Local state antimarking : Nonlocality without entanglement
Abstract
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, 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.
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BibTeX
@misc{chatterjee2026local,
title = {{Local state antimarking : Nonlocality without entanglement}},
author = {Biswadeep Chatterjee and Tathagata Gupta and Pratik Ghosal and Samrat Sen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.09710},
eprint = {2605.09710},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.09710},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Local state antimarking : Nonlocality without entanglement
AU - Biswadeep Chatterjee
AU - Tathagata Gupta
AU - Pratik Ghosal
AU - Samrat Sen
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2605.09710
UR - https://arxiv.org/abs/2605.09710
AB - 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, 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.
ER -