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Linear-optical fusion boosted by high-dimensional entanglement

Tomohiro Yamazaki, Koji Azuma

TL;DR

The paper tackles efficient entanglement fusion of high-dimensional qudits and scalable quantum repeater design by introducing a probabilistic Bell-state projection implemented with linear optics. It develops a bosonic stabilizer framework that maps LOC transfer matrices to unitaries via $B(U)$, enabling exact identification of the two-qudit measurements and Kraus operators for general ancilla resources, including Bell and GHZ-type states, with success probabilities of $1-d^{-1}$ (no ancilla) and $1-d^{-(k+1)}$ (GHZ ancilla). Applying this, the authors propose a fast quantum repeater protocol using three-qudit GHZ states and memories, and they compare performance against standard qubit-based fusion schemes, deriving scaling laws for entanglement-generation and swapping steps. Numerical results show that high-dimensional, ancilla-boosted fusion outperforms conventional methods across a range of detector efficiencies and distances, with second-generation schemes offering advantages under favorable parameters, though practical gains may require quantum-error-correcting codes for broader robustness.$ $p_f=1/2$ for standard fusion and $p_f=1-d^{-1}$ or $1-d^{-(k+1)}$ for boosted gates, with $P_s$ and $ au$ expressions governing distribution times. The work thus provides both a rigorous framework for high-dimensional LO fusion and practical guidance for implementing efficient quantum-repeaters in photonic networks.

Abstract

We propose a quantum measurement that probabilistically projects a pair of qudits of dimension $d$ onto a Bell state in a two-qubit subspace. It can be performed using linear-optical circuits with the success probabilities of $1-d^{-1}$ without ancilla photons and $1-d^{-(k+1)}$ with $2(2^{k}-1)$ ancilla photons. It allows us to entangle two independently-prepared high-dimensional entangled states two-dimensionally with higher probabilities than ones of linear-optical fusion gates on qubits. As an application, we propose a fast quantum repeater protocol with three-qudit GHZ states and quantum memories.

Linear-optical fusion boosted by high-dimensional entanglement

TL;DR

The paper tackles efficient entanglement fusion of high-dimensional qudits and scalable quantum repeater design by introducing a probabilistic Bell-state projection implemented with linear optics. It develops a bosonic stabilizer framework that maps LOC transfer matrices to unitaries via , enabling exact identification of the two-qudit measurements and Kraus operators for general ancilla resources, including Bell and GHZ-type states, with success probabilities of (no ancilla) and (GHZ ancilla). Applying this, the authors propose a fast quantum repeater protocol using three-qudit GHZ states and memories, and they compare performance against standard qubit-based fusion schemes, deriving scaling laws for entanglement-generation and swapping steps. Numerical results show that high-dimensional, ancilla-boosted fusion outperforms conventional methods across a range of detector efficiencies and distances, with second-generation schemes offering advantages under favorable parameters, though practical gains may require quantum-error-correcting codes for broader robustness.p_f=1/2p_f=1-d^{-1}1-d^{-(k+1)}P_s au$ expressions governing distribution times. The work thus provides both a rigorous framework for high-dimensional LO fusion and practical guidance for implementing efficient quantum-repeaters in photonic networks.

Abstract

We propose a quantum measurement that probabilistically projects a pair of qudits of dimension onto a Bell state in a two-qubit subspace. It can be performed using linear-optical circuits with the success probabilities of without ancilla photons and with ancilla photons. It allows us to entangle two independently-prepared high-dimensional entangled states two-dimensionally with higher probabilities than ones of linear-optical fusion gates on qubits. As an application, we propose a fast quantum repeater protocol with three-qudit GHZ states and quantum memories.
Paper Structure (10 sections, 1 theorem, 38 equations, 7 figures)

This paper contains 10 sections, 1 theorem, 38 equations, 7 figures.

Table of Contents

  1. Supplemental Material
  2. A. Analysis of linear-optical circuits based on bosonic stabilizer formalism
  3. Bosonic stabilizer formalism
  4. The case of a Bell-state ancilla
  5. The general cases
  6. B. Performance comparison among quantum repeater protocols
  7. Entanglement generation step
  8. Entanglement swapping step in first-generation quantum repeaters
  9. Entanglement swapping step in second-generation quantum repeaters
  10. Numerical simulations

Key Result

Lemma 1

Let states $\ket*{\Psi_+}$ and $\ket*{\Psi_-}$ in the $2^{k+1} d$-mode Fock space satisfy respectively, for an integer $p \in \{0,\dots, k\}$. Then, these states can be distinguished by the LOC consisting of the interferometric part specified by transfer matrix $H^{\otimes k+1} \otimes I_d$ and $2^{k+1} d$ detectors In the bosonic stabilizer formalism Yamazaki_2023, we say the LOC used i

Figures (7)

  • Figure S1:
  • Figure S5:
  • Figure S2:
  • Figure S3:
  • Figure S6:
  • ...and 2 more figures

Theorems & Definitions (3)

  • Lemma
  • proof
  • proof : Proof of Eq. \ref{['eq:lowerbound']}