Correlating thermal machines and the second law at the nanoscale

Thermodynamics at the nanoscale is known to differ significantly from its familiar macroscopic counterpart: the possibility of state transitions is not determined by free energy alone, but by an infinite family of free-energy-like quantities; strong fluctuations (possibly of quantum origin) allow to extract less work reliably than what is expected from computing the free energy difference. However, these known results rely crucially on the assumption that the thermal machine is not only exactly preserved in every cycle, but also kept uncorrelated from the quantum systems on which it acts. Here we lift this restriction: we allow the machine to become correlated with the microscopic systems on which it acts, while still exactly preserving its own state. Surprisingly, we show that this restores the second law in its original form: free energy alone determines the possible state transitions, and the corresponding amount of work can be invested or extracted from single systems exactly and without any fluctuations. At the same time, the work reservoir remains uncorrelated from all other systems and parts of the machine. Thus, microscopic machines can increase their efficiency via clever "correlation engineering" in a perfectly cyclic manner, which is achieved by a catalytic system that can sometimes be as small as a single qubit (though some setups require very large catalysts). Our results also solve some open mathematical problems on majorization which may lead to further applications in entanglement theory.Comment: 11+13 pages, 5 figures. Added some clarifications and corrections; results unchanged. Close to published versio

Mirages, anti-mirages, and further surprises in quantum corrals with non-magnetic impurities

We investigate the local density of states (LDOS) for non-interacting electrons in a hard wall ellipse in the presence of a single non-magnetic scattering center. Using a T-matrix analysis we calculate the local Green's function and observe a variety of quantum mirage effects for different impurity positions. Locating the impurity near positions with LDOS maxima for the impurity free corral can either lead to a reduction or an enhancement of the LDOS at the mirror image point, i.e. a mirage or anti-mirage effect, or even suppress LDOS maxima in the entire area of the corral.Comment: 6 pages, 7 figure

Quantum Horn's lemma, finite heat baths, and the third law of thermodynamics

Interactions of quantum systems with their environment play a crucial role in resource-theoretic approaches to thermodynamics in the microscopic regime. Here, we analyze the possible state transitions in the presence of "small" heat baths of bounded dimension and energy. We show that for operations on quantum systems with fully degenerate Hamiltonian (noisy operations), all possible state transitions can be realized exactly with a bath that is of the same size as the system or smaller, which proves a quantum version of Horn's lemma as conjectured by Bengtsson and Zyczkowski. On the other hand, if the system's Hamiltonian is not fully degenerate (thermal operations), we show that some possible transitions can only be performed with a heat bath that is unbounded in size and energy, which is an instance of the third law of thermodynamics. In both cases, we prove that quantum operations yield an advantage over classical ones for any given finite heat bath, by allowing a larger and more physically realistic set of state transitions.Comment: 15+4 pages, 6 figures. Version accepted for publication in Quantu

Higher-order interference and single-system postulates characterizing quantum theory

We present a new characterization of quantum theory in terms of simple physical principles that is different from previous ones in two important respects: first, it only refers to properties of single systems without any assumptions on the composition of many systems; and second, it is closer to experiment by having absence of higher-order interference as a postulate, which is currently the subject of experimental investigation. We give three postulates -- no higher-order interference, classical decomposability of states, and strong symmetry -- and prove that the only non-classical operational probabilistic theories satisfying them are real, complex, and quaternionic quantum theory, together with 3-level octonionic quantum theory and ball state spaces of arbitrary dimension. Then we show that adding observability of energy as a fourth postulate yields complex quantum theory as the unique solution, relating the emergence of the complex numbers to the possibility of Hamiltonian dynamics. We also show that there may be interesting non-quantum theories satisfying only the first two of our postulates, which would allow for higher-order interference in experiments while still respecting the contextuality analogue of the local orthogonality principle.Comment: 21 + 6 pages, 1 figure. v4: published version (includes several minor corrections