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Quantum Computing, Communication, and Simulation

High-dimensional entanglement in quantum frequency combs (Conference Presentation)

Chee Wei Wong, Zhenda Xie, Xiang Cheng, Kai-Chi Chang, Yoo Seung Lee, Xuan Cui, Alvin Peizhe Li

Published Mar 14, 2018• 0 citations
Publisher

Abstract

Quantum entanglement is a fundamental resource for secure information processing and communications. The canonical optical quantum information processing encodes a single qubit per photon, with remarkable demonstrations of secure quantum communications, linear optical quantum computing amongst others. Often the polarization qubit, a discrete variable with entangled Bell states, is used. Continuous variables such as energy-time modes and spatial modes, however, present a dramatically larger Hilbert space for quantum information processing. The high-dimensional entanglement capture more qubits per photon, enabling dramatically higher secure key rates over longer distances and with better error resilience. Here I will describe our results on high-dimensional entanglement in quantum frequency combs for dense quantum communications. We first demonstrate revival of the Hong-Ou-Mandel interferences, long postulated by theorists more than a decade ago, up to 19-dimensions and with visibilities up to 96.5%. The mode-locked two-photon state in high-dimensions is further witnessed through a stabilized Franson interferometer, as a generalized Bell’s inequality test and hyperentangled through multiple degrees-of-freedom. Entanglement revivals of the non-local interference at discrete time-bins are uncovered, up to 97.8% visibility, as a fundamental resource for dense secure information processing.

DOI
10.1117/12.2292463

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Quantum entanglement is a fundamental resource for secure information processing and communications. The canonical optical quantum information processing encodes a single qubit per photon, with remarkable demonstrations of secure quantum communications, linear optical quantum computing amongst others. Often the polarization qubit, a discrete variable with entangled Bell states, is used. Continuous variables such as energy-time modes and spatial modes, however, present a dramatically larger Hilbert space for quantum information processing. The high-dimensional entanglement capture more qubits per photon, enabling dramatically higher secure key rates over longer distances and with better error resilience. Here I will describe our results on high-dimensional entanglement in quantum frequency combs for dense quantum communications. We first demonstrate revival of the Hong-Ou-Mandel interferences, long postulated by theorists more than a decade ago, up to 19-dimensions and with visibilities up to 96.5%. The mode-locked two-photon state in high-dimensions is further witnessed through a stabilized Franson interferometer, as a generalized Bell’s inequality test and hyperentangled through multiple degrees-of-freedom. Entanglement revivals of the non-local interference at discrete time-bins are uncovered, up to 97.8% visibility, as a fundamental resource for dense secure information processing.
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).
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 High-dimensional quantum entanglement is currently one of the most prolific fields in quantum information processing due to its high information capacity and error resilience. A versatile method for harnessing high-dimensional entanglement has long been hailed as an absolute necessity in the exploration of quantum science and technologies. Here we exploit Hong-Ou-Mandel interference to manipulate discrete frequency entanglement in arbitrary-dimensional Hilbert space. The generation and characterization of two-, four- and six-dimensional frequency entangled qudits are theoretically and experimentally investigated, allowing for the estimation of entanglement dimensionality in the whole state space. Additionally, our strategy can be generalized to engineer higher-dimensional entanglement in other photonic degrees of freedom. Our results may provide a more comprehensive understanding of frequency shaping and interference phenomena, and pave the way to more complex high-dimensional quantum information processing protocols.
Photonic entanglement is a fundamental resource in quantum information processing and its distribution between distant parties is a key challenge in quantum communications. Optical satellite links allow transmitting entangled photons over longer distances than currently possible on ground and could provide a path towards global quantum communication networks. The majority of current photonic free-space quantum communication systems, including two recent quantum satellite experiments, use two-dimensional polarization encoding, where each photon can carry at most a single bit of quantum information. Encoding additional qubits in the high-dimensional spatio-temporal degrees of freedom could not only increase channel capacities but also improve robustness with respect to noise and eavesdropping in quantum cryptography. Here, we give an overview of our efforts towards exploiting high-dimensional entanglement in long-distance free-space quantum communications. We report on the results of a first feasibility study, in which we used polarization / energy-time hyperentanglement to increase the dimensionality of the state space and transmit genuine 4-dimensional entanglement via an intra-city free-space link. We discuss how we intend to extend this approach to applications in noise-tolerant large-alphabet quantum key distribution via free-space links, and, ultimately, experiments with satellites.
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.