Multipartite entanglement plays a crucial role in the Quantum Internet design, due to its potentiality of significantly increasing the network performance. In this paper, we identify the four key network functionalities for managing multipartite entanglement among remote nodes. And we discuss each functionality by considering - as case study - a specific multipartite state, which exhibits an attractive computing feature. Specifically, the designed state allows an arbitrary entangled node to calculate - in a distributed way - the sum of a set of values arbitrarily selected by the remaining entangled nodes.
Multipartite entanglement plays a crucial role in the Quantum Internet design, due to its potentiality of significantly increasing the network performance. In this paper, we identify the four key network functionalities for managing multipartite entanglement among remote nodes. And we discuss each functionality by considering - as case study - a specific multipartite state, which exhibits an attractive computing feature. Specifically, the designed state allows an arbitrary entangled node to calculate - in a distributed way - the sum of a set of values arbitrarily selected by the remaining entangled nodes.
Multipartite entanglement plays a crucial role for the design of the Quantum Internet, due to its potentiality of significantly increasing the network performance. In this paper, we design an entanglement access control protocol for multipartite state, which exhibits several attractive features. Specifically, the designed protocol is able to jointly extract in a distributed way an EPR pair from the original multipartite entangled state shared by the set of network nodes, and to univocally determines the identities of the transmitter node and the receiver node in charge of using the extracted EPR pair. Furthermore, the protocol avoids to delegate the signaling arising with entanglement access control to the classical network, with the exception of the unavoidable classical communications needed for EPR extraction and qubit teleportation. Finally, the protocol supports the anonymity of the entanglement accessing nodes.
Multipartite entanglement distribution is a key functionality of the Quantum Internet. However, quantum entanglement is very fragile, easily degraded by decoherence, which strictly constraints the time horizon within the distribution has to be completed. This, coupled with the quantum noise irremediably impinging on the channels utilized for entanglement distribution, may imply the need to attempt the distribution process multiple times before the targeted network nodes successfully share the desired entangled state. And there is no guarantee that this is accomplished within the time horizon dictated by the coherence times. As a consequence, in noisy scenarios requiring multiple distribution attempts, it may be convenient to stop the distribution process early. In this paper, we take steps in the direction of knowing when to stop the entanglement distribution by developing a theoretical framework, able to capture the quantum noise effects. Specifically, we first prove that the entanglement distribution process can be modeled as a Markov decision process. Then, we prove that the optimal decision policy exhibits attractive features, which we exploit to reduce the computational complexity. The developed framework provides quantum network designers with flexible tools to optimally engineer the design parameters of the entanglement distribution process.
Scaling the number of entangled nodes in a quantum network is a challenge with significant implications for quantum computing, clock synchronisation, secure communications, and quantum sensing. In a quantum network, photons interact with matter qubits at different nodes, flexibly enabling the creation of remote entanglement between them. Multipartite entanglement among multiple nodes will be crucial for many proposed quantum network applications, including quantum computational tasks and quantum metrology. To date, experimental efforts have primarily focused on generating bipartite entanglement between nodes, which is widely regarded as the fundamental quantum resource for quantum networks. However, relying exclusively on bipartite entanglement to form more complex multipartite entanglement introduces several challenges. These include the need for ancillary qubits, extensive local entangling operations which increases the preparation latency, and increasingly stringent requirements on coherence times as the number of nodes grows. Here, we analyse various schemes that achieve multipartite entanglement between nodes in a single step, bypassing the need for multiple rounds of bipartite entanglement. We demonstrate that different schemes can produce distinct multipartite entangled states, with varying fidelity and generation rates. Additionally, we discuss the applicability of these schemes across different experimental platforms, highlighting their primary advantages and disadvantages.
The Quantum Internet - i.e. an heterogeneous network enabling quantum communications among remote quantum nodes by leveraging on quantum transmission channels in synergy with classical transmission channels - is attracting worldwide academic and industrial interest [1, 2, 3, 4, 5, 6, 7], given its potential of enabling applications with no counterpart in the classical Internet [8]. Indeed, the Quantum Internet, by transmitting qubits and by distributing entangled quantum states, comes with a whole new dazzling functionalities [9, 10].
Superconducting and photonic technologies are envisioned to play a key role in the Quantum Internet. However the hybridization of these technologies requires functional quantum transducers for converting superconducting qubits, exploited in quantum computation, into ``flying'' qubits, able to propagate through the network (and vice-versa). In this paper, quantum transduction is theoretically investigated for a key functionality of the Quantum Internet, namely, multipartite entanglement distribution. Different communication models for quantum transduction are provided, in order to make the entanglement distribution possible. The proposed models departs from the large heterogeneity of hardware solutions available in literature, abstracting from the particulars of the specific solutions with a communication engineering perspective. Then, a performance analysis of the proposed models is conducted through key communication metrics, such as quantum capacity and entanglement generation probability. The analysis reveals that -- although the considered communication metrics depend on transduction hardware parameters for all the proposed models -- the particulars of the considered transduction paradigm play a relevant role in the overall entanglement distribution performance.
Chapter 14 transitions the focus to multipartite entanglement, a realm that broadens the discussion from bipartite systems to those involving multiple parties. This complex form of entanglement plays a crucial role in quantum computing, cryptography, and communication networks. The chapter introduces the foundational concepts of multipartite entanglement, including its characterization and the challenges associated with its classification. Significant attention is given to the classification of multipartite entangled states through SL-invariant polynomials, which provide tools for understanding the structure and properties of these states. Stochastic Local Operations and Classical Communication (SLOCC) are introduced as a means to classify entanglement. Furthermore, the chapter explores the entanglement of assistance and the monogamy of entanglement, two concepts that illustrate the limitations and potential for distributing entanglement among multiple parties. Through detailed explanations and examples in three and four qubits, this chapter offers insights into the intricate world of multipartite entanglement, revealing both its potential and challenges.