New bound on S1× S2-setting Bell locality of a nonseparable Werner state
Abstract
In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers S1,S2≥1 of generalized quantum measurements at two sites. In the present article, we find analytically a new general condition sufficient for a nonseparable Werner state with a dimension d≤min{S1,S2} to satisfy all Bell inequalities under every S1× S2-setting correlation scenario with outcomes of an arbitrary spectral type, discrete or continuous − that is, to be S1× S2-setting Bell local, for short. For a variety of measurement settings S1, S2, this new general bound is beyond (i) Werner's and Barrett's locality bounds for a nonseparable Werner state and (ii) the related result by Johnson and Viola [Phys. Rev. A 88, 032323 (2013)] on "sharability" of this state. When specialized to d = 2 and min{S1,S2} = 2, 3, our new general bound improves upon the corresponding results by Terhal et. al. in [Phys. Rev. Lett. 90, 157903 (2003)], moreover, for d=min{S1,S2} = 2, it reduces exactly to the bound derived for this case via the CHSH inequality. We prove also explicitly in operator terms the result of Terhal et. el. that every nonseparable Werner state with a dimension d >min{S1,S2} is S1× S2-setting Bell local. The new results presented in this article are important for both the theory of Bell nonlocality and quantum applications based on this fundamental concept.
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BibTeX
@misc{loubenets2026bound,
title = {{New bound on $S_1\times S_2$-setting Bell locality of a nonseparable Werner state}},
author = {Elena R. Loubenets},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.18050},
eprint = {2607.18050},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.18050},
}
RIS
TY - UNPB
TI - New bound on S_1× S_2-setting Bell locality of a nonseparable Werner state
AU - Elena R. Loubenets
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2607.18050
UR - https://arxiv.org/abs/2607.18050
AB - In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers S_1,S_2≥1 of generalized quantum measurements at two sites. In the present article, we find analytically a new general condition sufficient for a nonseparable Werner state with a dimension d≤min{S_1,S_2} to satisfy all Bell inequalities under every S_1× S_2-setting correlation scenario with outcomes of an arbitrary spectral type, discrete or continuous − that is, to be S_1× S_2-setting Bell local, for short. For a variety of measurement settings S_1, S_2, this new general bound is beyond (i) Werner's and Barrett's locality bounds for a nonseparable Werner state and (ii) the related result by Johnson and Viola [Phys. Rev. A 88, 032323 (2013)] on "sharability" of this state. When specialized to d = 2 and min{S_1,S_2} = 2, 3, our new general bound improves upon the corresponding results by Terhal et. al. in [Phys. Rev. Lett. 90, 157903 (2003)], moreover, for d=min{S_1,S_2} = 2, it reduces exactly to the bound derived for this case via the CHSH inequality. We prove also explicitly in operator terms the result of Terhal et. el. that every nonseparable Werner state with a dimension d >min{S_1,S_2} is S_1× S_2-setting Bell local. The new results presented in this article are important for both the theory of Bell nonlocality and quantum applications based on this fundamental concept.
ER -