In the quantum state discrimination game, there exist phenomena suggesting a complex, and as yet not well-explored, relation of the resource of entanglement in sets of quantum states with their local distinguishability, and in this work, we take a step towards filling this gap within the minimum-error quantum state discrimination protocol. We derive upper and lower bounds on the optimal discrimination probability of $k$-inseparable or $n$-entangled quantum states in an arbitrary multipartite ensemble in terms of the robustness of entanglement and the optimal discrimination probability of the corresponding closest $k$-separable or $n$-unentangled states. Our bounds hold regardless of the dimension of the constituent systems, the number of parties involved, the size of the ensemble, and whether the measurement strategies are local or global. Additionally, we determine further lower bounds on the difference between the success probability of discriminating $k$-inseparable (or $n$-entangled) states and that of discriminating the corresponding $k$-separable or $n$-unentangled states by analyzing two special cases of two-state multiparty ensembles: one where both states have equal entanglement and another where one state is $k$-separable or $n$-unentangled. The case of equal entanglement reveals that it is always easier to discriminate between entangled states than those in the corresponding closest separable ensemble, a phenomenon we refer to as “more indistinguishability with less entanglement.” The second case, however, does not assure the same. Further, for two-element ensembles, where the state with lesser entanglement is also more probable, we find that this entanglement must exceed a certain threshold for the ensemble to exhibit “more indistinguishability with less entanglement.”

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• Entanglement measures
• Quantum communication, protocols & technology
• Quantum entanglement