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LOCC-Maximized Quantum Fisher Information as a Necessary Condition for CHSH Violation
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We investigate the relationship between CHSH inequality violation and quantum Fisher information (QFI) maximized over local operations and classical communication (LOCC) for two-qubit systems. Through systematic analysis of 1000 random states, we discover that no state with Bell parameter M(ρ) exceeding maximized QFI violates the CHSH inequality, suggesting QFImax serves as a necessary condition. States partition into three classes: (1) M(ρ) > QFImax with CHSH violation (23%), (2) M(ρ) > QFImax without violation (41%), and (3) M(ρ) < QFImax without violation (36%). We identify relative entropy of entanglement thresholds (0.14 and 0.26) separating regions of guaranteed violation, ambiguous behavior, and no violation. Furthermore, 98% of states exhibit QFI values that cross the separability bound under local rotations. These results provide efficient pre-screening criteria for device-independent quantum protocols and reveal deep connections between quantum metrology and Bell nonlocality.
Title: LOCC-Maximized Quantum Fisher Information as a Necessary Condition for CHSH Violation
Description:
We investigate the relationship between CHSH inequality violation and quantum Fisher information (QFI) maximized over local operations and classical communication (LOCC) for two-qubit systems.
Through systematic analysis of 1000 random states, we discover that no state with Bell parameter M(ρ) exceeding maximized QFI violates the CHSH inequality, suggesting QFImax serves as a necessary condition.
States partition into three classes: (1) M(ρ) > QFImax with CHSH violation (23%), (2) M(ρ) > QFImax without violation (41%), and (3) M(ρ) < QFImax without violation (36%).
We identify relative entropy of entanglement thresholds (0.
14 and 0.
26) separating regions of guaranteed violation, ambiguous behavior, and no violation.
Furthermore, 98% of states exhibit QFI values that cross the separability bound under local rotations.
These results provide efficient pre-screening criteria for device-independent quantum protocols and reveal deep connections between quantum metrology and Bell nonlocality.
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