Bright Source of High-Dimensional Temporal Entanglement

Abstract

High-dimensional entanglement is considered to hold great potential for quantum key distribution (QKD) in high-loss and -noise scenarios. To harness its robustness, we construct a source for high-dimensional time-bin entangled photons optimized for high brightness, low complexity, and long-term stability. We certify the generated high-dimensional entanglement with a new witness employing nested Franson interferometry. Finally, we obtain key rates using a novel, noise-resilient QKD protocol. Our flexible evaluation method, centered around discretizations of the time stream, enables the same dataset to be processed while varying parameters such as state dimensionality and time bin length, allowing optimization of performance under given environmental conditions. Our results indicate regions within the accessible parameter space where high key rates per time are achievable for dimensionalities larger than two.

Figures (4)

• Figure 1: Experimental Setup. In the photon source, we pump a Type-0 ppKTP crystal, kept at a non-degenerate temperature, with a wavelength-locked 404.5nm laser. After focusing the pump into the crystal, we collimate the generated photons and filter out the pump before splitting the photon pairs apart using a dichroic mirror. We couple the photons into single-mode fibers and distribute them to the detection modules, Alice and Bob. The PBSs and HWPs in front of the MZIs impose diagonal polarization and act as additional filters of potential background noise. Each module consists of two nested, imbalanced MZIs constructed using PBSs. By rotating a HWP in the output of the MZIs, we switch between TOA and TSUP measurements. Alternatively, the HWPs in front of the MZIs could be rotated to achieve an equivalent effect. By monitoring the classical interference of the stabilized reference (pump) laser sent through the MZIs, we stabilize the interferometers using a piezo-actuated mirror stage.
• Figure 2: Discretizations of the time stream for different dimensions. We group $d$ time bins of length $\tau$ into interleaved time frames, indicated by identical colors. Time bins belonging to the same state are separated by one MZI delay to enable TSUP measurements. This structure requires the MZI delay to be an integer multiple of $\tau$. After $d$ MZI delays, the pattern repeats and a new block of interleaved time frames begins, indicated in grayed-out colors.
• Figure 3: Figures of merit for the source and proof-of-principle realization of the novel QKD protocol. Each quantity is computed both for the case when Alice and Bob use only the shorter MZI, effectively a single Franson interferometer, and for the full nested-Franson setup. By varying only the dimension while evaluating the same data set, we scan for optima along one axis of the discretization parameter space. All reported quantities should be understood as lower bounds. a) Schmidt numbers of the photonic state, certifying HD time-bin entanglement for all discretizations with $d>2$. b) Entanglement rate, quantifying the amount of maximally entangled qubits produced per second by the source. c) Asymptotic key rates computed using the novel QKD protocol. Higher dimensions with negative key rates are omitted for clarity. Lines serve as a guide to the eye.
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