High-dimensional time-frequency entanglement in a singly-filtered biphoton frequency comb
Xiang Cheng, Kai-Chi Chang, Murat Can Sarihan, Andrew Mueller, M. Spiropulu, Matthew D. Shaw, Boris A. Korzh, Andrei Faraon, Franco N. C. Wong, Jeffrey H. Shapiro, Chee Wei Wong
Abstract High-dimensional quantum entanglement is a cornerstone for advanced technology enabling large-scale noise-tolerant quantum systems, fault-tolerant quantum computing, and distributed quantum networks. The recently developed biphoton frequency comb (BFC) provides a powerful platform for high-dimensional quantum information processing in its spectral and temporal quantum modes. Here we propose and generate a singly-filtered high-dimensional BFC via spontaneous parametric down-conversion by spectrally shaping only the signal photons with a Fabry-Pérot cavity. High-dimensional energy-time entanglement is verified through Franson-interference recurrences and temporal correlation with low-jitter detectors. Frequency- and temporal- entanglement of our singly-filtered BFC is then quantified by Schmidt mode decomposition. Subsequently, we distribute the high-dimensional singly-filtered BFC state over a 10 km fiber link with a post-distribution time-bin dimension lower bounded to be at least 168. Our demonstrations of high-dimensional entanglement and entanglement distribution show the singly-filtered quantum frequency comb’s capability for high-efficiency quantum information processing and high-capacity quantum networks.
Abstract High-dimensional quantum entanglement is a cornerstone for advanced technology enabling large-scale noise-tolerant quantum systems, fault-tolerant quantum computing, and distributed quantum networks. The recently developed biphoton frequency comb (BFC) provides a powerful platform for high-dimensional quantum information processing in its spectral and temporal quantum modes. Here we propose and generate a singly-filtered high-dimensional BFC via spontaneous parametric down-conversion by spectrally shaping only the signal photons with a Fabry-Pérot cavity. High-dimensional energy-time entanglement is verified through Franson-interference recurrences and temporal correlation with low-jitter detectors. Frequency- and temporal- entanglement of our singly-filtered BFC is then quantified by Schmidt mode decomposition. Subsequently, we distribute the high-dimensional singly-filtered BFC state over a 10 km fiber link with a post-distribution time-bin dimension lower bounded to be at least 168. Our demonstrations of high-dimensional entanglement and entanglement distribution show the singly-filtered quantum frequency comb’s capability for high-efficiency quantum information processing and high-capacity quantum networks.
Abstract Qudit entanglement is an indispensable resource for quantum information processing since increasing dimensionality provides a pathway to higher capacity and increased noise resilience in quantum communications, and cluster-state quantum computations. In continuous-variable time–frequency entanglement, encoding multiple qubits per photon is only limited by the frequency correlation bandwidth and detection timing jitter. Here, we focus on the discrete-variable time–frequency entanglement in a biphoton frequency comb (BFC), generating by filtering the signal and idler outputs with a fiber Fabry–Pérot cavity with 45.32 GHz free-spectral range (FSR) and 1.56 GHz full-width-at-half-maximum (FWHM) from a continuous-wave (cw)-pumped type-II spontaneous parametric downconverter (SPDC). We generate a BFC whose time-binned/frequency-binned Hilbert space dimensionality is at least 324, based on the assumption of a pure state. Such BFC’s dimensionality doubles up to 648, after combining with its post-selected polarization entanglement, indicating a potential 6.28 bits/photon classical-information capacity. The BFC exhibits recurring Hong–Ou–Mandel (HOM) dips over 61 time bins with a maximum visibility of 98.4% without correction for accidental coincidences. In a post-selected measurement, it violates the Clauser–Horne–Shimony–Holt (CHSH) inequality for polarization entanglement by up to 18.5 standard deviations with an S-parameter of up to 2.771. It has Franson interference recurrences in 16 time bins with a maximum visibility of 96.1% without correction for accidental coincidences. From the zeroth- to the third-order Franson interference, we infer an entanglement of formation (Eof) up to 1.89 ± 0.03 ebits—where 2 ebits is the maximal entanglement for a 4 × 4 dimensional biphoton—as a lower bound on the 61 time-bin BFC’s high-dimensional entanglement. To further characterize time-binned/frequency-binned BFCs we obtain Schmidt mode decompositions of BFCs generated using cavities with 45.32, 15.15, and 5.03 GHz FSRs. These decompositions confirm the time–frequency scaling from Fourier-transform duality. Moreover, we present the theory of conjugate Franson interferometry—because it is characterized by the state’s joint-temporal intensity (JTI)—which can further help to distinguish between pure-state BFC and mixed state entangled frequency pairs, although the experimental implementation is challenging and not yet available. In summary, our BFC serves as a platform for high-dimensional quantum information processing and high-dimensional quantum key distribution (QKD).
