On the irreversibility of measurements of correlations

Abstract

Measurements on a bipartite system AB are classified into ones that are freely implementable with only classical communication between A and B (LOCC measurements), and the others that require consumption of entanglement if they are to be implemented with classical communication. When we notice that measurements on a bipartite system can also be used to create entanglement, we have another natural classification: measurements that are capable of creating entanglement, and the others that have no ability of producing entanglement (separable measurements). Interestingly, there exists a separable measurement that is not an LOCC measurement, namely, a measurement that requires entanglement to implement, but is not capable of creating entanglement at all. Such an example was found for a pair of three-level systems, in conjunction with a discrimination task of an intricate set of eight or nine states. Here we show an example of such a measurement on a pair of two-level systems (qubits), which arises in a discrimination task of just two states that look quite simple and have little intricacy. Such an example suggests that this kind of irreversibility is not only shown by a limited set of cleverly constructed measurements, but is also exhibited by a much larger class of measurements than we had expected.