The Leggett-Garg inequalities serve to test whether or not quantum correlations in time can be explained within a classical macrorealistic framework. We apply this test to thermodynamics and derive a set of Leggett- Garg inequalities for the statistics of fluctuating work done on a quantum system unitarily driven in time. It is shown that these inequalities can be violated in a driven two-level system, thereby demonstrating that there exists no general macrorealistic description of quantum work. These violations are shown to emerge within the standard Two-Projective-Measurement scheme as well as for alternative definitions of fluctuating work that are based on weak measurement. Our results elucidate the influences of temporal correlations on work extraction in the quantum regime and highlight a key difference between quantum and classical thermodynamics.
In contrast to Bell's inequalities which test the correlations between multiple spatially separated systems, the Leggett-Garg inequalities test the temporal correlations between measurements of a single system. We experimentally demonstrate the violation of the Leggett-Garg inequality in a classical optical system using only the polarization degree-of-freedom of a laser beam. Our results show maximal violations of the Leggett-Garg inequality.
Investigation the boundary between quantum mechanical description and classical realistic view is of fundamental importance. The Leggett-Garg inequality provides a criterion to distinguish between quantum systems and classical systems, and can be used to prove the macroscopic superposition state. A larger upper bound of the LG function can be obtained in a multi-level system. Here, we present an experimental violation of the Leggett-Garg inequality in a three-level system using nitrogen-vacancy center in diamond by ideal negative result measurement. The experimental maximum value of Leggett-Ga…
The Leggett-Garg inequalities impose restrictions on the values taken by some combinations of the two-time correlation functions of observables in order to be explainable by a noninvasive-realist classical model. While in the unitary dynamics, it is straightforward to compute these correlation functions, open system effects bring in subtleties. Specifically, for non-Markovian dynamics, which involves setting up of system-bath correlations, the Leggett-Garg measurements disrupt these correlations, making a full system-bath Hamiltonian approach natural. However, here we point out that the proble…
Macrorealism from entropic Leggett-Garg inequalities
我们制定熵Leggett-Garg不等式，其中放置的约束的时间相关性的观测的统计结果。如果宏观实在论成立，则信息论不等式成立。我们发现，量子转子的时间分离的自旋分量之间的相关性的量子统计模拟的自旋相关性在两个空间分离的自旋$s$粒子共享一个状态的零总自旋。这导致了熵Leggett-Garg不等式被旋转量子自旋$s$系统以类似于熵贝尔不等式的方式破坏（Phys. Rev. Lett. 61，662（1988））通过形成复合自旋单重态的一对自旋- $s$粒子来实现。
Macrorealism is a classical world view asserting that the properties of macro-objects exist independently and irrespective of observation. One practical approach to test this view in quantum theory is to observe the quantum coherence for macro-object in an interference experiment. An elegant and conceptually appealing approach for testing the notion of macrorealism in quantum theory is through the violation of Leggett-Garg inequality. However, a conclusive Leggett-Garg test hinges on how the non-invasive measurability criteria is guaranteed in an experiment and remains a debated issue till dat…
In 1862, George Boole derived an inequality for variables, now known as Boolean variables, that in his opinion represents a demarcation line between possible and impossible experience. This inequality forms an important milestone in the epistemology of probability theory and probability measures. In 1985 Leggett and Garg derived a physics related inequality, mathematically identical to Boole's, that according to them represents a demarcation between macroscopic realism and quantum mechanics. Their formalism, constructed for the magnetic flux of SQUIDS, includes general features and applies als…
We report an unusual buildup of the quantum coherence in a qubit subjected to non-Hermitian evolution generated by a Parity-Time ($\mathcal{PT}$) symmetric Hamiltonian, which is reinterpreted as a Hermitian system in a higher dimensional space using Naimark dilation. The coherence is found to be maximum about the exceptional points (EPs), i.e., the points of coalescence of the eigenvalues as well as the eigenvectors. The nontrivial physics about EPs has been observed in various systems, particularly in photonic systems. As a consequence of enhancement in coherence, the various formulations of …
Leggett-Garg inequality (LGI) studies the temporal correlation in the evolution of physical systems. Classical systems obey the LGI but quantum systems may violate it. The extent of the violation depends on the dimension of the quantum system and the state update rule. In this work, we experimentally test the LGI in a three-level trapped-ion system under the model of a large spin precessing in a magnetic field. The Von Neumann and Lüders state update rules are employed in our system for direct comparative analysis. The maximum observed value of Leggett-Garg correlator under the Von Neumann sta…
We investigate the Leggett-Garg inequalities (LGIs) for a boson system whose observables are given by deforming the Pegg-Barnett phase operators. We consider two observables and show that the quantum Fourier transform is useful in the realization of the required measurements. Deriving explicit forms for the LGIs using the coherent state $|α\rangle$ as the initial state, we explore the regimes where they are violated when the time difference between observations of the phase operators is varied. We show that the system remains nonclassical in the large amplitude limit without dissipation, howev…
In this study, we determine a violation of the Leggett-Garg inequalities due to gravitational interaction in a hybrid system consisting of a harmonic oscillator and a spatially localized superposed particle. The violation of the Leggett-Garg inequalities is discussed using the two-time quasiprobability in connection with the entanglement negativity generated by gravitational interaction. It is demonstrated that the entanglement suppresses the violation of the Leggett-Garg inequalities when one of the two times of the quasiprobability t_1 is chosen as the initial time. Further, it is shown that…
