Entanglement distribution: To herald or not to herald

Abstract

High-rate, high-fidelity entanglement distribution is essential for the creation of a quantum internet, and spontaneous parametric downconverters (SPDCs) are, at present, the preferred sources of entangled signal-idler photon pairs for transmission to Alice and Bob's quantum nodes. SPDCs using phase-matched spectral islands are especially attractive, in this regard, because they provide wavelength-division multiplexed signal-idler pairs with single-mode temporal behavior. This paper compares the entanglement distribution rates of three islands-based systems. Two use idler detections for heralding: islands-based zero-added-loss multiplexing (ZALM), and an islands-based Sagnac SPDC source with signal-path erasure. The third employs an unheralded Sagnac SPDC source. For 90% or lower heralding efficiencies, ZALM's per-pump-pulse entanglement distribution rate exceeds that of the signal-path erasure source, and both rates are inferior to unheralded operation's when all three systems employ $N_I$ spectral islands and allocate $N_M = N_I$ quantum memories to each pump pulse. These behaviors, however, must be weighed against the three systems' differing equipment requirements, e.g., ZALM requires a pair of perfectly-matched Sagnac sources, which is a significant burden not incurred by the signal-path erasure approach, and both heralded systems will suffer, in comparison with unheralded operation, if they cannot realize high heralding efficiencies.

Figures (20)

• Figure 1: Schematic of a Sagnac-configured SPDC source Wong2006 of signal-idler biphotons suitable for use with $N_I\ge 1$ in islands-based heralded operation using either the dual-Sagnac source or the Chahine et al. source. A periodically-poled lithium niobate (PPLN) crystal with $N_I$ phase-matched spectral islands footnote4 is bidirectionally pulse-pumped for type-0 nondegenerate phase matching. $D$, $H$, and $V$: diagonal, horizontal, and vertical polarizations. HR: high reflector. $\lambda$: wavelength. PBS: polarizing beam splitter. HWP: half-wave plate.
• Figure 2: Sketch of the frequency-domain wave function for a biphoton produced by 6 identical, spectrally-factorable phase-matched spectral islands, with signal-idler center frequencies $\{(\omega_{S_n},\omega_{I_n}): n=1,2,\ldots,6\}$.
• Figure 3: Schematic of islands-based ZALM's partial Bell-state measurement for heralding polarization-entangled photon pairs. Here $S_k$ and $I_k$ for $k = 1,2$ denote the signal ($S$) and idler ($I$) beams from the $k$th Sagnac source. $I_\pm$ denote the idler-beam outputs from the 50--50 beam splitter (BS); $I_{\pm P}$ for $P= H, V$ denote the horizontally ($H$) and vertically ($V$) polarized outputs from the polarizing beam splitter (PBS) illuminated by $I_\pm$; DWDM$_I$: idler-beam dense wavelength-division multiplexing filter. SPD: single-photon detector.
• Figure 4: Schematic of Chahine et al.'s islands-based source of heralded polarization-entangled photon pairs. $S^\perp_P$ for $P = V,H$ are auxiliary vacuum-state $P$-polarized modes needed to ensure that the $S_k = S_{k_H}S_{k_V}$ modes for $k=1,2$ have proper free-field commutators. DWDM$_I$: idler-beam dense wavelength-division multiplexing filter. SPD: single-photon detector. BS: 50--50 beam splitter.
• Figure 5: Schematic of islands-based source for unheralded distribution of polarization-entangled photon pairs. A periodically-poled lithium niobate (PPLN) crystal with $N_M$ phase-matched spectral islands footnote5 is bidirectionally pulse-pumped for type-0 nondegenerate phase matching. $D$, $H$, and $V$: diagonal, horizontal, and vertical polarizations. HR: high reflector. $\lambda$: wavelength. PBS: polarizing beam splitter. HWP: half-wave plate.