Multipartite entanglement percolation

We present percolation strategies based on multipartite measurements to propagate entanglement in quantum networks. We consider networks spanned on regular lattices whose bonds correspond to pure but non-maximally entangled pairs of qubits, with any quantum operation allowed at the nodes. Despite significant effort in the past, improvements over naive (classical) percolation strategies have been found for only few lattices, often with restrictions on the initial amount of entanglement in the bonds. In contrast, multipartite entanglement percolation outperform the classical percolation protocols, as well as all previously known quantum ones, over the entire range of initial entanglement and for every lattice that we considered.Comment: revtex4, 4 page

Distribution of entanglement in networks of bi-partite full-rank mixed states

We study quantum entanglement distribution on networks with full-rank bi-partite mixed states linking qubits on nodes. In particular, we use entanglement swapping and purification to partially entangle widely separated nodes. The simplest method consists of performing entanglement swappings along the shortest chain of links connecting the two nodes. However, we show that this method may be improved upon by choosing a protocol with a specific ordering of swappings and purifications. A priori, the design that produces optimal improvement is not clear. However, we parametrize the choices and find that the optimal values depend strongly on the desired measure of improvement. As an initial application, we apply the new improved protocols to the Erd\"os--R\'enyi network and obtain results including low density limits and an exact calculation of the average entanglement gained at the critical point.Comment: 15 pages, 19 figures. New version includes improvements suggested in referee repor

Entanglement Percolation with Bipartite Mixed States

We develop a concept of entanglement percolation for long-distance singlet generation in quantum networks with neighboring nodes connected by partially entangled bipartite mixed states. We give a necessary and sufficient condition on the class of mixed network states for the generation of singlets. States beyond this class are insufficient for entanglement percolation. We find that neighboring nodes are required to be connected by multiple partially entangled states and devise a rich variety of distillation protocols for the conversion of these states into singlets. These distillation protocols are suitable for a variety of network geometries and have a sufficiently high success probability even for significantly impure states. In addition to this, we discuss possible further improvements achievable by using quantum strategies including generalized forms of entanglement swapping.Comment: 6+ pages, 5 figures; Published versio

From quantum fusiliers to high-performance networks

Our objective was to design a quantum repeater capable of achieving one million entangled pairs per second over a distance of 1000km. We failed, but not by much. In this letter we will describe the series of developments that permitted us to approach our goal. We will describe a mechanism that permits the creation of entanglement between two qubits, connected by fibre, with probability arbitrarily close to one and in constant time. This mechanism may be extended to ensure that the entanglement has high fidelity without compromising these properties. Finally, we describe how this may be used to construct a quantum repeater that is capable of creating a linear quantum network connecting two distant qubits with high fidelity. The creation rate is shown to be a function of the maximum distance between two adjacent quantum repeaters.Comment: 2 figures, Comments welcom

Differentiating and quantifying carbonaceous (tire, bitumen, and road marking wear) and non-carbonaceous (metals, minerals, and glass beads) non-exhaust particles in road dust samples from a traffic environment

Tires, bitumen, and road markings are important sources of traffic-derived carbonaceous wear particles and microplastic (MP) pollution. In this study, we further developed a machine-learning algorithm coupled to an automated scanning electron microscopy/energy dispersive X-ray spectroscopy (SEM/EDX) analytical approach to classify and quantify the relative number of the following subclasses contained in environmental road dust: tire wear particles (TWP), bitumen wear particles (BiWP), road markings, reflecting glass beads, metallics, minerals, and biogenic/organics. The method is non-destructive, rapid, repeatable, and enables information about the size, shape, and elemental composition of particles 2–125 μm. The results showed that the method enabled differentiation\ua0between TWP and BiWP for particles > 20 μm with satisfying results. Furthermore, the relative number concentration of the subclasses was similar in both analyzed size fractions (2–20 μm and 20–125 μm), with minerals as the most dominant subclass (2–20 μm x̄ = 78%, 20–125 μm x̄ = 74%) followed by tire and bitumen wear particles, TBiWP, (2–20 μm x̄ = 19%, 20–125 μm x̄ = 22%). Road marking wear, glass beads, and metal wear contributed to x̄ = 1%, x̄ = 0.1%, and x̄ = 1% in the 2–20-μm fraction and to x̄ = 0.5%,x̄ = 0.2%, and x̄ = 0.4% in the 20–125-μm fraction. The present results show that road dust appreciably consists of TWP and BiWP within both the coarse and the fine size fraction. The study delivers quantitative evidence of the importance of tires, bitumen, road marking, and glass beads besides minerals and metals to wear particlesand MP pollution in traffic environments based on environmental (real-world) sample

One-shot entanglement generation over long distances in noisy quantum networks

We consider the problem of creating a long-distance entangled state between two stations of a network, where neighboring nodes are connected by noisy quantum channels. We show that any two stations can share an entangled pair if the effective probability for the quantum errors is below a certain threshold, which is achieved by using local redundant encoding to preserve the global phase and network-based correction for the bit-flip errors. In contrast to the convensional quantum repeater schemes we are not limited by the memory coherence time, because all quantum operations only use one-way classical communication and can be done in one shot. Meanwhile, the overhead of local resources only increases logarithmically with the size of the network, making our proposal favorable to practical applications of long-distance quantum communication.Comment: revtex4, 6 pages, 5 figures (.eps

Google in a Quantum Network

We introduce the characterization of a class of quantum PageRank algorithms in a scenario in which some kind of quantum network is realizable out of the current classical internet web, but no quantum computer is yet available. This class represents a quantization of the PageRank protocol currently employed to list web pages according to their importance. We have found an instance of this class of quantum protocols that outperforms its classical counterpart and may break the classical hierarchy of web pages depending on the topology of the web.Comment: RevTeX 4 file, color figure