title: Limitations on the Evolution of Quantum Coherences: Towards Fully Quantum Second Laws of Thermodynamics.
abstract: The second law of thermodynamics places a limitation into which states a system can evolve into. For systems in contact with a heat bath, it can be combined with the law of energy conservation, and it says that a system can only evolve into another if the free energy goes down. Recently, it's been shown that there are actually many second laws, and that it is only for large macroscopic systems that they all become equivalent to the ordinary one. These additional second laws also hold for quantum systems, and are, in fact, often more relevant in this regime. They place a restriction on how the probabilities of energy levels can evolve. Here, we consider additional restrictions on how the coherences between energy levels can evolve. Coherences can only go down, and we provide a set of restrictions which limit the extent to which they can be maintained. We find that coherences over energy levels must decay at rates that are suitably adapted to the transition rates between energy levels. We show that the limitations are matched in the case of a single qubit, in which case we obtain the full characterization of state-to-state transformations. For higher dimensions, we conjecture that more severe constraints exist. We also introduce a new class of thermodynamical operations which allow for greater manipulation of coherences and study its power with respect to a class of operations known as thermal operations.
authors.affiliation: Institute of Theoretical Physics and Astrophysics, University of Gdańsk, 80-952 Gdańsk, Poland.|National Quantum Information Centre of Gdańsk, 81-824 Sopot, Poland.
authors.forename: Piotr
authors.initials: P
authors.lastname: Ćwikliński
authors.affiliation: Institute of Theoretical Physics and Astrophysics, University of Gdańsk, 80-952 Gdańsk, Poland.|National Quantum Information Centre of Gdańsk, 81-824 Sopot, Poland.
authors.forename: Michał
authors.initials: M
authors.lastname: Studziński
authors.affiliation: Institute of Theoretical Physics and Astrophysics, University of Gdańsk, 80-952 Gdańsk, Poland.|National Quantum Information Centre of Gdańsk, 81-824 Sopot, Poland.
authors.forename: Michał
authors.initials: M
authors.lastname: Horodecki
authors.affiliation: Department of Physics and Astronomy, University College of London, and London Interdisciplinary Network for Quantum Science, London WC1E 6BT, United Kingdom.
authors.forename: Jonathan
authors.initials: J
authors.lastname: Oppenheim