and derive the feedforward and adjacency constraints required to preserve measurement causality. For simple network topologies, we present an algorithm that yields optimal measurement schedules. Overall, the proposed time-division model provides a practical coordination layer that bridges the classical network timing with quantum measurement processing, enabling reliable and scalable measurement-based quantum networking.

Temporal Framework for Causality-Preserving Scheduling of Measurements in Quantum Networks

TL;DR

This paper tackles causality ambiguity in measurement-based quantum networks caused by heterogeneous hardware timing by introducing a time-division coordination framework with quantum slots of duration and classical slots of duration . It formalizes feedforward and adjacency constraints to ensure a unique, interpretable causal order of measurements and demonstrates scheduling strategies on 1D cluster states, including sequential and parallel regimes. The main contributions include a precise temporal model, analytic bounds and algorithms for slot assignment, and simulations illustrating the transition from sequential to parallel operation as grows, with streaming reliability benefits. The framework provides a practical coordination layer that links classical timing with quantum measurement processing, enabling more robust and scalable MBQNs, while outlining directions for tighter optimality results and fault-tolerant extensions.

Abstract

Distributed quantum protocols rely on classical feedforward information to process measurement outcomes, but heterogeneous hardware and uncertain local timing can make the causal order of measurements ambiguous when inferred solely from arrival times. Even in simple line networks with only Pauli measurements, end nodes cannot distinguish whether a missing outcome is caused by slow measurement or by delayed classical propagation. To resolve this ambiguity, we propose a time-division architecture for quantum networks in which nodes perform measurements in pre-assigned slots, ensuring a unique causal interpretation of outcomes. We formalize this temporal framework and derive the feedforward and adjacency constraints required to preserve measurement causality. For simple network topologies, we present an algorithm that yields optimal measurement schedules. Overall, the proposed time-division model provides a practical coordination layer that bridges the classical network timing with quantum measurement processing, enabling reliable and scalable measurement-based quantum networking.
Paper Structure (20 sections, 12 equations, 3 figures, 1 table, 1 algorithm)

This paper contains 20 sections, 12 equations, 3 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Model
  3. Graph states
  4. Network model
  5. Time-Division Framework
  6. Measurement Scheduling Constraints
  7. Feedforward
  8. Adjacency
  9. Network Topology and Resource State
  10. Streaming Reliability
  11. Problem Statement
  12. Sequential and Parallel Measurements
  13. Sequential
  14. Parallel
  15. Intermediate Quantum Slot Regimes
  16. ...and 5 more sections

Figures (3)

  • Figure 1: Four-node network illustrating measurement causality ambiguity. (a) Topology with initial resource state and single-hop communication channels. (b) Asynchronous measurements: heterogeneous durations cause end nodes to see different measurement orders. (c) Time-slotted measurements enforce a shared causal structure, enabling consistent interpretation of outcomes.
  • Figure 2: Total number of measurement slots $T^*$ as a function of distance $D$ between source and receiver for selected values of $T_q$.
  • Figure 3: Total number of measurement slots $T^*$ as a function of $T_q$ for several fixed distances $D$. The inset highlights the behavior for small $T_q$ and small $D$, showing that near-optimal schedules are achieved even at modest feedforward speeds.