Heralded quasi-deterministic entanglement sources based on spontaneous parametric down-conversion

Abstract

A double-heralding technique is presented for producing heralded entangled photon pairs from spontaneous parametric down-conversion (SPDC). Compared to the swap-heralded schemes studied in previous cascaded SPDC and zero-added-loss multiplexing (ZALM) proposals, this double-heralding technique is found to yield the most resource-efficient implementation in terms of minimizing the total number of sources and detectors required to achieve a specified rate and fidelity. This is achieved by reducing the number of modes and mode-sorting optics needed on the heralding path. Specifically, by immediately detecting any two signal photons from an array of down-converters, the corresponding idler photons can be projected onto an anti-correlated pair state which is shown to be unitarily equivalent to the state produced by swap-heralded sources, and hence can be used directly for long-range entanglement distribution in a ZALM architecture. Quasi-deterministic operation through two distinct multiplexing techniques is analyzed. The analysis derives expressions for the heralded pair probability and fidelity assuming realistic detectors with losses, dark counts, and partial photon number resolution (PNR), providing a framework for implementation of the source on a photonic integrated circuit (PIC).

Figures (13)

• Figure 1: Swap-heralded pair source based on a partial BSM between two polarization-entangled SPDC sources, each producing a D-TMSV state. Solid horizontal lines represent optical modes, with the signal (idler) modes always drawn on the left (right). Filled and open circles joined by a vertical line represent beam-splitter (BS) and polarizing beam-splitter (PBS) unitaries between two modes. The heralded states $|\varepsilon^\pm\rangle\pm|\Psi^\pm\rangle$ are described in \ref{['eq:bellstates']}-\ref{['eq:errorterms']}.
• Figure 2: Double-heralded pair source configurations based on 4-photon emissions from two TMSV sources, heralded by two single-photon detections on the signal modes. The $\times$-PBS denotes a diagonally oriented polarizing beam-splitter which produces a partial Bell state in the basis $c=\sqrt{1/2}(a+b)$, $d=\sqrt{1/2}(a-b)$.
• Figure 3: Double-heralded $M$-TMSV configurations based on a 2-photon emission from each of two $M$-TMSV arrays, heralded by a single photon detection on the signal modes from each array. The operator $U_M$ represents an $M$-mode QFT or Hadamard unitary. For $M=2$, $U_2$ is just a 50:50 beam-splitter and this configuration is formally equivalent to the swap-heralded configuration of Fig. \ref{['fig:swapheraldedeps']} (Appendix \ref{['app:symmetry']}).
• Figure 4: Double-heralded $M$-TMSV in a complete multiplexing configuration with active mode-conversion into a prescribed set of $M$ modes for injection into a network. If at least two $M$-TMSV sources produce a pair, the corresponding idler modes are switched into the output channel with one photon of each polarization superposed on $M$ modes. Dotted lines represent classical control signals. The controlled-$X$ gate represents a half-wave plate swapping polarizations, and the controlled-PBS selectively switches the modes which contain a heralded photon into the output channel. The indices $1\leq k,l\leq M$ of the detectors which registered a click are distributed with the anti-correlated pair to apply the corresponding phase shifts.
• Figure 5: Double-heralded $M$-TMSV in a bipartite multiplexing configuration for frequency-multiplexed ZALM with $n=N/2$ spectral modes. If at least one $M$-TMSV source from each set produces a pair, the corresponding idler modes are switched into the output frequency $\omega_0$ via polarization-dependent frequency-conversion $U_x(\Delta\omega_x)$ which applies a frequency shift $\Delta\omega_x = \omega_0 - \omega_x$ to all $MN/2$ modes with polarization $x$.