<p>A set of orthogonal quantum states is said to be locally indistinguishable if it cannot be perfectly distinguished by local operations and classical communication (LOCC); otherwise, it is locally distinguishable. Motivated by the idea of converting information from a locally accessible to a locally hidden form, the activation of hidden nonlocality studies how a locally distinguishable set may be deterministically transformed into a locally indistinguishable one. In this work, we investigate such activations in multipartite and high-dimensional quantum systems. We explicitly construct locally distinguishable sets-in bipartite, tripartite, and multipartite scenarios-that can be converted into locally indistinguishable sets. For bipartite systems, we show that hidden nonlocality can be activated through suitable local measurements. In tripartite systems, we classify activatable sets into two distinct categories. Furthermore, in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\mathbb {C}^{2m+1}\otimes \mathbb {C}^n\otimes \mathbb {C}^{2m+1}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mrow> <mn>2</mn> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> <mo>⊗</mo> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mi>n</mi> </msup> <mo>⊗</mo> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mrow> <mn>2</mn> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation> systems, we present a class of locally distinguishable sets whose nonlocality cannot be revealed by any local operation alone; instead, joint measurements between two parties are required. By contrast, we also construct locally distinguishable sets in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\mathbb {C}^{2m+1}\otimes \mathbb {C}^{2n}\otimes \mathbb {C}^{2m+1}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mrow> <mn>2</mn> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> <mo>⊗</mo> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mrow> <mn>2</mn> <mi>n</mi> </mrow> </msup> <mo>⊗</mo> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mrow> <mn>2</mn> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation> systems in which only one party’s operation is sufficient to hide information, and we generalize this construction to multipartite systems of the form <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\mathbb {C}^{2m+1}\otimes (\mathbb {C}^{2n})^{(n-2)}\otimes \mathbb {C}^{2m+1}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mrow> <mn>2</mn> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> <mo>⊗</mo> <msup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mrow> <mn>2</mn> <mi>n</mi> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo>-</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msup> <mo>⊗</mo> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mrow> <mn>2</mn> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>. Compared with the former class, the latter can be regarded as possessing a higher degree of nonlocality. Our results establish a hierarchy among locally distinguishable sets based on their activation properties and are promising for information hiding protocols.</p>

Genuine Activation of Hidden Nonlocality in Multipartite Quantum Systems

期刊论文
发表日期：

2026年5月19日

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Jia-Xin Ma,
Chen-Ming Bai,
Su-Juan Zhang,
Lu Liu

摘要

A set of orthogonal quantum states is said to be locally indistinguishable if it cannot be perfectly distinguished by local operations and classical communication (LOCC); otherwise, it is locally distinguishable. Motivated by the idea of converting information from a locally accessible to a locally hidden form, the activation of hidden nonlocality studies how a locally distinguishable set may be deterministically transformed into a locally indistinguishable one. In this work, we investigate such activations in multipartite and high-dimensional quantum systems. We explicitly construct locally distinguishable sets-in bipartite, tripartite, and multipartite scenarios-that can be converted into locally indistinguishable sets. For bipartite systems, we show that hidden nonlocality can be activated through suitable local measurements. In tripartite systems, we classify activatable sets into two distinct categories. Furthermore, in $\mathbb {C}^{2m+1}\otimes \mathbb {C}^n\otimes \mathbb {C}^{2m+1}$ $C^{2 m + 1} \otimes C^{n} \otimes C^{2 m + 1}$ systems, we present a class of locally distinguishable sets whose nonlocality cannot be revealed by any local operation alone; instead, joint measurements between two parties are required. By contrast, we also construct locally distinguishable sets in $\mathbb {C}^{2m+1}\otimes \mathbb {C}^{2n}\otimes \mathbb {C}^{2m+1}$ $C^{2 m + 1} \otimes C^{2 n} \otimes C^{2 m + 1}$ systems in which only one party’s operation is sufficient to hide information, and we generalize this construction to multipartite systems of the form $\mathbb {C}^{2m+1}\otimes (\mathbb {C}^{2n})^{(n-2)}\otimes \mathbb {C}^{2m+1}$ $C^{2 m + 1} \otimes {(C^{2 n})}^{(n - 2)} \otimes C^{2 m + 1}$ . Compared with the former class, the latter can be regarded as possessing a higher degree of nonlocality. Our results establish a hierarchy among locally distinguishable sets based on their activation properties and are promising for information hiding protocols.