Mode-locked biphoton frequency combs exhibit multiple discrete comblike temporal correlations from the Fourier transform of its phase-coherent frequency spectrum. Both temporal correlation and Franson interferometry are valuable tools for analyzing the joint properties of biphoton frequency combs, and the latter has proven to be essential for testing the fundamental quantum nature, the time-energy entanglement distribution, and the large-alphabet quantum key distributions. However, the Franson recurrence interference visibility in biphoton frequency combs unavoidably experiences a falloff that deteriorates the quality of time-energy entanglement and channel capacity for longer cavity round trips. In this paper, we provide a new method to address this problem towards optimum Franson interference recurrence. We first observe mode-locked temporal oscillations in a 5.03 GHz free-spectral range singly filtered biphoton frequency comb using only commercial detectors. Then, we observe similar falloff trend of time-energy entanglement in 15.15 GHz and 5.03 GHz free-spectral range singly filtered biphoton frequency combs, whereas, the optimum central time-bin accidental-subtracted visibility over 97% for both cavities. Here, we find that by increasing the cavity finesse F , we can enhance the detection probability in temporal correlations and towards optimum Franson interference recurrence in our singly filtered biphoton frequency combs. For the first time, via a higher cavity finesse F of 45.92 with a 15.11 GHz free-spectral range singly filtered biphoton frequency comb, we present an experimental ≈3.13-fold improvement of the Franson visibility compared to the Franson visibility with a cavity finesse F of 11.14 at the sixth time bin. Near optimum Franson interference recurrence and a time-bin Schmidt number near 16 effective modes in similar free-spectral range cavity are predicted with a finesse F of 200. Our configuration is versatile and robust against changes in cavity parameters that can be designed for various quantum applications, such as high-dimensional time-energy entanglement distributions, high-dimensional quantum key distributions, and wavelength-multiplexed quantum networks.
Quantum networks enable fundamentally secure communications and entanglement distribution in parallelized quantum computation. Here we describe our high-dimensional quantum network based on frequency-multiplexed time-bin encoding. Our multi-user 21-km experimental testbed is designed for robustness and scalability, with frequency- and temporal-multiplexing for high-rate interconnects while preserving minimal resource usage and multi-party access through simultaneous key or entanglement distribution. Our measurements are in the high-dimensional frequency and temporal conjugate subspaces, via our biphoton frequency comb qudit. Non-local Franson interferometry provide a measured lower-bound of our entanglement-of-formation, and the Schmidt mode decomposition provide an estimate of the accessible quantum information. We highlight adaptive optimization and singly-filtered biphoton combs as a practical architecture in our high-rate quantum network testbed. We describe the photon information efficiency, Shannon capacity, entanglement distribution, raw key rates, security measurements, dispersive bases, code-efficient non-binary error correction, and Holevo bounds embedded in our network.
High-dimensional entanglement with larger Hilbert spaces enable an encoding of more bits per photon and thus promise increased communication capacities over quantum channels. Quantum frequency combs, which are intrinsically multimode in the temporal and frequency degrees of freedom within a single spatial mode, naturally facilitating the generation and measurement of high-dimensional entanglement. Current challenges include the extension of well-known methods for two qubits to high-dimensional quantum systems and their application in entanglement experiments with photons. More specifically, the major challenge is the certification of high-dimensional entanglement by a number of accessible experimental measurements. In this paper, we increase the Hilbert space dimensionality and provide versatile tools for quantifying and certifying high-dimensional entanglement in a biphoton frequency comb. We quantify the time binned Schmidt number up to 18 and certify entanglement of formation with 1.89 ebits. We have demonstrated a 648- dimensional Hilbert spaces with time-frequency entanglement in a biphoton frequency comb, enabling a computational space up to 13 photonic qubits, and 6.28 bits/photon classical information capacity. This high-dimensional time frequency multimode quantum states of biphoton frequency comb significantly boosting the photon information capacity that is critical for large-scale quantum information processing. Biphoton frequency comb has indeed demonstrated an attractive and powerful approach towards achieving this fundamental goal with applications in high-dimensional quantum information processing, time-frequency cluster-state quantum computation, high-dimensional encoding in quantum networks, and high-dimensional quantum simulations.
Abstract A frequency-multiplexed entangled photon pair and a high-dimensional hyperentangled photon pair are useful to realize a high-capacity quantum communication. A biphoton frequency comb (BFC) with entanglement can be used to prepare both states. We demonstrate polarization entangled BFCs with over 1400 frequency modes, which is approximately two orders of magnitude larger than those of earlier entangled BFCs, by placing a singly resonant periodically poled LiNbO3 waveguide resonator within a Sagnac loop. The BFCs are demonstrated by measuring the joint spectral intensity, cross-correlation, and autocorrelation. Moreover, the polarization entanglement at representative groups of frequency modes is verified by quantum state tomography, where each fidelity is over 0.7. The efficient generation of a massive-mode entangled BFC is expected to accelerate the increase of capacity in quantum communication.