Detecting Errors in a Quantum Network with Pauli Checks

TL;DR

The paper addresses maintaining high-fidelity entanglement across noisy quantum networks by adapting Pauli Check Sandwiching (PCS) into a distributed protocol. It introduces analytical fidelity and postselection formulas for PCS with X checks and X&Z checks, and develops a recursive PCS scheme that yields a family of distance-2 codes locally equivalent to CSS codes. The work demonstrates, through simulations, that PCS can outperform BBPSSW in comparable scenarios and that protecting both flying and memory qubits generally yields better fidelity, with recursive PCS offering further gains at manageable qubit cost. These results suggest PCS is a practical, low-overhead alternative for error detection in quantum networks and can integrate with graph-state-based repeaters to enhance robust entanglement distribution.

Abstract

We apply the quantum error detection scheme Pauli check sandwiching (PCS) to quantum networks by turning it into a distributed multiparty protocol. PCS provides protection on the targeted qubits and generally requires less resource overhead than standard quantum error correction and detection codes. We provide analytical equations for the final fidelity and postselection rate for different PCS checks. We also introduce a recursive version of PCS that generates a family of distance 2 quantum codes that are locally equivalent to Calderbank-Shor-Steane (CSS) codes. Our analytical results are benchmarked against the Bennet-Brassard-Popescu-Schumacher-Smolin-Wooters (BBPSSW) protocol in comparable scenarios. We also perform simulations with noisy gates for entanglement swapping and attain fidelity improvements. Lastly, we discuss various setups and graph state properties of PCS.

Figures (14)

• Figure 1: Entanglement Swapping Protocol with PCS. The orange gates make up the left Pauli checks and the blue gates make up the right Pauli checks. $\mathcal{E}$ denotes traversals through the network to Charlie and is a noise channel. We denote the origin repeater of a qubit by the subscript $a$ or $b$. Fig. \ref{['fig:pcs_x_circ']} only has X checks, whereas Fig. \ref{['fig:npcs_xz']} has both X and Z checks.
• Figure 2: PCS and BBPSSW purification scenarios. Note that having local noise channels on both halves of the Bell state in the BBPSSW protocol does not change as a function of the initial fidelity the original BBPSSW fidelity and postselection equations. The overline in the subscripts in the PCS scenario denotes multiple qubits. All the noise channels are single qubit depolarizing channels. Bennett_1996bbpssw.
• Figure 3: Analytical scenario for only PCS X checks.
• Figure 4: Plots of the final fidelity $F'$ vs the initial fidelity $F$ of the noisy Bell state.
• Figure 5: Analytical scenario for PCS X&Z checks.