Lu Wei, Zhian Jia, Dagomir Kaszlikowski, Sheng Tan
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Antilinear superoperator, quantum geometric invariance, and antilinear symmetry for higher-dimensional quantum systems
We present a systematic investigation of antilinear superoperators and their applications in studying open quantum systems, particularly focusing on quantum geometric invariance, entanglement distribution, and symmetry. We study several classes of antilinear superoperators, including antilinear quantum channels, antilinearly unital superoperators, antiunitary superoperators, and generalized \(\Theta \)-conjugation. Using the Bloch representation, we present a systematic investigation of quantum geometric transformations in higher-dimensional quantum systems. By choosing different generalized \(\Theta \)-conjugations, we obtain various metrics for the space of Bloch space-time vectors, including the Euclidean and Minkowskian metrics. Utilizing these geometric structures, we then investigate the entanglement distribution over a multipartite system constrained by quantum geometric invariance. The strong and weak antilinear superoperator symmetries of the open quantum system are also discussed. Additionally, Kramers’ degeneracy and conserved quantities are examined in detail.
期刊介绍:
Quantum Information Processing is a high-impact, international journal publishing cutting-edge experimental and theoretical research in all areas of Quantum Information Science. Topics of interest include quantum cryptography and communications, entanglement and discord, quantum algorithms, quantum error correction and fault tolerance, quantum computer science, quantum imaging and sensing, and experimental platforms for quantum information. Quantum Information Processing supports and inspires research by providing a comprehensive peer review process, and broadcasting high quality results in a range of formats. These include original papers, letters, broadly focused perspectives, comprehensive review articles, book reviews, and special topical issues. The journal is particularly interested in papers detailing and demonstrating quantum information protocols for cryptography, communications, computation, and sensing.