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Quantum Error Correction via Noise Guessing Decoding

Quantum error correction codes (QECCs) play a central role both in quantum communications and in quantum computation, given how error-prone quantum technologies are. Practical quantum error correction codes, such as stabilizer codes, are generally structured to suit a specific use, and present rigid code lengths and code rates, limiting their adaptability to changing requirements. This paper shows that it is possible to both construct and decode QECCs that can attain the maximum performance of the finite blocklength regime, for any chosen code length and when the code rate is sufficiently high. A recently proposed strategy for decoding classical codes called GRAND (guessing random additive noise decoding) opened doors to decoding classical random linear codes (RLCs) that perform near the capacity of the finite blocklength regime. By making use of the noise statistics, GRAND is a noise-centric efficient universal decoder for classical codes, providing there is a simple code membership test. These conditions are particularly suitable for quantum systems and therefore the paper extends these concepts to quantum random linear codes (QRLCs), which were known to be possible to construct but whose decoding was not yet feasible. By combining QRLCs and a newly proposed quantum GRAND, this paper shows that decoding versatile quantum error correction is possible, allowing for QECCs that are simple to adapt on the fly to changing conditions. The paper starts by assessing the minimum number of gates in the coding circuit needed to reach the QRLCs' asymptotic performance, and subsequently proposes a quantum GRAND algorithm that makes use of quantum noise statistics, not only to build an adaptive code membership test, but also to efficiently implement syndrome decoding

Distributing Multipartite Entanglement over Noisy Quantum Networks

A quantum internet aims at harnessing networked quantum technologies, namely by distributing bipartite entanglement between distant nodes. However, multipartite entanglement between the nodes may empower the quantum internet for additional or better applications for communications, sensing, and computation. In this work, we present an algorithm for generating multipartite entanglement between different nodes of a quantum network with noisy quantum repeaters and imperfect quantum memories, where the links are entangled pairs. Our algorithm is optimal for GHZ states with 3 qubits, maximising simultaneously the final state fidelity and the rate of entanglement distribution. Furthermore, we determine the conditions yielding this simultaneous optimality for GHZ states with a higher number of qubits, and for other types of multipartite entanglement. Our algorithm is general also in the sense that it can optimise simultaneously arbitrary parameters. This work opens the way to optimally generate multipartite quantum correlations over noisy quantum networks, an important resource for distributed quantum technologies.Comment: More detailed calculations of the metrics and minor changes. Keywords: Quantum Internet, QLANs, Multipartite Entanglement, Entanglement Distribution, Multi-objective Routing, Quantum Network

Entanglement Routing Based on Fidelity Curves for Quantum Photonics Channels

The quantum internet promises to extend entanglement correlations from nearby neighbors to any two nodes in a network. How to efficiently distribute entanglement over large-scale networks is still an open problem that greatly depends on the technology considered. In this work, we consider quantum networks composed of photonic channels characterized by a trade-off between the entanglement generation rate and fidelity. For such networks we look at the two following problems: the one of finding the best path to connect any two given nodes in the network bipartite entanglement routing, and the problem of finding the best starting node in order to connect three nodes in the network multipartite entanglement routing. We consider two entanglement distribution models: one where entangled qubit are distributed one at a time, and a flow model where a large number of entangled qubits are distributed simultaneously. We propose the use of continuous fidelity curves (i.e., entanglement generation fidelity vs rate) as the main routing metric. Combined with multi-objective path-finding algorithms, the fidelity curves describing each link allow finding a set of paths that maximize both the end-to-end fidelity and the entanglement generation rate. For the models and networks considered, we prove that the algorithm always converges to the optimal solution, and we show through simulation that its execution time grows polynomial with the number of nodes in the network. Our implementation grows with the number of nodes with a power between $1$ and $1.4$ depending on the network. This work paves the way for the development of path-finding algorithms for networks with complex entanglement distribution protocols, in particular for other protocols that exhibit a trade-off between generation fidelity and rate, such as repeater-and-purify protocols

