TY - JOUR

T1 - Hardy-type paradoxes for an arbitrary symmetric bipartite Bell scenario

AU - Chen, Kai Siang

AU - Mal, Shiladitya

AU - Tabia, Gelo Noel M.

AU - Liang, Yeong Cherng

N1 - Publisher Copyright:
© 2024 American Physical Society.

PY - 2024/4

Y1 - 2024/4

N2 - As with a Bell inequality, Hardy's paradox manifests a contradiction between the prediction given by quantum theory and local hidden-variable theories. In this work, we give two generalizations of Hardy's arguments for manifesting such a paradox to an arbitrary, but symmetric, Bell scenario involving two observers. Our constructions recover that of Meng et al. [Phys. Rev. A 98, 062103 (2018)10.1103/PhysRevA.98.062103] and that first discussed by Cabello [Phys. Rev. A 65, 032108 (2002)1050-294710.1103/PhysRevA.65.032108] as special cases. Among the two constructions, one can be naturally interpreted as a demonstration of the failure of the transitivity of implications (FTI). Moreover, one of their special cases is equivalent to a ladder-proof-type argument for Hardy's paradox. Through a suitably generalized notion of success probability called degree of success, we provide evidence showing that the FTI-based formulation exhibits a higher degree of success compared with all other existing proposals. Moreover, this advantage seems to persist even if we allow imperfections in realizing the zero-probability constraints in such paradoxes. Explicit quantum strategies realizing several of these proofs of nonlocality without inequalities are provided.

AB - As with a Bell inequality, Hardy's paradox manifests a contradiction between the prediction given by quantum theory and local hidden-variable theories. In this work, we give two generalizations of Hardy's arguments for manifesting such a paradox to an arbitrary, but symmetric, Bell scenario involving two observers. Our constructions recover that of Meng et al. [Phys. Rev. A 98, 062103 (2018)10.1103/PhysRevA.98.062103] and that first discussed by Cabello [Phys. Rev. A 65, 032108 (2002)1050-294710.1103/PhysRevA.65.032108] as special cases. Among the two constructions, one can be naturally interpreted as a demonstration of the failure of the transitivity of implications (FTI). Moreover, one of their special cases is equivalent to a ladder-proof-type argument for Hardy's paradox. Through a suitably generalized notion of success probability called degree of success, we provide evidence showing that the FTI-based formulation exhibits a higher degree of success compared with all other existing proposals. Moreover, this advantage seems to persist even if we allow imperfections in realizing the zero-probability constraints in such paradoxes. Explicit quantum strategies realizing several of these proofs of nonlocality without inequalities are provided.

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U2 - 10.1103/PhysRevA.109.042206

DO - 10.1103/PhysRevA.109.042206

M3 - Article

AN - SCOPUS:85189929192

SN - 2469-9926

VL - 109

JO - Physical Review A

JF - Physical Review A

IS - 4

M1 - 042206

ER -