Quantum Internet Addressing

• Quantum internet addressing is a method that defines node identities as quantum states, enabling coherent superposition and entanglement-driven routing.
• It integrates quantum registers and controlled operations to combine routing, resource management, and dynamic topological links in a unified framework.
• Protocols employ entanglement swapping and superposed state resolution to overcome classical limitations and ensure scalable, robust quantum network connectivity.

Quantum addressing is a foundational paradigm for the Quantum Internet, superseding classical address schemes with identifiers that exploit quantum coherence, entanglement, and superposition. In quantum-native architectures, node addresses become quantum states (not bit strings), thereby embedding routing, resource allocation, and identity directly into the quantum fabric of the network. This approach is fundamentally necessitated by the stateful and non-local properties of entangled resources, and it enables functionalities such as superposed routing, programmable multicast, and compact routing state unattainable in classical networks (Cacciapuoti et al., 2023, Miguel-Ramiro et al., 2020, Caleffi et al., 25 Jul 2025).

1. Conceptual Foundations of Quantum Addressing

Quantum Internet addressing departs from static, location-bound digital labels. Instead, an address is a quantum state (often a multi-qubit register) that encodes a node’s identity in the computational basis and admits coherent superposition across network elements. The quantum-native address:

• Can point to multiple nodes simultaneously ($$|\psi_{\mathrm{addr}}\rangle = \sum_i \alpha_i |i\rangle$$).
• Supports entanglement with infrastructure or other addresses (GHZ or W states).
• Obeys quantum constraints such as the no-cloning theorem, mandating unique distribution and resolution via quantum operations (Cacciapuoti et al., 2023, Caleffi et al., 25 Jul 2025).

Coherent addressing directly intertwines topology with quantum phenomena. Identity, connectivity, and routing are expressed by the amplitudes and entanglement structure of the address register, supplanting hierarchical clustering with “topological augmentation” through dynamic overlay links (Cacciapuoti et al., 2023).

2. Mathematical Formalism and Network Models

Quantum addressing utilizes Hilbert space basis states to represent network nodes. For $n$ nodes, an $N = \lceil \log_2 n \rceil$-qubit register yields $|x\rangle$ where $x \in \{0,1\}^N$ is assigned to a node. Individual node addresses are orthogonal basis states, but the register can encode superposed group addresses:

• Uniform superposition over subset $S$: $$|A_S\rangle = \frac{1}{\sqrt{|S|}} \sum_{v\in S}|v\rangle$$.
• Multipartite overlays: GHZ and W states for robust entanglement across clusters.

Quantum control registers (e.g., GHZ-prepared qudits) are leveraged to specify routing tasks and destinations in coherent superposition (Miguel-Ramiro et al., 2020). For multicast, the control register weights branches that deliver quantum data to $m$ recipients: $$|\psi_R\rangle_c = \sum_{k=0}^{m-1}\alpha_k|k\rangle_c^{\otimes n}$$.

Resource assignment and address resolution are governed by quantum channels (address generation), entanglement swapping operators (neighborhood reconfiguration), and projective or POVM measurements (resolution) (Cacciapuoti et al., 2023). Unitary dilation constructs, such as controlled-SWAP chains, mediate the transfer of quantum data in accordance with the control register (Miguel-Ramiro et al., 2020).

3. Protocol Operations and Routing Integration

Quantum addressing is positioned as an intermediate layer—above the physical/link layer and beneath quantum network/routing layers. Key operations include:

• Generation: Preparation and distribution of addressable quantum states or entangled resources (EPR, GHZ, W).
• Distribution: Teleportation or transmission of qubits to network nodes, usually paired with purification stages for fidelity control.
• Resolution: Conditional measurement or entanglement swapping to “select” or collapse the superposed address to a single node or set of nodes.
• Routing: Quantum packets can traverse multiple network paths in superposition by implementing controlled SWAPs and quantum switches, while classical side channels disseminate measurement outcomes for error correction and synchronization (Cacciapuoti et al., 2023, Miguel-Ramiro et al., 2020).

In quantum-native hierarchical architectures, Entanglement Service Providers (ESPs) and an Entanglement-Defined Controller (EDC) oversee overlay topology, resource management, and quantum routing rule installation. The ESP maintains entanglement with a limited e-neighborhood and an anchor set, supporting compact routing tables of size $\tilde{O}(\sqrt{n_e})$ (Caleffi et al., 25 Jul 2025).

4. Address Lookup, Table Structure, and Quantum Oracles

Routing with quantum addresses requires matching quantum destination states against stored superpositions without measurement-induced collapse. The quantum address splitting operation, realized via Schrödinger’s oracle:

• Embeds table entry labels in a superposed quantum register.
• Applies controlled oracles to detect if the destination state $|d\rangle$ matches any basis component of stored superpositions $|A_j^\ell\rangle$.
• Grover-style amplitude amplification isolates relevant entries, with a final measurement yielding a valid match (Caleffi et al., 25 Jul 2025).

Each ESP stores:

• Basis addresses $|v_j\rangle$ for e-neighbors.
• Superposed addresses $|A_j\rangle$ for anchor/tracked sets.
• Reverse-neighborhood entries as required for routing table completeness.

Route selection algorithms process quantum packets with destination $|d\rangle$ via direct match, superposition-based lookup, or multi-hop anchor relaying, yielding entangling stretch factors ES that are constant (≤3 or 5) and routing state that scales sublinearly (Caleffi et al., 25 Jul 2025).

5. Superposed Addressing and Genuine Quantum Networks

Protocols supporting superposed addressing extend network functionality:

• Quantum-parallel delivery: A single invocation of the channel distributes quantum information to multiple recipients in superposition (Miguel-Ramiro et al., 2020).
• Robustness via superposed entanglement: Superpositions of GHZ states maintain entanglement under node losses more effectively than mixtures or individual GHZ states.
• Programmable multicast and secret sharing: Using superposed addressing, a data qubit can be multicast or encoded into multipartite codewords across the network.
• Superposed path selection: Controlled measurement sequences realize quantum routes that remain indeterminate until deferred measurement (Miguel-Ramiro et al., 2020).

Dummy registers are essential for protocol validity—ensuring each non-recipient branch leaves identical marginals to preclude which-path information leakage.

6. Implementation Challenges and Open Research Directions

Major practical limitations include decoherence management, synchronization of multipartite entanglement, quantum memory constraints, and fast, fidelity-preserving address update mechanisms. Hardware requirements encompass controlled-SWAP gates, high-fidelity entanglement sources, quantum memories, and robust classical control infrastructure (Cacciapuoti et al., 2023, Miguel-Ramiro et al., 2020).

Open questions involve:

• Optimal hierarchy and clustering of entangled resources (EPR vs. GHZ vs. W per layer).
• Quantum algorithmic design for distributed routing (Grover search over entanglement overlays).
• Simulation of large-scale quantum networks under realistic resource contention and error correction.
• Integration of classical resolution methods with quantum address management without meta-information leakage (Cacciapuoti et al., 2023).

Quantum-native addressing enables universal, programmable, and robust Quantum Internet functionalities, tightly coupling node identity, topology and routing through the quantum state space. These architectures demonstrate compact scalability and offer unique operations—such as quantum address splitting and superposed path routing—that have no classical analogues (Caleffi et al., 25 Jul 2025, Cacciapuoti et al., 2023, Miguel-Ramiro et al., 2020).