Constructions of orthogonal product state sets with genuine hidden nonlocality in bipartite system
Abstract
A set of orthogonal quantum states has genuine hidden nonlocality, if there is an orthogonality preserving local measurement such that the locally distinguishable and locally redundant set become locally indistinguishable under it.If the cardinality of the postmeasurement sets is equal to the cardinality of the original set, then we say the original set has genuine hidden nonlocality of type uppercaseexpandafterromannumeral 1; otherwise, we say it has genuine hidden nonlocality of type uppercaseexpandafterromannumeral 2 In this study, we mainly study the constructions of orthogonal product state sets with genuine hidden nonlocality, and the main results are as follows. We first construct a product set with genuine hidden nonlocality of type uppercaseexpandafterromannumeral 1in mathbbC^d_1⊗mathbbC^d_2d_1geq8, d_2geq10, d_iis even). In addition, we present a type-uppercaseexpandafterromannumeral 2genuine hidden nonlocal set without entanglement in mathbbC^d⊗mathbbC^2ddgeq3). In particular, we found the product state set with genuine hidden nonlocality of type uppercaseexpandafterromannumeral2in mathbbC³⊗ mathbbC^6, which has the smallest local dimension.
