Entanglement-assisted discrimination of orthogonal quantum states exhibiting quantum nonlocality is a frontier topic in quantum information theory. In this paper, we investigate the role of multipartite entanglement and develop resource-efficient LOCC discrimination protocols for nonlocal sets of orthogonal states, including multipartite orthogonal product-state sets and entangled-state sets with different nonlocal features. By incorporating controlled-NOT (CNOT) operations into the discrimination procedure, we construct protocols for genuinely nonlocal GHZ bases in four- and five-qubit systems that require only a single EPR pair. For the same target sets, we compare different entanglement-assisted schemes and identify those with lower entanglement consumption. We further observe that, on average, protocols avoiding teleportation consume fewer resources than teleportation-based approaches. In addition, when higher-partite GHZ-type resources (with
n>3) are available among suitable subsystems, they can in some cases reduce the overall entanglement cost. Our results highlight the operational significance of multipartite entanglement and provide practical protocols for the local discrimination of orthogonal state sets exhibiting quantum nonlocality.
Abstract We explore entanglement as a resource to distinguish locally indistinguishable orthogonal quantum states. Specifically, we consider sets which contain states from an unextendible product basis along with a pure entangled state. We establish a connection between the aforesaid problem and the entanglement-assisted discrimination of a certain class of many-copy indistinguishable sets. The entanglement-assisted protocols that we construct here are quite efficient, as they render the teleportation-based protocols sub-optimal. In fact, a central aspect of our study is to explore the role of Schmidt rank as a resource to distinguish the states of locally indistinguishable sets. Interestingly, we identify an instance where a set of locally indistinguishable orthogonal states remains locally indistinguishable even with access to any finite number of copies, yet becomes perfectly distinguishable using entangled resources of relatively low cost. This fact makes it possible to compare the degrees of local indistinguishability associated with several locally indistinguishable sets within the same Hilbert space. Consequently, we report a hierarchy of local indistinguishability among the many-copy indistinguishable sets. Thereafter, based on our analysis, we present a theoretical proposal for an information processing protocol exhibiting secure locking of information and its resource-efficient extraction. Furthermore, we also find that the hierarchical difference in local indistinguishability can increase with increasing dimension of the Hilbert space.
One-way local operations and classical communication (LOCC) can fail to distinguish four orthogonal maximally entangled states in every local dimension
d≥4. We show that every set of
k pairwise orthogonal maximally entangled states in
Cd⊗Cd is perfectly distinguishable by an
A→B→A protocol whenever
d≥Ck4[log(2k)]ν, for universal constants
C,ν>0. A single feedback message therefore raises the number of candidates that can always be distinguished from a constant to
Ω(d1/4/(logd)ν/4), establishing a polynomial separation between one-way and two-way LOCC. In our protocol, Alice preserves exact orthogonality while reducing overlaps between Bob's conditional subspaces. Bob reduces the candidates to a singleton or an orthogonal pair and refines his outcome so that Alice can complete the discrimination. As a corollary, nine copies suffice for perfect two-way LOCC discrimination of any orthogonal maximally entangled set in all sufficiently large local dimensions.