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Quantum separable operations are defined as those that cannot produceentanglement from separable states, and it is known that they strictly surpasslocal operations and classical communication (LOCC) in a number of tasks, whichis sometimes referred to as "quantum nonlocality without entanglement." Here weconsider a task with such a gap regarding the trade-off between statediscrimination and preservation of entanglement. We show that this task alongwith the gap has an analogue in a purely classical setup, indicating that thequantum properties are not essential in the existence of a nonzero gap betweenthe separable operations and LOCC.

Does "quantum nonlocality without entanglement" have quantum origin?