Quantum Dimension Witness and Assisted Quantum State Discrimination

The relevance between quantum information processing tasks such as witnessing the dimension of an unknown quantum system and quantum state discrimination is indebted to the statistics obtained from the quantum measurement. A quantum dimension witness (QDW) provides a lower bound on the minimum dimensions that are necessary to describe the quantum correlation originated from the measurements on an unknown quantum system. Such measurement-based quantum correlations (MbQCs) are not only observer dependent but also depend on how strongly an observer perturbs the unobserved system. Based on the aforementioned measurement scenario, we present a quantitative measure that is both the QDW and MbQC measure for arbitrary dimensional bipartite quantum systems. The quantitative measure serves well for bipartite mixed quantum systems and vanishes only for a non-quantum system. We also show that MbQCs are more general than traditional quantum correlations in an optimal assisted quantum state discrimination task.