Probing various formulations of macrorealism for unsharp quantum measurements

Abstract

Standard Leggett and Garg inequalities (SLGIs) were formulated for testing the incompatibility between the classical worldview of macrorealism and quantum mechanics. In recent times, various other formulations, such as Wigner form of LGIs (WLGIs), entropic LGIs (ELGIs) and the no-signaling in time (NSIT) condition have also been proposed. It is also recently argued that no set of SLGIs can provide the necessary and sufficient conditions for macrorealism but a suitable conjunction of NSIT conditions provides the same. In this paper, we first provide a comparative study of the various formulations of LGIs for testing macrorealism pertaining to the two different unsharp measurements. While the violations of WLGIs are more robust than SLGIs and ELGIs for spin-POVMs, here we demonstrate that for the case of biased POVMs, the quantum violations of both SLGIs and ELGIs provide the same robustness as WLGIs. Importantly, the violations of all formulations of LGIs can be achieved for \textit{any non-zero value} of unsharpness parameter. We have also studied the connection between LGIs and NSIT conditions. Further, we investigate the role of the joint measurability of the POVMs in the violation of LGIs and found that there is no generic connection.

Revised version. Accepted for publication in Phys. Rev. A

References in corpus (8)

• Large Quantum Superpositions and Interference of Massive Nanometer-Sized Objects
• Necessary and sufficient conditions for macroscopic realism from quantum mechanics
• A scattering quantum circuit for measuring Bell's time inequality: a nuclear magnetic resonance demonstration using maximally mixed states
• Coexistence of qubit effects
• Wigner's form of the Leggett-Garg inequality, No-Signalling in Time, and Unsharp Measurements
• Experimental violation of the Leggett-Garg inequality in a 3-level system
• Comparing Conditions for Macrorealism: Leggett-Garg Inequalities vs No-Signaling in Time
• Inequivalent Leggett-Garg inequalities

Cited by in corpus (21)

• Macroscopic quantum states: measures, fragility and implementations
• Interference experiment, anomalous weak value and Leggett-Garg test of macrorealism
• Leggett-Garg tests of macrorealism: checks for non-invasiveness and generalizations to higher-order correlators
• Quantum violation of variants of LGIs upto algebraic maximum for qubit system
• On the violation of L$\ddot{u}$ders bound of macrorealist and noncontextual inequalities
• Fine's Theorem for Leggett-Garg tests with an arbitrary number of measurement times
• Self-testing of binary Pauli measurements requiring neither entanglement nor any dimensional restriction
• Conservation laws in quantum noninvasive measurements
• $\mathcal{P}\mathcal{T}$ symmetric evolution, coherence and violation of Leggett-Garg inequalities
• Conditions for Macrorealism for Systems Described by Many-Valued Variables
• Probing inequivalent forms of Legget-Garg inequality in subatomic systems
• Persistence of quantum violation of macrorealism for large spins even under coarsening of measurement times
• Wigner Inequalities for Test of Hypothesis of Realism and Concepts of Macroscopic and Local Realism
• Effect of memory on the violation of Leggett-Garg inequality
• Quantum violation of macrorealism under multi-outcome two-parameter generalised measurements
• Lüders bounds of Leggett-Garg inequalities, $\mathcal{P}\mathcal{T}$- symmetric evolution and arrow-of-time
• Role of nonclassical temporal correlation in powering quantum random access codes
• L$\ddot{u}$der rule, von Neumann rule and Cirelson's bound of Bell CHSH inequality
• Quantum violations of Lüders bound Leggett-Garg inequalities for quantum channel
• Nonclassical correlations in decaying systems
• Projective measurements under qubit quantum channels