Reduction-induced the Variation of Partial Von Neumann Entropy

Abstract: The organization and structure of bipartite mixed-state quantum entanglement (QE) is more complicated and less well understood than that of bipartite pure-state QE. Bipartite mixed-state QEs and their measures play a crucial role in both theory and practical applications. Existing measures comprise two classes: one class involves quantifying the minimum QE and reflect the inherently complex nature of their computation, while the other is only applicable to highly limited-dimensional quantum systems. In this context, we propose a method termed Reduction-induced Variation of Partial Von Neumann Entropy (RIVPVNE) to quantify QE in any bipartite states especially for any bipartite mixed-states, which is essentially an extension of Partial Von Neumann Entropy for measuring QE from bipartite pure states to any bipartite states. This method exhibits minimal computational complexity and broad applicability. Its intuitive and clear physical representation, combined with easy computation and wide applicability, facilitates exploring its potential applications. Furthermore, we present examples to demonstrate the superiorities of this method in identifying bipartite QE by comparing with other existing bipartite mixed-state QE measures through both their physical implications and mathematical structures.