2025/06/30 by Amish Gogia, Gogia, Amish, Satyabrata Adhikari +4
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2506.23727
openalex publication_date 2025/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Computable Cross Norm (CCN), or realignment criterion, is a widely used method for entanglement detection in quantum systems; however, it typically provides only a necessary condition. In this work, we advance the applicability of the realignment criterion by deriving a condition that is both necessary and sufficient for detecting entanglement in two-qubit. X-states derive their name from the characteristic 'X' shape of their density matrix, which contains seven independent matrix parameters. Notably, they incorporate several important subclasses of entangled states, including Bell states, Werner states, and maximally entangled mixed states. X-states have proven highly useful in entanglement studies due to their sparse structure and the ease with which entanglement-related quantities can be computed. This refined criterion improves the identification of entangled states that the standard CCN approach fails to detect, thereby extending the utility of the method.