Multicopy Adaptive Local Discrimination: Strongest Possible Two-Qubit Nonlocal Bases.

Ensembles of composite quantum states can exhibit nonlocal behavior in the sense that their optimal discrimination may require global operations. Such an ensemble containing N pairwise orthogonal pure states, however, can always be perfectly distinguished under an adaptive local scheme if (N-1) copies of the state are available. In this Letter, we provide examples of orthonormal bases in two-qubit Hilbert space whose adaptive discrimination require three copies of the state. For this composite system, we analyze multicopy adaptive local distinguishability of orthogonal ensembles in full generality which, in turn, assigns varying nonlocal strength to different such ensembles. We also come up with ensembles whose discrimination under an adaptive separable scheme require less numbers of copies than adaptive local schemes. Our construction finds important application in multipartite secret sharing tasks and indicates toward an intriguing superadditivity phenomenon for locally accessible information.

Strong Quantum Nonlocality without Entanglement.

Quantum nonlocality is usually associated with entangled states by their violations of Bell-type inequalities. However, even unentangled systems, whose parts may have been prepared separately, can show nonlocal properties. In particular, a set of product states is said to exhibit "quantum nonlocality without entanglement" if the states are locally indistinguishable; i.e., it is not possible to optimally distinguish the states by any sequence of local operations and classical communication. Here, we present a stronger manifestation of this kind of nonlocality in multiparty systems through the notion of local irreducibility. A set of multiparty orthogonal quantum states is defined to be locally irreducible if it is not possible to locally eliminate one or more states from the set while preserving orthogonality of the postmeasurement states. Such a set, by definition, is locally indistinguishable, but we show that the converse does not always hold. We provide the first examples of orthogonal product bases on C^{d}⊗C^{d}⊗C^{d} for d=3, 4 that are locally irreducible in all bipartitions, where the construction for d=3 achieves the minimum dimension necessary for such product states to exist. The existence of such product bases implies that local implementation of a multiparty separable measurement may require entangled resources across all bipartitions.