Temporal quantum correlations and Leggett-Garg inequalities in multilevel systems

Area of Science:

• Quantum Information Science
• Foundations of Quantum Mechanics

Background:

• The Leggett-Garg inequality provides a test for macrorealism, analogous to Bell's inequality for non-locality.
• Existing bounds for Leggett-Garg inequality violations are known, but their dependence on experimental parameters is not fully understood.

Purpose of the Study:

• To investigate the quantum bound for temporal correlations in Leggett-Garg tests.
• To determine the influence of the number of accessible measurement levels (N) on these bounds.
• To explore the potential for violating the Leggett-Garg inequality with varying N.

Main Methods:

• Analysis of quantum bounds for temporal correlations in Leggett-Garg tests.
• Derivation of exact bounds for small numbers of measurement levels (N).
• Investigation of the asymptotic behavior of these bounds as N approaches infinity.

Main Results:

• The quantum bound for temporal correlations in Leggett-Garg tests is strongly dependent on the number of accessible levels (N).
• Exact bounds for small N were derived, exceeding the previously known bound for the Leggett-Garg inequality.
• In the limit of N approaching infinity, the Leggett-Garg inequality can be violated up to its algebraic maximum.

Conclusions:

• The number of measurement levels (N) is a critical parameter in determining the strength of temporal correlations in quantum systems.
• The findings suggest that experiments with a higher number of accessible levels can achieve stronger violations of the Leggett-Garg inequality.
• This work provides a more refined understanding of quantum bounds in the context of temporal correlations and macrorealism tests.