Quantum violation of variants of LGIs upto algebraic maximum for qubit system

Abstract

In 1985, Leggett and Garg formulated a class of inequalities for testing the compatibility between macrorealism and quantum mechanics. In this paper, we point out that based on the same assumptions of macrorealism that are used in the derivation of Leggett-Garg inequalities (LGIs) , there is a scope of formulating another class of inequalities different from standard LGIs. By considering the three-time measurement scenario in a dichotomic system, we first propose an interesting variant of standard LGIs and show that its quantum violation is larger than the standard LGI. By extending this formulation to $n$-time measurement scenario, we found that the quantum violations of variants of LGIs for a \emph{qubit} system increase with $n$, and for a sufficiently large $n$ algebraic maximum can be reached. Further, we compare the quantum violations of our formulated LGIs with the standard LGIs and no-signaling in time formulation of macrorealism.

References in corpus (25)

• Dynamical Reduction Models
• Leggett-Garg Inequalities
• Experimental violation of a Bell's inequality in time with weak measurement
• Violation of the Leggett-Garg inequality with weak measurements of photons
• Violation of a Leggett-Garg inequality with ideal non-invasive measurements
• Classical world arising out of quantum physics under the restriction of coarse-grained measurements
• Condition for macroscopic realism beyond the Leggett-Garg inequalities
• Opening up the Quantum Three-Box Problem with Undetectable Measurements
• The conditions for quantum violation of macroscopic realism
• A strict experimental test of macroscopic realism in a superconducting flux qubit
• Temporal quantum correlations and Leggett-Garg inequalities in multi-level systems
• Quantatitive relations between measurement incompatibility, quantum steering, and nonlocality
• Bounding temporal quantum correlations
• No Fine theorem for macrorealism: Limitations of the Leggett-Garg inequality
• Necessary and sufficient conditions for macroscopic realism from quantum mechanics
• The Leggett-Garg Inequalities and No-Signalling in Time: A Quasi-Probability Approach
• Wigner's form of the Leggett-Garg inequality, No-Signalling in Time, and Unsharp Measurements
• Leggett--Garg inequality violations with a large ensemble of qubits
• Quantum non-demolition measurement enables macroscopic Leggett-Garg tests
• Comparing Conditions for Macrorealism: Leggett-Garg Inequalities vs No-Signaling in Time
• The Leggett-Garg inequality in electron interferometers
• Probing various formulations of macrorealism for unsharp quantum measurements
• Towards an equivalence between maximal entanglement and maximal quantum nonlocality
• Inequivalent Leggett-Garg inequalities
• On the violation of L$\ddot{u}$ders bound of macrorealist and noncontextual inequalities

Cited by in corpus (15)

• Interference experiment, anomalous weak value and Leggett-Garg test of macrorealism
• Detecting violations of macrorealism when the original Leggett-Garg inequalities are satisfied
• Leggett-Garg tests for macrorealism: interference experiments and the simple harmonic oscillator
• Fine's Theorem for Leggett-Garg tests with an arbitrary number of measurement times
• Algebraic maximum violation of the Leggett-Garg inequality in a two-level system under PT symmetric dynamics
• Probing inequivalent forms of Legget-Garg inequality in subatomic systems
• Conditions for Macrorealism for Systems Described by Many-Valued Variables
• $\mathcal{P}\mathcal{T}$ symmetric evolution, coherence and violation of Leggett-Garg inequalities
• Temporal correlation beyond quantum bounds in non-hermitian dynamics
• Leggett-Garg violations for continuous variable systems with gaussian states
• Certification of two-qubit quantum systems with temporal inequality
• Lüders bounds of Leggett-Garg inequalities, $\mathcal{P}\mathcal{T}$- symmetric evolution and arrow-of-time
• Quantum violations of Lüders bound Leggett-Garg inequalities for quantum channel
• Fractional Conformal Map, Qubit Dynamics and the Leggett-Garg Inequality
• Certification of multi-qubit quantum systems with temporal inequalities