title: No-Go Theorem for the Characterization of Work Fluctuations in Coherent Quantum Systems.
abstract: An open question of fundamental importance in thermodynamics is how to describe the fluctuations of work for quantum coherent processes. In the standard approach, based on a projective energy measurement both at the beginning and at the end of the process, the first measurement destroys any initial coherence in the energy basis. Here we seek extensions of this approach which can possibly account for initially coherent states. We consider all measurement schemes to estimate work and require that (i) the difference of average energy corresponds to average work for closed quantum systems and that (ii) the work statistics agree with the standard two-measurement scheme for states with no coherence in the energy basis. We first show that such a scheme cannot exist. Next, we consider the possibility of performing collective measurements on several copies of the state and prove that it is still impossible to simultaneously satisfy requirements (i) and (ii). Nevertheless, improvements do appear, and in particular, we develop a measurement scheme that acts simultaneously on two copies of the state and allows us to describe a whole class of coherent transformations.
authors.affiliation: ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain.
authors.forename: Martí
authors.initials: M
authors.lastname: Perarnau-Llobet
authors.affiliation: ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain.|Institute for Theoretical Physics, ETH Zurich, 8093 Zürich, Switzerland.
authors.forename: Elisa
authors.initials: E
authors.lastname: Bäumer
authors.affiliation: ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain.
authors.forename: Karen V
authors.initials: KV
authors.lastname: Hovhannisyan
authors.affiliation: Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain.|Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria.
authors.forename: Marcus
authors.initials: M
authors.lastname: Huber
authors.affiliation: ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain.|ICREA, Pg. Lluís Companys 23, 08010 Barcelona, Spain.
authors.forename: Antonio
authors.initials: A
authors.lastname: Acin