Necessary and Sufficient Condition for the Equivalence of Two Pure Multipartite States under Stochastic Local Incoherent Operations and Classical Communications

TL;DR

This paper establishes a precise criterion for when two pure multipartite quantum states are equivalent under stochastic local incoherent operations and classical communication, advancing the classification of quantum states in coherence resource theory.

Contribution

It provides the first necessary and sufficient condition for state equivalence under SLICC and LICC, including a complete characterization of three-qubit pure states.

Findings

Infinite SLICC inequivalent classes for three-qubit states

Derived necessary and sufficient conditions for state equivalence

Classified states under local incoherent operations

Abstract

Resource theory of quantum coherence originated like entanglement in quantum information theory. However, still now proper classification of quantum states is missing under coherence. In this work, we have provided a classification of states under local incoherent operations. We have succeeded in deriving the necessary and sufficient condition for which two pure multipartite states are equivalent under stochastic local incoherent operations and classical communications (SLICC) and local incoherent operations and classical communications (LICC). In particular, we have succeeded in characterizing three qubit pure states under SLICC. Our result reveals the existence of infinite number of SLICC inequivalent classes for three qubit systems.