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1. Entanglement Purification with Quantum LDPC Codes and Iterative Decoding

   https://doi.org/10.22331/q-2024-01-24-1233  

   Rengaswamy, Narayanan ; Raveendran, Nithin ; Raina, Ankur ; Vasić, Bane ( January 2024 , Quantum)

   Recent constructions of quantum low-density parity-check (QLDPC) codes provide optimal scaling of the number of logical qubits and the minimum distance in terms of the code length, thereby opening the door to fault-tolerant quantum systems with minimal resource overhead. However, the hardware path from nearest-neighbor-connection-based topological codes to long-range-interaction-demanding QLDPC codes is likely a challenging one. Given the practical difficulty in building a monolithic architecture for quantum systems, such as computers, based on optimal QLDPC codes, it is worth considering a distributed implementation of such codes over a network of interconnected medium-sized quantum processors. In such a setting, all syndrome measurements and logical operations must be performed through the use of high-fidelity shared entangled states between the processing nodes. Since probabilistic many-to-1 distillation schemes for purifying entanglement are inefficient, we investigate quantum error correction based entanglement purification in this work. Specifically, we employ QLDPC codes to distill GHZ states, as the resulting high-fidelity logical GHZ states can interact directly with the code used to perform distributed quantum computing (DQC), e.g. for fault-tolerant Steane syndrome extraction. This protocol is applicable beyond the application of DQC since entanglement distribution and purification is a quintessential task of any quantum network. We use the min-sum algorithm (MSA) based iterative decoder with a sequential schedule for distilling$3$-qubit GHZ states using a rate$0.118$family of lifted product QLDPC codes and obtain an input fidelity threshold of$\approx 0.7974$under i.i.d. single-qubit depolarizing noise. This represents the best threshold for a yield of$0.118$for any GHZ purification protocol. Our results apply to larger size GHZ states as well, where we extend our technical result about a measurement property of$3$-qubit GHZ states to construct a scalable GHZ purification protocol.

    

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2. Continuous entanglement distribution from an AlGaAs-on-insulator microcomb for quantum communications

   https://doi.org/10.1364/OPTICAQ.510032  

   Steiner, Trevor J. ; Shen, Maximilian ; Castro, Joshua E. ; Bowers, John E. ; Moody, Galan ( December 2023 , Optica Quantum)

   Using an aluminum gallium arsenide microring resonator, we demonstrate a bright quantum optical microcomb with >300 nm (>40 THz) bandwidth and more than 20 sets of time–energy entangled modes, enabling spectral demultiplexing with simple, off-the-shelf commercial telecom components. We report high-rate continuous entanglement distribution for two sets of entangled-photon pair frequency modes exhibiting up to 20 GHz/mW²pair generation rate. As an illustrative example of entanglement distribution, we perform a continuous-wave time-bin quantum key distribution protocol with 8 kbps sifted key rates while maintaining less than 10% error rate and sufficient two-photon visibility to ensure security of the channel. When the >20 frequency modes are multiplexed, we estimate >100 kbps entanglement-based key rates or the creation of a multi-user quantum communications network. The entire system requires less than 110 µW of on-chip optical power, demonstrating an efficient source of entangled frequency modes for quantum communications. As a proof of principle, a quantum key is distributed across 12 km of deployed fiber on the University of California Santa Barbara (UCSB) campus and used to encrypt a 21 kB image with <9% error.

    

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3. 648 Hilbert-space dimensionality in a biphoton frequency comb: entanglement of formation and Schmidt mode decomposition

   https://doi.org/10.1038/s41534-021-00388-0  

   Chang, Kai-Chi ; Cheng, Xiang ; Sarihan, Murat Can ; Vinod, Abhinav Kumar ; Lee, Yoo Seung ; Zhong, Tian ; Gong, Yan-Xiao ; Xie, Zhenda ; Shapiro, Jeffrey H. ; Wong, Franco N. C. ; et al ( March 2021 , npj Quantum Information)

   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 anS-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 (E_of) 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).

    

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4. Distance-Independent Entanglement Generation in a Quantum Network using Space-Time Multiplexed Greenberger–Horne–Zeilinger (GHZ) Measurements

   https://doi.org/10.1109/QCE52317.2021.00050  

   Patil, Ashlesha ; Jacobson, Joshua I. ; Van Milligen, Emily ; Towsley, Don ; Guha, Saikat ( November 2021 , 2021 IEEE International Conference on Quantum Computing and Engineering (QCE))

   In a quantum network that successfully creates links—shared Bell states between neighboring repeater nodes—with probability p in each time slot, and performs Bell State Measurements at nodes with success probability q < 1, the end-to-end entanglement generation rate drops exponentially with the distance between consumers, despite multi-path routing. If repeaters can perform multi-qubit projective measurements in the GHZ basis that succeed with probability q, the rate does not change with distance in a certain (p,q) region, but decays exponentially outside. This region where the distance-independent rate occurs is the super-critical region of a new percolation problem. We extend this GHZ protocol to incorporate a time-multiplexing blocklength k, the number of time slots over which a repeater can mix-and-match successful links to perform fusion on. As k increases, the super-critical region expands. For a given (p,q), the entanglement rate initially increases with k, and once inside the super-critical region for a high enough k, it decays as 1/k GHZ states per time slot. When memory coherence time exponentially distributed with mean μ is incorporated, it is seen that increasing k does not indefinitely increase the super-critical region; it has a hard μ-dependent limit. Finally, we find that incorporating space-division multiplexing, i.e., running the above protocol independently in up to d disconnected network regions, where d is the network’s node degree, one can go beyond the 1 GHZ state per time slot rate that the above randomized local-link-state protocol cannot surpass. As (p,q) increases, one can approach the ultimate min-cut entanglement-generation capacity of d GHZ states per slot. 

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5. Entanglement generation in a quantum network at distance-independent rate

   https://doi.org/10.1038/s41534-022-00536-0  

   Patil, Ashlesha ; Pant, Mihir ; Englund, Dirk ; Towsley, Don ; Guha, Saikat ( May 2022 , npj Quantum Information)

   We develop a protocol for entanglement generation in the quantum internet that allows a repeater node to usen-qubit Greenberger-Horne-Zeilinger (GHZ) projective measurements that can fusensuccessfully entangledlinks, i.e., two-qubit entangled Bell pairs shared acrossnnetwork edges, incident at that node. Implementingn-fusion, forn ≥ 3, is in principle not much harder than 2-fusions (Bell-basis measurements) in solid-state qubit memories. If we allow even 3-fusions at the nodes, we find—by developing a connection to a modified version of the site-bond percolation problem—that despite lossy (hence probabilistic) link-level entanglement generation, and probabilistic success of the fusion measurements at nodes, one can generate entanglement between end parties Alice and Bob at a rate that stays constant as the distance between them increases. We prove that this powerful network property is not possible to attain with any quantum networking protocol built with Bell measurements and multiplexing alone. We also design a two-party quantum key distribution protocol that converts the entangled states shared between two nodes into a shared secret, at a key generation rate that is independent of the distance between the two parties.

    

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