Deterministic distribution of W-class states in quantum networks

TL;DR

The paper addresses deterministic distribution of non-symmetric W-class states, specifically |W_{ m mod}⟩ with one ebit across a bipartition, in quantum networks using a central-node architecture. It develops three distribution protocols—direct transmission, teleportation-based entanglement swapping, and multipartite joint-measurement—and analyzes their performance under isotropic depolarizing noise by computing fidelities and entanglement measures (two-tangles and their average). Key results show that |W_{ m mod}⟩ outperforms standard W and GHZ states in fidelity under noise, enables deterministic teleportation and dense coding, and exhibits robust multipartite entanglement across multiple network scenarios; the work also explores how varying state coefficients m += affects robustness and fidelity, revealing saturation effects for large m. The findings provide practical guidance for designing scalable quantum networks that leverage W_{ m mod} resources for deterministic quantum communication and computation, while highlighting avenues for error mitigation such as distillation and error correction.

Abstract

Multipartite entangled states possess a number of non-intuitive properties, making them a useful resource for various quantum information-processing tasks. The three-qubit W-state is one such example where every state is robust to single-qubit loss. However, this state is not suitable for deterministic distribution, and deterministic communication protocols. Here, we focus on the distribution of a non-symmetric version of such states, namely $W_{\mathrm{mod}}$ states. These states belong to the W-class, and have one ebit of entanglement across a specific bipartition, enabling deterministic teleportation and superdense coding. In particular, we describe a few protocols through which these multipartite entangled states can be distributed {\it deterministically} in a quantum network by first preparing them locally in a central node and then transmitting individual qubits to the end nodes. We analyse the performance of these protocols based on the fidelity of the final distributed state, considering all types of noises that can act during the distribution. Finally, we compare the performance of the protocols to the case where the distribution is performed without any central node.

Figures (12)

• Figure 1: Schematic diagram showing direct distribution of a $W_{\mathrm{mod}}$ state. The central node has no memory. It locally prepares the target state and then sends each qubit through direct transmission to the end nodes.
• Figure 2: Distribution of a $W_{\mathrm{mod}}$ state using a central node and a chain of repeaters. The central node first locally prepares the target state. Then Bell states are shared starting from the central node to the end node, where qubit 3 will be sent. The central first directly sends two qubits to two end nodes. Later through consecutive Bell measurements at the central and each repeater nodes, qubit 3 is sent to the end node, and the final target state is shared between the end nodes.
• Figure 3: A $W_{\mathrm{mod}}$ state can be distributed between two central nodes using an intermediate node in between them. The two central nodes first locally prepare two $W_{\mathrm{mod}}$ states. Then one of the central nodes sends two qubits and another one sends one qubit of their respective $W_{\text{mod}}$ states to the intermediate node. A joint three-qubit measurement is performed at the intermediate node and the target state is distributed between the central nodes.
• Figure 4: Variation of a) fidelity difference b) percentage fidelity difference with respect to noise parameter $p$. The red, green, and blue lines represent the fidelity difference between $W_{\text{mod}}$ and $GHZ$, $W$ and $GHZ$, and $W_{\text{mod}}$ and $W$ states, respectively.
• Figure 5: Decay of global entanglement of distributed $W_{\mathrm{mod}}$ state when the qubits are sent directly to the end nodes from the central node. The vertical dotted blue and red lines enclose the regions in which tangle between qubits 1 and 2 and tangle between qubits 3 and other two are non-zero, respectively. The white and gray regions represent non-zero and zero global entanglement, respectively.

Theorems & Definitions (2)

• proof
• proof