Violation of Leggett—Garg inequalities for quantum-classical hybrids

Jerzy Dajka,Marcin Łobejko

doi:10.1088/1742-6596/626/1/012038

Abstract

Violation of Leggett-Garg inequalities can serve as a signature of a failure of (macroscopic) realism. We investigate violation of the simplest Leggett-Garg inequality for a qubit coupled to an integer j spin (angular momentum). Such a system effectively reveals quantum-classical hybrid behavior in the limit of large j values. We show that a maximal violation of the Leggett- Garg inequality is larger for quantum-classical hybrids than for fully quantum systems.

Highlights

Discoveries of entanglement [1] and other types of quantum correlations like quantum discord [2] play essential role in a way of seeing and understanding of the microscopic and macroscopic reality
In this paper we consider a simple composite system consisting of a qubit coupled to an integer spin exhibiting well defined classical limit
In theclassical limit of large j, the smaller are the values of m of the integer spin projection on quantization axis, the longer is the period of K3 oscillation

Summary

Introduction

Discoveries of entanglement [1] and other types of quantum correlations like quantum discord [2] play essential role in a way of seeing and understanding of the microscopic and macroscopic reality. Well known violation of Bell inequalities [3] is the best evidence of the existence of such spatial correlations which cannot be understand in terms of some ”classical” local hidden variables. In analogy to the spatial correlations quantified by the Bell inequalities [3] one predicts and observes violations of the so called Leggett-Garg inequalities (LGI) [4]. LGI are derived under two assumptions: macroscopic realism and non–invasive measurability of the system. The first requirement, the macroscopicity, is often abandoned as the LGI are interesting by its own in microscopic systems [5]

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