The paper explores the concept of quantum nonlocality in systems composed of two or three particles, where the states are orthogonal but cannot be reliably distinguished by separated observers, even with the help of classical communication. The authors present a set of nine orthogonal product states of two three-state particles that can be reliably distinguished by a joint measurement but not by any sequence of local measurements. This demonstrates a form of nonlocality that is stronger than that exhibited by entangled states, which can be described using Bell-type inequalities. The paper also discusses the implications of these findings for entanglement purification protocols and the thermodynamics of local state measurement. The authors prove that some separable superoperators cannot be implemented by bilocal operations, indicating that further investigations into entanglement purification protocols involving separable superoperators require caution. The paper provides a detailed analysis of the measurement process and derives an upper bound on the mutual information attainable by local operations, showing that it is less than the mutual information obtainable in a fully nonlocal measurement.The paper explores the concept of quantum nonlocality in systems composed of two or three particles, where the states are orthogonal but cannot be reliably distinguished by separated observers, even with the help of classical communication. The authors present a set of nine orthogonal product states of two three-state particles that can be reliably distinguished by a joint measurement but not by any sequence of local measurements. This demonstrates a form of nonlocality that is stronger than that exhibited by entangled states, which can be described using Bell-type inequalities. The paper also discusses the implications of these findings for entanglement purification protocols and the thermodynamics of local state measurement. The authors prove that some separable superoperators cannot be implemented by bilocal operations, indicating that further investigations into entanglement purification protocols involving separable superoperators require caution. The paper provides a detailed analysis of the measurement process and derives an upper bound on the mutual information attainable by local operations, showing that it is less than the mutual information obtainable in a fully nonlocal measurement.