Dr Ramadas N, Post-Doctoral Fellow, Physics, Division of Sciences, SIAS, published a research paper titled Minimal decomposition entropy and optimal representations of absolutely maximally entangled states in Physical Review A.
Abstract
Understanding and classifying multipartite entanglement is fundamental to quantum information processing. This work focuses on absolutely maximally entangled (AME) states, a class of highly entangled states characterized by their maximal entanglement across any bipartitions. To analyze and classify AME states, we employ the minimal decomposition entropy, defined as the minimum R\'{e}nyi entropy $S_q$ associated with the state’s decomposition over all local product bases. This quantity identifies the product bases in which the state is maximally localized, thereby yielding optimal representations for analyzing properties of AME states.
The team develops an efficient algorithm for computing the minimal decomposition entropy for finite $q>1$ and compare AME and Haar-random states for ( q = 2 ) and ( q = \infty ) in qubit, qutrit, and ququad systems. For ( q = 2 ), AME states of four qutrits and ququads show lower minimal entropy than generic states, indicating sparser optimal forms. For ( q = \infty ) – related to the geometric measure ofentanglement – AME states exhibit higher entanglement. The algorithm also simplifies known AME states into sparser representations, aiding in distinguishing genuinely quantum AME states from those constructible from classical combinatorial designs. The results advance the classification of AME states and demonstrate the utility of minimal decomposition entropy as both a local unitary invariant and a tool for state simplification.