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arXiv:2602.13545 · Quantum Information Processing

Efficient discrimination schemes for unextendible product bases with strong quantum nonlocality

Qiqi Feng, Huaqi Zhou, Limin Gao

quant-phSubmitted Feb 14, 2026• Announced Feb 17, 2026• 0 citations• Revised Aug 1, 2026 (v2)
v1 · Feb 14, 2026v2 · Aug 1, 2026
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Abstract

Entanglement is a central resource in quantum information science, and it is therefore important to design local discrimination protocols that minimize entanglement cost. In this paper, we propose several entanglement-assisted discrimination schemes for the local discrimination of a representative strongly nonlocal unextendible product basis (UPB) in a \(3\otimes 3\otimes 3\) system. By exploiting the structure of the UPB and the properties of maximally entangled resources, we generalize the protocols to a family of strongly nonlocal UPBs in \(d\otimes d\otimes d\) systems. In particular, we show that these UPBs can be perfectly distinguished using two bipartite maximally entangled states, distributed between different pairs of parties, without employing quantum teleportation. We further compare the total supplied and average consumed entanglement under a clearly specified accounting convention. The results demonstrate that avoiding teleportation can reduce the required entanglement in suitable resource-allocation scenarios and clarify the operational role of low-dimensional maximally entangled resources.

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Entanglement is a central resource in quantum information science, and it is therefore important to design local discrimination protocols that minimize entanglement cost. In this paper, we propose several entanglement-assisted discrimination schemes for the local discrimination of a representative strongly nonlocal unextendible product basis (UPB) in a (3\otimes 3\otimes 3) system. By exploiting the structure of the UPB and the properties of maximally entangled resources, we generalize the protocols to a family of strongly nonlocal UPBs in (d\otimes d\otimes d) systems. In particular, we show that these UPBs can be perfectly distinguished using two bipartite maximally entangled states, distributed between different pairs of parties, without employing quantum teleportation. We further compare the total supplied and average consumed entanglement under a clearly specified accounting convention. The results demonstrate that avoiding teleportation can reduce the required entanglement in suitable resource-allocation scenarios and clarify the operational role of low-dimensional maximally entangled resources.
Any set of states which cannot be perfectly distinguished by local operations and classical communication (LOCC) alone can always be locally distinguished using quantum teleportation with a maximally entangled state as resource. However, in quantum information theory, entanglement is a very valuable resource, so it leaves the following problem: How to accomplish this task more efficiently than teleportation, that is, design the local discrimination protocol using less entanglement. In this paper, we first present two protocols to locally distinguish a particular unextendible product bases (UPB) in $5\ensuremath{\bigotimes}5$ by using different entanglement resource. Then, we generalize the distinguishing methods for a class of UPB in $d\ensuremath{\bigotimes}d$, where ddd is odd and $d\ensuremath{\geqslant}3$. Furthermore, for a class of UPB in $d\ensuremath{\bigotimes}d$, where ddd is even and $d\ensuremath{\geqslant}4$, we prove that these states can also be distinguished by LOCC with multiple copies of low-dimensional entanglement resource. These results offer rather general insight into how to use entanglement resource more efficiently and also reveal the phenomenon of less nonlocality with more entanglement.
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>3n>3n>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 A set of multipartite orthogonal product states is strongly nonlocal if it is locally irreducible in every bipartition, which shows the phenomenon of strong quantum nonlocality without entanglement. It is known that unextendible product bases (UPBs) can show the phenomenon of quantum nonlocality without entanglement. Thus it is interesting to investigate the strong quantum nonlocality for UPBs. Most of the UPBs with the minimum size cannot demonstrate strong quantum nonlocality. In this paper, we construct a series of UPBs with different large sizes in d A ⊗ d B ⊗ d C and d A ⊗ d B ⊗ d C ⊗ d D for d A , d B , d C , d D ⩾ 3, and we also show that these UPBs have strong quantum nonlocality, which answers an open question given by Halder et al (2019 Phys. Rev. Lett. 122 040403) and Yuan et al (2020 Phys. Rev. A 102 042228) for any possible three and four-partite systems. Furthermore, we propose an entanglement-assisted protocol to locally discriminate the UPB in 3 ⊗ 3 ⊗ 4, and it consumes less entanglement resource than the teleportation-based protocol. Our results build the connection between strong quantum nonlocality and UPBs.
It is known that the states in an unextendible product basis (UPB) cannot be distinguished perfectly when the parties are restricted to local operations and classical communication (LOCC). Previous discussions of such bases have left open the following question: What entanglement resources are necessary and/or sufficient for this task to be possible with LOCC? In this paper, I present protocols which use entanglement more efficiently than teleportation to distinguish certain classes of UPB's. The ideas underlying my approach to this problem offer rather general insight into why entanglement is useful for such tasks.
Genuine nonlocality arises when a set of multipartite orthogonal states is locally indistinguishable under any bipartition of the subsystems. The entanglement-assisted discrimination of such genuinely nonlocal orthogonal product sets has attracted significant attention in quantum information. Based on the criterion of local irreducibility, genuine nonlocality is classified into Type I (reducible) and Type II (irreducible). We present entanglement-assisted discrimination schemes for both types of genuinely nonlocal sets that use minimal resources. For low-dimensional cases, Type I sets require only a single EPR pair, whereas Type II sets necessitate only one GHZ state. We extend these protocols to higher-dimensional systems: the discrimination of Type I sets requires only one maximally entangled state in a two-qutrit system, while that of Type II sets similarly demands a single maximally entangled state in a three-qutrit system. For nnn-partite (n>3n > 3n>3) systems, Type I sets continue to require only one maximally entangled state, whereas Type II sets necessitate just one additional EPR pair compared to their Type I counterparts. These results provide a robust framework for the efficient discrimination of genuinely nonlocal sets using minimal quantum resources.
An orthogonal product basis of a composite Hilbert space is genuinely nonlocal if the basis states are locally indistinguishable across every bipartition. From an operational point of view, such a basis corresponds to a separable measurement that cannot be implemented by local operations and classical communication unless all the parties come together in a single location. In this work we classify genuinely nonlocal product bases into different categories. Our classification is based on the state elimination property of the set via orthogonality-preserving measurements when all the parties are spatially separated or different subsets of the parties come together. We then study local state discrimination protocols for several such bases with additional entangled resources shared among the parties. Apart from consuming less entanglement than teleportation-based schemes, our protocols indicate operational significance of the proposed classification and exhibit nontrivial use of genuine entanglement in the local state discrimination problem.