<p>Recently, the constructions of strongly nonlocal orthogonal states have attracted much attention. However, for these sets of orthogonal states with stronger nonlocality, there has been little research on how to effectively use entanglement to distinguish them by local operations and classical communication (LOCC). The entanglement-assisted discrimination protocols for genuinely nonlocal orthogonal product bases were first given by Rout et al. (Phys. Rev. A 100:032321, 2019). Inspired by their protocols, this paper concentrates on the entanglement-assisted local discrimination of the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$6(d-1)^2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>6</mn> <msup> <mrow> <mo stretchy="false">(</mo> <mi>d</mi> <mo>-</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> <mn>2</mn> </msup> </mrow> </math></EquationSource> </InlineEquation> strongly nonlocal orthogonal product states (OPSs) in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$(\mathbb {C}^d)^{\otimes 3}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mi>d</mi> </msup> <mo stretchy="false">)</mo> </mrow> <mrow> <mo>⊗</mo> <mn>3</mn> </mrow> </msup> </math></EquationSource> </InlineEquation> (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">$d\ge 3$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>d</mi> <mo>≥</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>) which were constructed by Yuan et al. (Phys. Rev. A 102:042228, 2020). First, we use an average of three 2-qubit maximally entangled states (MESs) to locally identify strongly nonlocal OPSs in <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$(\mathbb {C}^4)^{\otimes 3}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mn>4</mn> </msup> <mo stretchy="false">)</mo> </mrow> <mrow> <mo>⊗</mo> <mn>3</mn> </mrow> </msup> </math></EquationSource> </InlineEquation>. Subsequently, the discrimination method can be extended to the OPSs in <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$(\mathbb {C}^d)^{\otimes 3}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mi>d</mi> </msup> <mo stretchy="false">)</mo> </mrow> <mrow> <mo>⊗</mo> <mn>3</mn> </mrow> </msup> </math></EquationSource> </InlineEquation>, proving that multiple copies of <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$2\otimes 2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2</mn> <mo>⊗</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> MESs can be used to exactly identify them. Our protocol not only indicates the crucial function of MESs in distinguishing strongly nonlocal OPSs but also reveals that the high entanglement cost makes it easier to overcome the states’ strongly nonlocality under the enhanced LOCC.</p>

Entanglement-assisted local discrimination of strongly nonlocal tripartite orthogonal product states

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发表日期：

2026年4月15日

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Tian-Qing Cao,
Shu-Na Peng,
Qiao-Ling Xin

摘要

Recently, the constructions of strongly nonlocal orthogonal states have attracted much attention. However, for these sets of orthogonal states with stronger nonlocality, there has been little research on how to effectively use entanglement to distinguish them by local operations and classical communication (LOCC). The entanglement-assisted discrimination protocols for genuinely nonlocal orthogonal product bases were first given by Rout et al. (Phys. Rev. A 100:032321, 2019). Inspired by their protocols, this paper concentrates on the entanglement-assisted local discrimination of the $6(d-1)^2$ $6 {(d - 1)}^{2}$ strongly nonlocal orthogonal product states (OPSs) in $(\mathbb {C}^d)^{\otimes 3}$ ${(C^{d})}^{\otimes 3}$ ( $d\ge 3$ $d \geq 3$ ) which were constructed by Yuan et al. (Phys. Rev. A 102:042228, 2020). First, we use an average of three 2-qubit maximally entangled states (MESs) to locally identify strongly nonlocal OPSs in $(\mathbb {C}^4)^{\otimes 3}$ ${(C^{4})}^{\otimes 3}$ . Subsequently, the discrimination method can be extended to the OPSs in $(\mathbb {C}^d)^{\otimes 3}$ ${(C^{d})}^{\otimes 3}$ , proving that multiple copies of $2\otimes 2$ $2 \otimes 2$ MESs can be used to exactly identify them. Our protocol not only indicates the crucial function of MESs in distinguishing strongly nonlocal OPSs but also reveals that the high entanglement cost makes it easier to overcome the states’ strongly nonlocality under the enhanced LOCC.