An open question of fundamental importance in thermodynamics is howto 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.

1 aPerarnau-Llobet, Marti1 aBaumer, Elisa1 aHovhannisyan, Karen, V.1 aHuber, Marcus1 aAcín, Antonio uhttps://grupsderecerca.uab.cat/giq/node/85500629nas a2200169 4500008003900000245003900039210003900078260001600117490000600133100002700139700002800166700001800194700002100212700002100233700001900254856018600273 2015 d00aExtractable Work from Correlations0 aExtractable Work from Correlations cJan-10-20150 v51 aPerarnau-Llobet, Marti1 aHovhannisyan, Karen, V.1 aHuber, Marcus1 aSkrzypczyk, Paul1 aBrunner, Nicolas1 aAcín, Antonio uhttps://link.aps.org/doi/10.1103/PhysRevX.5.041011http://harvest.aps.org/v2/journals/articles/10.1103/PhysRevX.5.041011/fulltexthttp://link.aps.org/article/10.1103/PhysRevX.5.04101100701nas a2200169 4500008003900000022001400039245007900053210006900132260001600201490000700217100002600224700002700250700001900277700002800296700001800324856018900342 2015 d a1539-375500aThermodynamics of creating correlations: Limitations and optimal protocols0 aThermodynamics of creating correlations Limitations and optimal cJan-03-20150 v911 aBruschi, David Edward1 aPerarnau-Llobet, Marti1 aFriis, Nicolai1 aHovhannisyan, Karen, V.1 aHuber, Marcus uhttps://link.aps.org/doi/10.1103/PhysRevE.91.032118http://harvest.aps.org/v2/journals/articles/10.1103/PhysRevE.91.032118/fulltexthttp://link.aps.org/article/10.1103/PhysRevE.91.032118