Comparing the three W-like states with the W state

The study investigates the properties of three specific W-like quantum states—denoted as |θ'⟩, |η'⟩, and |ξ'⟩—and compares them to the standard W state. While the W state is a well-known resource in quantum information, its utility in certain communication protocols is limited. The author seeks to determine if these W-like variants offer superior performance in entanglement measures and quantum communication tasks.

The author employs four primary entanglement measures to evaluate the states: the 2-tangle (τxy), the negativity, von Neumann entanglement entropy (vNEE), and the tangle (τx(yz)). By calculating these values for the three W-like states and the standard W state, the study identifies specific properties—such as maximal vNEE and tangle—that distinguish the W-like states. The author also tests the suitability of these states for perfect teleportation and superdense coding protocols.

The analysis reveals that the W-like states |θ'⟩, |η'⟩, and |ξ'⟩ possess higher robustness against particle loss compared to the W state. Specifically, when one qubit is traced out, the remaining two-qubit systems in these W-like states exhibit higher entanglement than the corresponding two-qubit systems derived from the W state. Furthermore, the study demonstrates that these three W-like states can be used for perfect teleportation and superdense coding, tasks for which the standard W state is insufficient.

This research expands the catalog of useful quantum states for communication protocols. By identifying states that outperform the standard W state in robustness and protocol efficiency, the paper provides researchers with more versatile resources for quantum information processing, particularly in scenarios where particle loss is a concern.