# Wigner's form of the Leggett-Garg inequality, the no-signaling-in-time condition, and unsharp measurements

@article{Saha2015WignersFO,
title={Wigner's form of the Leggett-Garg inequality, the no-signaling-in-time condition, and unsharp measurements},
author={Debashis Saha and Shiladitya Mal and Prasanta K. Panigrahi and Dipankar Home},
journal={Physical Review A},
year={2015},
volume={91},
pages={032117}
}
• D. Saha
• Published 3 September 2014
• Physics
• Physical Review A
Wigner's form of the local realist inequality is used to derive its temporal version for an oscillating two-level system involving two-time joint probabilities. Such an inequality may be regarded as a novel form of the Leggett-Garg inequality (LGI) constituting a necessary condition for macrorealism. The robustness of its quantum mechanical (QM) violation against unsharpness of measurement is investigated by using a suitable model of unsharp measurements. It is found that there exists a range…
30 Citations
Leggett-Garg Inequality and Quantumness Under the Influence of Random Telegraph Noise
• M. Ban
• Physics
International Journal of Theoretical Physics
• 2019
The violation of the Leggett-Garg inequality and the quantum witness of a two-level system are investigated under the influence of stochastic dephasing which is described by a non-stationary and
Quantum mechanical violation of macrorealism for large spin and its robustness against coarse-grained measurements
• Physics
• 2016
For multilevel spin systems, robustness of the quantum mechanical (QM) violation of macrorealism (MR) with respect to coarse-grained measurements is investigated using three different necessary
Fine's theorem for Leggett-Garg tests with an arbitrary number of measurement times
• Mathematics
Physical Review A
• 2019
If the time evolution of a system can be understood classically, then there must exist an underlying probability distribution for the variables describing the system at all times. It is well known
Quantum violation of variants of Leggett-Garg inequalities up to the algebraic maximum for a qubit system
• Physics
Physical Review A
• 2018
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
The Leggett-Garg inequality and Page-Wootters mechanism
• Physics
• 2016
Violation of the Leggett-Garg inequality (LGI) implies quantum phenomena. In this light we establish that the Moreva \textit{et al.} \cite{moreva} experiment demonstrating the Page-Wootter's
Canonical Leggett-Garg inequality: Nonclassicality of temporal quantum correlations under energy constraint
• Mathematics
Physical Review A
• 2018
Nonclassicality of temporal correlations pertaining to noncommutative sequential measurements is defined through the violation of macrorealistic inequalities, known as Leggett-Garg inequalities
Probing inequivalent forms of Leggett–Garg inequality in subatomic systems
• Physics
• 2019
We study various formulations of Leggett-Garg inequality (LGI), specifically, the Wigner and Clauser-Horne forms of LGI, in the context of subatomic systems, in particular, three flavor neutrino as
Wigner inequalities for testing the hypothesis of realism and concepts of macroscopic and local realism
• Mathematics
Physical Review A
• 2019
We propose a new Wigner inequality suitable for test of the hypothesis of realism. We show that this inequality is not identical neither to the well-known Wigner inequality nor to the Leggett-Garg

## References

SHOWING 1-10 OF 43 REFERENCES
Leggett-Garg Inequalities
• Physics
• 2013
In contrast to the spatial Bell's inequalities, which probe entanglement between spatially-separated systems, the Leggett-Garg inequalities test the correlations of a single system measured at
Condition for macroscopic realism beyond the Leggett-Garg inequalities
• Philosophy
• 2012
In 1985, Leggett and Garg put forward the concept of macroscopic realism (macrorealism) and, in analogy to Bell's theorem, derived a necessary condition in terms of inequalities, which are now known
A scattering quantum circuit for measuring Bell's time inequality: a nuclear magnetic resonance demonstration using maximally mixed states
• Physics
• 2011
In 1985, Leggett and Garg (1985 Phys. Rev. Lett. 54 857) proposed a Bell-like inequality to test (in)compatibility between two fundamental concepts of quantum mechanics. The first concept is
Temporal quantum correlations and Leggett-Garg inequalities in multilevel systems.
• Mathematics
Physical review letters
• 2014
We show that the quantum bound for temporal correlations in a Leggett-Garg test, analogous to the Tsirelson bound for spatial correlations in a Bell test, strongly depends on the number of levels N
Leggett-Garg inequalities and the geometry of the cut polytope
• Mathematics
• 2010
The Bell and Leggett-Garg tests offer operational ways to demonstrate that nonclassical behavior manifests itself in quantum systems, and experimentalists have implemented these protocols to show
THE paradox of Einstein, Podolsky and Rosen [1] was advanced as an argument that quantum mechanics could not be a complete theory but should be supplemented by additional variables. These additional
Contextuality for preparations, transformations, and unsharp measurements
The Bell-Kochen-Specker theorem establishes the impossibility of a noncontextual hidden variable model of quantum theory, or equivalently, that quantum theory is contextual. In this paper, an
Unsharp Quantum Reality
• Philosophy
• 2010
It will be shown that potentiality can be viewed as a causal agency that evolves in a well-defined way and its role in addressing the tensions between quantum and classical accounts of the physical world will be elucidated.
Leggett-Garg inequality with a kicked quantum pump.
• Physics
Physical review letters
• 2006
A kicked quantum nondemolition measurement is introduced, where a qubit is weakly measured by pumping current, and results are applied to violate a generalization of the Leggett-Garg inequality.
On Hidden Variables and Quantum Mechanical Probabilities
An argument, due originally to J. S. Bell, is somewhat simplified and made more specific. It deals primarily with a quantum mechanical system consisting of the spins of two spin-12 particles. It