In d-dimensional lattices of coupled quantum harmonic oscillators, we analyze the heat current caused by two thermal baths of different temperatures, which are coupled to opposite ends of the lattice, with a focus on the validity of Fourier's law of heat conduction. We provide analytical solutions of the heat current through the quantum system in the nonequilibrium steady state using the rotating-wave approximation and bath interactions described by a master equation of Lindblad form. The influence of local dephasing in the transition of ballistic to diffusive transport is investigated.

We analyze the steady-state energy transfer in a chain of coupled two-level systems connecting two thermal reservoirs. Through an analytic treatment we find that the energy current is independent of the system size, hence violating Fourier's law of heat conduction. The classical diffusive behavior in Fourier's law of heat conduction can be recovered by introducing decoherence to the quantum systems constituting the chain. We relate these results to recent discussions of energy transport in biological light-harvesting systems, and discuss the role of quantum coherence and entanglement.

We describe a new and experimentally feasible protocol for performing fundamental tests of quantum mechanics with massive objects. In our approach a single two level system is used to probe the motion of a nanomechanical resonator via multiple Ramsey interference measurements. This scheme enables the measurement of modular variables of macroscopic continuous variable systems and we show that correlations thereof violate a Leggett-Garg inequality and can be applied for tests of quantum contextuality. Our method can be implemented with a variety of different solid state or photonic qubit-resonator systems and provides a clear experimental signature to distinguish the predictions of quantum mechanics from those of other alternative theories at a macroscopic scale. In his celebrated paper in 1964 Bell showed that the laws of quantum mechanics are inconsistent with a description of our world based on local elements of reality [1]. Bell derived an experimentally testable inequality, which bounds the correlations between bipartite measurements for any local hidden variable theory, but which is violated by quantum mechanics. Since then the results constraining the permissible types of hidden variable models of quantum mechanics have attracted much attention and have been reformulated as the problem of contextual measurements by Kochen and Specker [2] and in terms of temporal correlations by Leggett and Garg [3]. Today these concepts have been tested in various experiments with photons [4], ions [5], impurity spins [6,7] or superconducting qubits [8,9] confirming quantum mechanics on a microscopic level. The challenge is now to verify or disprove these predictions also with more massive objects [10], where quantum physics conflicts with our daily life perceptions as well as with alternative theories and (gravity-induced) collapse models [11][12][13][14][15][16][17][18].In recent years a rapid progress towards the quantum control of nano-and micromechanical systems has been achieved: resonators with masses in the picogram regime have been cooled close to the quantum ground state [19][20][21][22] and first steps for coupling mechanical resonators to single electronic spins [23,24] or superconducting qubits [19,25,26] have been implemented. In this work we show, how these techniques can be directly applied for testing the most fundamental aspects of quantum mechanics on a macroscopic scale. The general idea is illustrated in Fig. 1, where a microscopic two level system (qubit) is coupled to a massive mechanical resonator and is used to probe the resonator displacement via multiple Ramsey measurements (RMs) [2,24,28]. Our analysis shows that the correlations between two subsequent RMs can violate a Leggett-Garg inequality (LGI) [3, 4], and thereby provide a clear experimental signature for distinguishing the predictions of quantum mechanics from those of other realistic theories. More generally, our scheme allows the measurement of so-called modular variables, which, for example, play an important role for the detection of n...

We show that a special type of measurements, called symmetric informationally complete positive operator-valued measures (SIC POVMs), provide a stronger entanglement detection criterion than the computable cross-norm or realignment criterion based on local orthogonal observables. As an illustration, we demonstrate the enhanced entanglement detection power in simple systems of qubit and qutrit pairs. This observation highlights the significance of SIC POVMs for entanglement detection.