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 aAcĂn, Antonio uhttp://grupsderecerca.uab.cat/giq/node/85501441nas a2200205 4500008003900000022002500039245011200064210006900176490000700245520074100252653005500993653002001048100002301068700002701091700002501118700001701143700001801160700002101178856003601199 2016 d a2469-9950, 2469-996900aAutonomous {Quantum} {Refrigerator} in a {Circuit}-{QED} {Architecture} {Based} on a {Josephson} {Junction}0 aAutonomous Quantum Refrigerator in a Circuit QED Architecture Ba0 v943 aAn implementation of a small quantum absorption refrigerator in a circuit QED architecture is proposed. The setup consists of three harmonic oscillators coupled to a Josephson unction. The refrigerator is autonomous in the sense that it does not require any external control for cooling, but only thermal contact between the oscillators and heat baths at different temperatures. In addition, the setup features a built-in switch, which allows the cooling to be turned on and off. If timing control is available, this enables the possibility for coherence-enhanced cooling. Finally, we show that significant cooling can be achieved with experimentally realistic parameters and that our setup should be within reach of current technology.10aCondensed Matter - Mesoscale and Nanoscale Physics10aQuantum Physics1 aHofer, Patrick, P.1 aPerarnau-Llobet, Marti1 aBrask, Jonatan, Bohr1 aSilva, Ralph1 aHuber, Marcus1 aBrunner, Nicolas uhttp://arxiv.org/abs/1607.05218