Thermodynamic uncertainty relations (TURs) place strict bounds on the fluctuations of thermodynamic quantities in terms of the associated entropy production. In this work we identify the tightest (and saturable) matrixvalued TUR that can be derived from the exchange fluctuation theorems describing the statistics of heat and particle flow between multiple systems of arbitrary dimensions. Our result holds for both quantum and classical systems, undergoing general finite-time, non-stationary processes. Moreover, it provides bounds not only for the variances, but also for the correlations between thermodynamic quantities. To demonstrate the relevance of TURs to the design of nanoscale machines, we consider the operation of a two-qubit SWAP engine undergoing an Otto cycle and show how our results can be used to place strict bounds on the correlations between heat and work.

We explore the connection between two recently introduced notions of non-Markovian quantum dynamics and the validity of the so-called quantum regression theorem. While non-Markovianity of a quantum dynamics has been defined looking at the behaviour in time of the statistical operator, which determines the evolution of mean values, the quantum regression theorem makes statements about the behaviour of system correlation functions of order two and higher. The comparison relies on an estimate of the validity of the quantum regression hypothesis, which can be obtained exactly evaluating two points correlation functions. To this aim we consider a qubit undergoing dephasing due to interaction with a bosonic bath, comparing the exact evaluation of the non-Markovianity measures with the violation of the quantum regression theorem for a class of spectral densities. We further study a photonic dephasing model, recently exploited for the experimental measurement of non-Markovianity. It appears that while a non-Markovian dynamics according to either definition brings with itself violation of the regression hypothesis, even Markovian dynamics can lead to a failure of the regression relation.Comment: 11 pages, 4 figure

Autonomous engines operating at the nano-scale can be prone to deleterious fluctuations in the heat and particle currents which increase, for fixed power output, the more reversible the operation regime is. This fundamental trade-off between current fluctuations and entropy production forms the basis of the so-called thermodynamic uncertainty relations (TURs). Importantly, recent studies have shown that they can be violated in the quantum regime, thus motivating the search for analogous quantum counterparts. In this paper we show that the geometry of quantum non-equilibrium steady-states alone directly implies the existence of TUR, but with a looser bound, which is not violated by the above recent findings. The geometrical nature of this result makes it extremely general, establishing a fundamental limit for the thermodynamics of precision. Our proof is based on the McLennan-Zubarev ensemble, which provides an exact description of non-equilibrium steady-states. We first prove that the entropy production of this ensemble can be expressed as a quantum relative entropy. The TURs are then shown to be a direct consequence of the Cramer-Rao bound, a fundamental result from parameter estimation theory. By combining techniques from many-body physics and information sciences, our approach also helps to shed light on the delicate relationship between quantum effects and current fluctuations in autonomous machines, where new general bound on the power output are found and discussed.

Charge qubits can be created and manipulated in solid-state double-quantum-dot (DQD) platforms. Typically, these systems are strongly affected by quantum noise stemming from coupling to substrate phonons. This is usually assumed to lead to decoherence towards steady states that are diagonal in the energy eigenbasis. In this letter we show, to the contrary, that due to the presence of phonons the equilibrium steady state of the DQD charge qubit may be engineered to display coherence in the energy eigenbasis. The magnitude of the coherence can be controlled by tuning the DQD parameters and regimes of high purity maybe found. In addition, we show that the steady-state coherence can be used to drive an auxiliary cavity mode coupled to the DQD. arXiv:1906.06271v1 [cond-mat.mes-hall]