# Quantum Entanglement Mnf Full Version

## Quantum Entanglement MNF Full Version

Quantum entanglement is one of the most fascinating and mysterious phenomena in quantum physics. It describes a situation where two or more particles are so strongly correlated that their quantum states cannot be described independently, even when they are separated by large distances. This means that measuring one particle will instantly affect the state of the other, regardless of how far apart they are. This phenomenon has been called "spooky action at a distance" by Albert Einstein, who was skeptical of its existence.

Quantum entanglement has many applications in quantum information science, such as quantum cryptography, quantum teleportation, quantum computation, and quantum metrology. However, generating and manipulating entangled states is not easy, especially for large-scale systems with many particles. In this article, we will review some of the recent advances in creating and controlling multidimensional and multipartite entangled states using integrated optics and subgraph complementations.

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## Multidimensional Quantum Entanglement with Large-Scale Integrated Optics

One way to increase the amount of information that can be encoded in a quantum system is to use higher-dimensional states, such as qudits, instead of qubits. A qudit is a quantum system that can exist in d possible states, where d is any integer greater than 2. For example, a qutrit is a three-level system that can be in any superposition of 0>, 1>, or 2>. A qudit can be realized by using different degrees of freedom of a photon, such as polarization, orbital angular momentum, time-bin, or frequency.

A multidimensional entangled state is a state where two or more qudits are entangled with each other. For example, a two-qudit entangled state can be written as Ïˆ> = i=0 ci i>Ai>B, where ci are complex coefficients and i>A and i>B are the basis states of qudits A and B, respectively. A multidimensional entangled state can carry more information than a two-qubit entangled state, and can also exhibit stronger nonlocal correlations and higher resistance to noise.

To generate and manipulate multidimensional entangled states, one needs a platform that can support large-scale integration of optical components, such as waveguides, couplers, splitters, phase shifters, and detectors. One promising candidate is silicon photonics, which uses silicon as the material for creating photonic circuits on a chip. Silicon photonics has many advantages, such as low cost, high reliability, compatibility with existing fabrication techniques, and potential for integration with electronic circuits.

In 2018, a team of researchers from China, UK, Denmark, Spain, and Australia demonstrated a multidimensional integrated quantum photonic platform that can robustly generate, control and analyze high-dimensional entanglement. They realized a programmable bipartite entangled system with dimension up to 15 15 on a large-scale silicon-photonics quantum circuit. The device integrated more than 550 photonic components on a single chip, including 16 identical photon-pair sources. They verified the high precision, generality and controllability of their multidimensional technology, and further exploited these abilities to demonstrate key quantum applications experimentally unexplored before, such as quantum randomness expansion and self-testing on multidimensional states.

## Multipartite Entanglement in Quantum Networks using Subgraph Complementations

Another way to increase the complexity and functionality of a quantum system is to use multipartite entangled states, where more than two particles are entangled with each other. For example, a three-qubit entangled state can be written as Ïˆ> = Î±000> + Î²111>, where Î± and Î² are complex coefficients and 000> and 111> are the basis states of three qubits. A multipartite entangled state can exhibit different types of correlations among its subsystems, such as genuine multipartite entanglement (GME), biseparable entanglement (BSE), or fully separable (FS).

Multipartite entanglement has many applications in quantum networks, which consist of nodes that can store and process quantum information and links that can transmit quantum information between nodes. Quantum networks can enable distributed quantum computation, quantum communication, quantum metrology, and quantum sensing. However, creating and maintaining multipartite entangled states in quantum networks is challenging, due to the effects of noise, decoherence, and loss.

In 2023, a team of researchers from India proposed a novel method for generating multipartite entangled states in quantum networks using subgraph complementations. They showed that by applying local operations and classical communication (LOCC) on a subset of nodes in a quantum network, one can transform the network into its complementary subgraph, which is obtained by deleting the subset of nodes and connecting the remaining nodes with new links. They proved that this transformation can preserve or enhance the entanglement of the network, and can also create new types of entangled states that are not possible in the original network. They illustrated their method with several examples of quantum networks, such as star graphs, cycle graphs, and complete graphs.

## Conclusion

Quantum entanglement is a powerful resource for quantum information science, but it is also difficult to generate and manipulate. In this article, we reviewed some of the recent advances in creating and controlling multidimensional and multipartite entangled states using integrated optics and subgraph complementations. These techniques can potentially enable new applications and protocols for quantum communication, computation, and metrology.