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Efficient Entanglement Swapping in High-Dimensions with only Linear Optics

Baghdasar Baghdasaryan, Kaushik Joarder, Fabian Steinlechner

TL;DR

This work tackles enabling high-dimensional entanglement swapping for quantum repeaters using linear optics and ancillary photons, addressing the bottleneck of Bell state measurements in HD encoding. It develops a scheme capable of HD BSM up to six dimensions, analyzes the four-, five-, and six-dimensional cases, and quantifies how PNR detectors can boost heralding success while balancing fidelity losses from HOM interference. A concrete experimental proposal is provided for four-dimensional swapping using hyper-entanglement in time-bin and polarization, including ancilla preparation and post-selection strategies with entangled-state analyzers. Overall, the paper highlights a practical, ancilla-assisted, linear-optics route to HD entanglement swapping, discusses performance trade-offs, and outlines a pathway toward HD quantum networks, while noting current limitations for very high dimensions and the pivotal role of detector capabilities.

Abstract

Entanglement swapping is a fundamental building block for realizing first-generation quantum repeaters, which are essential for building global quantum networks. Current quantum repeater systems still struggle to achieve practical communication rates. High-dimensional (HD) encoding can significantly improve repeater efficiency by boosting information capacity and enhancing noise tolerance and security. However, the experimental demonstration of this protocol so far has been limited only to two-dimensional systems due to the requirement of strong nonlinear interactions. Here, we introduce an efficient linear-optics protocol for HD entanglement swapping that uses ancillary photons and is compatible with arbitrary photonic degrees of freedom (DOFs). We further show that photon-number-resolving detectors substantially enhance the performance of the setup and become especially valuable for dimensions beyond six. For a four-dimensional scenario, we present an experimental design using hyper-entanglement in polarization and time-bin DOFs. This setup resolves the most challenging part of the ancillary photons-based approach, namely the necessary preparation of the ancilla state and analysis of the resulting swapped state.

Efficient Entanglement Swapping in High-Dimensions with only Linear Optics

TL;DR

This work tackles enabling high-dimensional entanglement swapping for quantum repeaters using linear optics and ancillary photons, addressing the bottleneck of Bell state measurements in HD encoding. It develops a scheme capable of HD BSM up to six dimensions, analyzes the four-, five-, and six-dimensional cases, and quantifies how PNR detectors can boost heralding success while balancing fidelity losses from HOM interference. A concrete experimental proposal is provided for four-dimensional swapping using hyper-entanglement in time-bin and polarization, including ancilla preparation and post-selection strategies with entangled-state analyzers. Overall, the paper highlights a practical, ancilla-assisted, linear-optics route to HD entanglement swapping, discusses performance trade-offs, and outlines a pathway toward HD quantum networks, while noting current limitations for very high dimensions and the pivotal role of detector capabilities.

Abstract

Entanglement swapping is a fundamental building block for realizing first-generation quantum repeaters, which are essential for building global quantum networks. Current quantum repeater systems still struggle to achieve practical communication rates. High-dimensional (HD) encoding can significantly improve repeater efficiency by boosting information capacity and enhancing noise tolerance and security. However, the experimental demonstration of this protocol so far has been limited only to two-dimensional systems due to the requirement of strong nonlinear interactions. Here, we introduce an efficient linear-optics protocol for HD entanglement swapping that uses ancillary photons and is compatible with arbitrary photonic degrees of freedom (DOFs). We further show that photon-number-resolving detectors substantially enhance the performance of the setup and become especially valuable for dimensions beyond six. For a four-dimensional scenario, we present an experimental design using hyper-entanglement in polarization and time-bin DOFs. This setup resolves the most challenging part of the ancillary photons-based approach, namely the necessary preparation of the ancilla state and analysis of the resulting swapped state.

Paper Structure

This paper contains 8 sections, 20 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Scheme and analysis for HD entanglement swapping
  3. Four-dimensional entanglement swapping
  4. Five- and six-dimensional entanglement swapping
  5. Success probability
  6. Proposal: experimental setup for four-dimensional entanglement swapping
  7. Conclusion
  8. Three-dimensional entanglement swapping

Figures (3)

  • Figure 1: Schematic of three- and four-dimensional entanglement swapping with three 50:50 beam splitters (BS). In addition to two initially maximally entangled states, the setup also contains a two-dimensional ancilla state for performing the BSM. EPS: entangled photon-pair source; PD: photon detector.
  • Figure 2: Schematic of five- and six-dimensional entanglement swapping with two two-dimensional ancilla Bell states.
  • Figure 3: Proposed experimental setup for four-dimensional entanglement swapping using hyper-entanglement in time-bin and polarization DOFs. PEPS: polarization-entangled photon-pair source; BSA: Bell state analyzer; ESA: entangled state analyzer.