High-dimensional Path-Encoded Entanglement Distribution Between Photonic Chips Enabled by Multimode Phase Stabilisation

TL;DR

This work tackles distributing high-dimensional path-encoded entanglement over noisy inter-chip fibre links by introducing a multimode active phase-stabilisation algorithm that requires no extra hardware and completes a stabilization iteration in two measurement rounds for any number of modes. The approach enables reliable preparation, transmission, and complete quantum state tomography of four-dimensional entangled qudits between photonic chips, achieving a fidelity of $\mathcal{F}=0.86$ and entanglement entropy $\mathcal{E}=0.995\pm0.002$, facilitated by phase coherence across all $d$ path modes. The combination of scalable phase control, loss-balancing, and MUB-based tomography demonstrates robust HD entanglement distribution and paves the way for high-rate quantum networking between integrated quantum processors; future speedups from faster electronics and electro-optic modulators could further boost fidelity and duty cycle. Overall, the work validates path-encoded HD entanglement distribution on chip-to-chip links and outlines a practical tomography framework enabled by multimode phase stabilisation.

Abstract

The reliable distribution of high-dimensional entangled quantum states, an important resource in quantum technologies, through optical fibre networks is challenging due to the need to maintain coherence across multiple modes. Here we demonstrate the distribution of four-dimensional path-encoded entangled quantum states between photonic chips, enabled by a novel multimode phase stabilisation algorithm. The algorithm utilises the reconfigurability of the integrated photonic circuits to complete one iteration of phase stabilisation in just two measurement rounds for an arbitrary number of modes, and requires no additional hardware to the quantum measurements it enables. As a result, we are able to perform complete quantum state tomography across two chips using the minimum number of local projective measurements to verify the fidelity of the distributed entangled state to be 86% (compared to 8.1% without the phase stabilisation) with an entanglement entropy of 0.995+/-0.002.

Figures (15)

• Figure 1: (a) Schematic of the experimental set-up consisting of two integrated photonic circuits, Alice and Bob, connected by optical fibres. The pairs of entangled qudits are prepared in section $\hat{G}$ of the Alice chip and projective measurements are performed by Alice and Bob with the reconfigurable interferometers $\hat{A}$ and $\hat{B}$. (b) Interference fringes in optical power (classical) and coincidence counts (quantum) due to time reversed Hong-Ou-Mandel interference. (c) RHOM interference visibilities of all ring pairs, quantifying indistinguishability.
• Figure 2: (a) Workflow of measurement of the relative phase between two modes, interleaved with iterations of the desired quantum measurement. (b) Interferometer configurations for two rounds of the phase stabilisation of our four-dimensional system, where MZIs are set to 50:50; identity, $\hat{I}$; or swap, $\hat{S}$, to interfere different pairs of modes and route light to off-chip powermeters. The powermeters highlighted in green and pink are those used to measure fringes in the phase stabilisation. In round one we measure $\Delta_{0,1}$ and $\Delta_{2,3}$ and in round two we measure $\Delta_{0,3}$ and $\Delta_{1,2}$. (c) Fidelity of the classical $H_4^+$ Hadamard basis state measurement over time without and with phase stabilisation. (d) Fidelity decay at time $\Delta t$ since stabilisation - an iteration of the phase stabilisation is complete at $\Delta t =0s$. This is compared to the fidelity of the computational basis state $C_4^0=(1 \,\, 0 \,\, 0\,\, 0)^T$.
• Figure 3: (a) Number of projective measurements required for $N$ qudits with dimension $d=4$ (b) Number of projective measurements required for $N=2$ qudits with dimension $d$. (c) Ideal, (d) non-stabilised, and (e) stabilised reconstructed density matrix for the experimentally prepared, distributed, and measured $\ket{\Phi^+_4}$ state.
• Figure S\fpeval4-3: Schematic of the experimental set-up including off-chip components.
• Figure S\fpeval5-3: MRR (top) and AMZI (bottom) spectrum.