Efficient entanglement purification based on noise guessing decoding

In this paper, we propose a novel bipartite entanglement purification protocol built upon hashing and upon the guessing random additive noise decoding (GRAND) approach recently devised for classical error correction codes. Our protocol offers substantial advantages over existing hashing protocols, requiring fewer qubits for purification, achieving higher fidelities, and delivering better yields with reduced computational costs. We provide numerical and semi-analytical results to corroborate our findings and provide a detailed comparison with the hashing protocol of Bennet et al. Although that pioneering work devised performance bounds, it did not offer an explicit construction for implementation. The present work fills that gap, offering both an explicit and more efficient purification method. We demonstrate that our protocol is capable of purifying states with noise on the order of 10% per Bell pair even with a small ensemble of 16 pairs. The work explores a measurement-based implementation of the protocol to address practical setups with noise. This work opens the path to practical and efficient entanglement purification using hashing-based methods with feasible computational costs. Compared to the original hashing protocol, the proposed method can achieve some desired fidelity with a number of initial resources up to one hundred times smaller. Therefore, the proposed method seems well-fit for future quantum networks with a limited number of resources and entails a relatively low computational overhead.Comment: 16 page

Modulation of the Effects of Lung Immune Response on Bone Marrow by Oral Antigen Exposure

Allergic airway inflammation is attenuated by oral tolerization (oral exposure to allergen, followed by conventional sensitization and challenge with homologous antigen), which decreases airway allergen challenge-induced eosinophilic infiltration of the lungs and bone marrow eosinophilia. We examined its effects on bone marrow eosinophil and neutrophil production. Mice of wild type (BP-2, BALB/c, and C57BL/6) and mutant strains (lacking iNOS or CD95L) were given ovalbumin (OVA) or water (vehicle) orally and subsequently sensitized and challenged with OVA (OVA/OVA/OVA and H2O/OVA/OVA groups, resp.). Anti-OVA IgG and IgE, bone marrow eosinophil and neutrophil numbers, and eosinophil and neutrophil production ex vivo were evaluated. T lymphocytes from OVA/OVA/OVA or control H2O/OVA/OVA donors were transferred into naïve syngeneic recipients, which were subsequently sensitized/challenged with OVA. Alternatively, T lymphocytes were cocultured with bone marrow eosinophil precursors from histocompatible sensitized/challenged mice. OVA/OVA/OVA mice of the BP-2 and BALB/c strains showed, relative to H2O/OVA/OVA controls, significantly decreased bone marrow eosinophil counts and ex vivo eosinopoiesis/neutropoiesis. Full effectiveness in vivo required sequential oral/subcutaneous/intranasal exposures to the same allergen. Transfer of splenic T lymphocytes from OVA/OVA/OVA donors to naive recipients prevented bone marrow eosinophilia and eosinopoiesis in response to recipient sensitization/challenge and supressed eosinopoiesis upon coculture with syngeneic bone marrow precursors from sensitized/challenged donors

Measurement of the cross-section and charge asymmetry of WW bosons produced in proton-proton collisions at s=8\sqrt{s}=8 TeV with the ATLAS detector

This paper presents measurements of the $W^+ \rightarrow \mu^+\nu$ and $W^- \rightarrow \mu^-\nu$ cross-sections and the associated charge asymmetry as a function of the absolute pseudorapidity of the decay muon. The data were collected in proton--proton collisions at a centre-of-mass energy of 8 TeV with the ATLAS experiment at the LHC and correspond to a total integrated luminosity of 20.2~\mbox{fb^{-1}}. The precision of the cross-section measurements varies between 0.8% to 1.5% as a function of the pseudorapidity, excluding the 1.9% uncertainty on the integrated luminosity. The charge asymmetry is measured with an uncertainty between 0.002 and 0.003. The results are compared with predictions based on next-to-next-to-leading-order calculations with various parton distribution functions and have the sensitivity to discriminate between them.Comment: 38 pages in total, author list starting page 22, 5 figures, 4 tables, submitted to EPJC. All figures including auxiliary figures are available at https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/STDM-2017-13