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• W4386498372 abstract "An orthogonal set of states in multipartite systems is called to be strong quantum nonlocality if it is locally irreducible under every bipartition of the subsystems cite{Halder19}. In this work, we study a subclass of locally irreducible sets: the only possible orthogonality preserving measurement on each subsystems are trivial measurements. We call the set with this property is locally stable. We find that in the case of two qubits systems locally stable sets are coincide with locally indistinguishable sets. Then we present a characterization of locally stable sets via the dimensions of some states depended spaces. Moreover, we construct two orthogonal sets in general multipartite quantum systems which are locally stable under every bipartition of the subsystems. As a consequence, we obtain a lower bound and an upper bound on the size of the smallest set which is locally stable for each bipartition of the subsystems. Our results provide a complete answer to an open question (that is, can we show strong quantum nonlocality in <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msup><mml:mrow class=MJX-TeXAtom-ORD><mml:mi mathvariant=double-struck>C</mml:mi></mml:mrow><mml:mrow class=MJX-TeXAtom-ORD><mml:msub><mml:mi>d</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:msup><mml:mo>&#x2297;</mml:mo><mml:msup><mml:mrow class=MJX-TeXAtom-ORD><mml:mi mathvariant=double-struck>C</mml:mi></mml:mrow><mml:mrow class=MJX-TeXAtom-ORD><mml:msub><mml:mi>d</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:msup><mml:mo>&#x2297;</mml:mo><mml:mo>&#x22EF;</mml:mo><mml:mo>&#x2297;</mml:mo><mml:msup><mml:mrow class=MJX-TeXAtom-ORD><mml:mi mathvariant=double-struck>C</mml:mi></mml:mrow><mml:mrow class=MJX-TeXAtom-ORD><mml:msub><mml:mi>d</mml:mi><mml:mi>N</mml:mi></mml:msub></mml:mrow></mml:msup></mml:math> for any <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mi>d</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>&#x2265;</mml:mo><mml:mn>2</mml:mn></mml:math> and <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mn>1</mml:mn><mml:mo>&#x2264;</mml:mo><mml:mi>i</mml:mi><mml:mo>&#x2264;</mml:mo><mml:mi>N</mml:mi></mml:math>?) raised in a recent paper cite{Shi22N}. Compared with all previous relevant proofs, our proof here is quite concise." @default.
• W4386498372 created "2023-09-07" @default.
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• W4386498372 date "2023-09-07" @default.
• W4386498372 modified "2023-10-16" @default.
• W4386498372 title "Bounds on the smallest sets of quantum states with special quantum nonlocality" @default.
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• W4386498372 doi "https://doi.org/10.22331/q-2023-09-07-1101" @default.
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