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arXiv:2602.15452

Nonlocality without entanglement in exclusion of quantum states

Satyaki Manna, Anandamay Das Bhowmik

quant-phSubmitted Feb 17, 2026• Announced Feb 18, 2026• 0 citations
v1 · Feb 17, 2026v2 · Jul 21, 2026
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Abstract

We study the task of quantum state exclusion, focusing on antidistinguishability and its generalization to $x$-antidistinguishability, under global measurements and local operations with classical communication (LOCC). We also introduce weak and strong notions of antidistinguiahbaility ($x$-antidistinguishability) depending on whether all states or all $x$-tuples are exhaustively eliminated. Our results reveal striking differences between state exclusion and the more familiar task of state discrimination. In particular, we show that LOCC antidistinguishability of multipartite product states is symmetric with respect to the initiating party but this symmetry breaks down for higher-order $x$-antidistinguishability. Most notably, we establish a manifestation of \emph{nonlocality without entanglement} in the context of state exclusion: we prove that three bipartite product states can be globally antidistinguishable while failing to be LOCC antidistinguishable, demonstrating that three is the minimal number of states required for this phenomenon. We further extend this separation to $2$-antidistinguishability and present example exhibiting the same type of nonlocality. At last, we provide an antidistinguishable tripartite product states that are not LOCC antidistinguishable across any bipartition, which ensures the phenomenon of \emph{genuine nonlocality without entanglement} in this framework.

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We study the task of quantum state exclusion, focusing on antidistinguishability and its generalization to xxx-antidistinguishability, under global measurements and local operations with classical communication (LOCC). We also introduce weak and strong notions of antidistinguiahbaility (xxx-antidistinguishability) depending on whether all states or all xxx-tuples are exhaustively eliminated. Our results reveal striking differences between state exclusion and the more familiar task of state discrimination. In particular, we show that LOCC antidistinguishability of multipartite product states is symmetric with respect to the initiating party but this symmetry breaks down for higher-order xxx-antidistinguishability. Most notably, we establish a manifestation of \emph{nonlocality without entanglement} in the context of state exclusion: we prove that three bipartite product states can be globally antidistinguishable while failing to be LOCC antidistinguishable, demonstrating that three is the minimal number of states required for this phenomenon. We further extend this separation to 222-antidistinguishability and present example exhibiting the same type of nonlocality. At last, we provide an antidistinguishable tripartite product states that are not LOCC antidistinguishable across any bipartition, which ensures the phenomenon of \emph{genuine nonlocality without entanglement} in this framework.
A set of quantum states is said to be antidistinguishable if, upon being given a randomly chosen state from the set, it is possible to exclude with certainty a state that was definitely not prepared. We study quantum nonlocality within the framework of local state exclusion and prove that any set of multipartite pure states containing a state that is orthogonal to all the others is locally antidistinguishable. Next, we introduce the task of local state antimarking\textit{local state antimarking}local state antimarking, where, instead of a single state, a non-repetitive sequence of states from a known set of multipartite states is randomly selected and distributed to spatially separated parties, whose objective is to identify, using LOCC, at least one sequence that was not supplied. We present an ensemble of product states that is not globally antidistinguishable; yet, by choosing states from it without replacement, one can construct sequences that can be perfectly excluded globally but, importantly, not locally. This reveals a hitherto unexplored form of `nonlocality without entanglement'. Finally, for a given ensemble, we compare its local antidistinguishability and antimarkability with its conclusive local distinguishability and markability. We demonstrate that no strict hierarchy exists between these paradigms: there exist product-state ensembles that permit one task while strictly forbidding the other, and vice versa.
We show that a pair of two-qubit product measurements can be perfectly distinguished when accessed jointly, yet cannot be perfectly distinguished when their local components are distributed between distant parties restricted to local quantum operations and classical communication (LOCC). This establishes a measurement analogue of nonlocality without entanglement that, unlike its state-based counterpart, emerges in a remarkably simple setting. We further uncover a hierarchy of LOCC discrimination strategies: adaptive protocols, in which the probe used at one site may depend on classical information obtained from another, can strictly outperform restricted non-adaptive protocols, as demonstrated by a set of six bipartite qutrit product measurements. We also show that LOCC distinguishability of bipartite measurements can be intrinsically directional, depending on which party initiates the protocol. More generally, we construct pairs of nnn-qubit product measurements that are globally perfectly distinguishable but cannot be perfectly distinguished across any bipartition, even when all parties on either side of the bipartition are allowed arbitrary joint quantum operations. Finally, we show how quantum data hiding based on quantum-process nonlocality without entanglement can be realized using elementary optical components.
An ensemble of product states is said to exhibit “quantum nonlocality without entanglement” if it cannot be optimally discriminated using local operations and classical communication (LOCC). We show that this property can depend on the chosen discrimination measure. Specifically, we construct a family of ensembles, each consisting of six linearly independent, equally probable bipartite product states, for which LOCC fails to achieve optimal minimum-error discrimination but succeeds in achieving optimal unambiguous discrimination. We further extend our construction to multipartite systems and provide strong numerical evidence that a similar separation between local and global optima is present for minimum-error discrimination, but not for unambiguous discrimination.
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.
Recently, based on some quantum states which are locally irreducible in all bipartitions, strong quantum nonlocality has been presented by Halder et al. [Phys. Rev. Lett. 122, 040403 (2019)]. However, the remaining questions are whether a set of quantum states can reveal strong quantum nonlocality when these states are locally irreducible in all tripartitions or more multipartitions and how to construct strong nonlocality of orthogonal product states in more than tripartite quantum systems. Here we present a general definition of strong quantum nonlocality based on the local irreducibility. Then, using a $3\ensuremath{\bigotimes}3\ensuremath{\bigotimes}3$ quantum system as an example, we show three sets of locally indistinguishable orthogonal product states to explain the general definition of strong quantum nonlocality. Furthermore, in $3\ensuremath{\bigotimes}3\ensuremath{\bigotimes}3\ensuremath{\bigotimes}3$, we construct a set of strong nonlocality of orthogonal product states; these states do not form a complete basis. Our results demonstrate the phenomenon of strong nonlocality without entanglement for the multipartite quantum systems.
A set of orthogonal product states is said to exhibit "quantum nonlocality without entanglement" if it is locally indistinguishable, i.e. no sequence of local operations and classical communication (LOCC) can perfectly discriminate the states. Building on this foundational idea, recent studies have highlighted the phenomenon of "genuine activation of hidden nonlocality", where a set of initially distinguishable orthogonal states becomes locally indistinguishable through orthogonality-preserving LOCC transformations. In this letter, we establish that any complete orthogonal product basis that is initially locally distinguishable remains so under all orthogonality-preserving local projective measurements, thereby ruling out activation via orthogonality-preserving local projective measurements and classical communication. We further introduce and formalise the notions of "strongly local sets", namely locally distinguishable sets that remain non-activable under all bipartitions. Interestingly, the study of "local activability" of distinguishable sets is useful to characterise the boundary between LOCC distinguishability and its irreversible loss in multipartite systems. Our results provide a rigorous structural understanding of local-to-nonlocal transitions in quantum state discrimination.