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This is a great question! The goal of entanglement-based networks is to generate entanglement between end-users. This entanglement can then be utilized for all sorts of amazing applications. Typically, the generated distributed entanglement is in the form of a Bell state. This is because many of the most common entanglement-based applications (e.g., Quantum Teleportation, Superdense Coding, BBM92 Key Distribution, among many others) utilize distributed Bell states. Unfortunately, during the distribution process, decoherence degrades our Bell states to mixed states with reduced entanglement. To combat this decoherence, we can use entanglement purification. It is possible to purify quantum states that are quite distinct from Bell states to near-perfect Bell states (that is, entangled states with arbitrarily high fidelity relative to a target Bell state). In fact, the paper from which the purification protocol discussed in the webinar originates shows that mixed states (with fidelity greater than .5) can be purified to a smaller number of near-perfect Bell states. It is important to note that there are states that cannot be purified to near-perfect Bell states using this -- or any other -- protocol. Such states are known as "bound entangled." For example, any entangled state with a density matrix that has a positive partial transpose is bound entangled. This is the paper from which the purification protocol discussed in the webinar originates: arxiv.org/pdf/quant-ph/9511027 These are two references that you might also find useful: github.com/PaddlePaddle/Quantum/blob/master/tutorials/locc/EntanglementDistillation_BBPSSW_EN.ipynb arxiv.org/pdf/quant-ph/0608095 We hope that this response answers your question! Please let us know if you have further questions.

@@alirotech Wow, great!. Thanks for your response and for sharing this vital resources. I will take a look at them.

Thank you for the kind words, Gabriel. We would recommend that you learn more from these full length webinars we have created on our Quantum Networking channel here www.brighttalk.com/channel/19861/ You can view our open positions and prerequisites on our job listings here www.aliroquantum.com/careers-aliro Best of Luck!

Entanglement swapping occurs when two entangled particles (i.e., 1 and 2) become entangled with another set of particles (i.e., 3 and 4), respectively. This swapping results in entanglement between particles 1 and 3 (which were not entangled to one another prior to entanglement swapping). This quantum phenomena allows for the extension of entanglement over longer distances through repeaters and other devices.

@MikeWood-zt3yg Thank you! So if not for the repeaters, the entanglement would be lost?

Quantum repeaters are not necessary to maintain entanglement between two points although the distance between those two points is limited due to the degradation of the qubits over longer distances. Entanglement can be performed on point to point optical networks today for example. Entanglement swapping through quantum repeaters enables one to extend the distance between two qubits which can be entangled with one another (i.e., from a local area network to a wide area network).

Yes, mixed states lie inside the Bloch sphere, while pure states lie on the surface.

You can watch the entire webinar on teleportation here:www.brighttalk.com/webcast/19861/584141

Correct, third generation repeaters do not use entanglement swapping. Whereas first and second generation repeaters are “two-way”, third generation repeaters are “one-way”. In the one-way scenario, at each hop in the path, the repeater uses error correction to correct for any errors that the logical quantum state may have incurred while traveling from the previous node. This is analogously similar to classical networks with feed-forward error correction. For the case of entanglement distribution from node A to node Z, the entangled state can just be physically transported from A to Z via third generation repeaters. For first and second generation repeaters, each link in the path from A to Z will need to establish link-wise entanglement independently, and these are subsequently “glued” together via entanglement swapping to generate the end-to-end entanglement between A and Z.

@@alirotech Thanks for talking the time ti reply. I appreciate it. does one way and two way signalling mean the classical signals containing information about bell state measurements transferred to nodes being entangled?

That’s correct, there will be two-way signaling in first-generation quantum networks for classical communication about Bell state measurements to the end nodes of the entanglement. There may also be two-way quantum signaling. For example, in a meet-in-the-middle architecture, the two end nodes send quantum signals to the middle repeater, and thus are traveling in opposite directions. However, the higher-level distinction of third-generation “one-way” repeaters is that the flow of the quantum signals (in this case a multi-photon state) physically travels unidirectionally from source to destination.

@@alirotech Are these higher dimensional entangled states cluster states?