We generalize the recently proposed resource theory of coherence (or superposition) [T. Baumgratz et al., Phys. Rev. Lett. 113, 140401 (2014); A. Winter and D. Yang, Phys. Rev. Lett. 116, 120404 ( 2016)] to the setting where not just the free (”incoherent”) resources, but also the manipulated objects, are quantum operations rather than states. In particular, we discuss an information theoretic notion of the coherence capacity of a quantum channel and prove a single-letter formula for it in the case of unitaries. Then we move to the coherence cost of simulating a channel and prove achievability results for unitaries and general channels acting on a d-dimensional system; we show that a maximally coherent state of rank d is always sufficient as a resource if incoherent operations are allowed, and one of rank d(2) for “strictly incoherent” operations. We also show lower bounds on the simulation cost of channels that allow us to conclude that there exists bound coherence in operations, i.e., maps with nonzero cost of implementing them but zero coherence capacity; this is in contrast to states, which do not exhibit bound coherence.

%B PHYSICAL REVIEW A %V 95 %R 10.1103/PhysRevA.95.062327 %0 Journal Article %J Quantum Science and Technology %D 2016 %T Realising a quantum absorption refrigerator with an atom-cavity system %A Mitchison, Mark T. %A Huber, Marcus %A Prior, Javier %A Woods, Mischa P. %A Plenio, Martin B. %X An autonomous quantum thermal machine comprising a trapped atom or ion placed inside an optical cavity is proposed and analysed. Such a machine can operate as a heat engine whose working medium is the quantised atomic motion or as an absorption refrigerator that cools without any work input. Focusing on the refrigerator mode, we predict that it is possible with state-of-the-art technology to cool a trapped ion almost to its motional ground state using a thermal light source such as sunlight. We nonetheless find that a laser or a similar reference system is necessary to stabilise the cavity frequencies. Furthermore, we establish a direct and heretofore unacknowledged connection between the abstract theory of quantum absorption refrigerators and practical sideband cooling techniques. We also highlight and clarify some assumptions underlying several recent theoretical studies on self-contained quantum engines and refrigerators. Our work indicates that cavity quantum electrodynamics is a promising and versatile experimental platform for the study of autonomous thermal machines in the quantum domain. %B Quantum Science and Technology %V 1 %P 015001 %U http://stacks.iop.org/2058-9565/1/i=1/a=015001 %R 10.1088/2058-9565/1/1/015001 %0 Journal Article %J Phys. Rev. Lett. %D 2016 %T Relations between Coherence and Path Information %A E. Bagan %A Bergou, János A. %A Cottrell, Seth S. %A Hillery, Mark %B Phys. Rev. Lett. %I American Physical Society %V 116 %P 160406 %8 Apr %G eng %U http://link.aps.org/doi/10.1103/PhysRevLett.116.160406 %R 10.1103/PhysRevLett.116.160406 %0 Journal Article %J Journal of Physics A: Mathematical and Theoretical %D 2016 %T The role of quantum information in thermodynamics—a topical review %A Goold, John %A Huber, Marcus %A Riera, Arnau %A Rio, Lídia del %A Paul Skrzypczyk %B Journal of Physics A: Mathematical and Theoretical %V 49 %P 143001 %G eng %U http://stacks.iop.org/1751-8121/49/i=14/a=143001?key=crossref.ce80cac2171964cc6d6c51ed12d1e014 %R 10.1088/1751-8113/49/14/143001 %0 Journal Article %J Journal of Physics A: Mathematical and Theoretical %D 2015 %T Relaxations of separability in multipartite systems: Semidefinite programs, witnesses and volumes %A Lancien, Cécilia %A Gühne, Otfried %A Sengupta, Ritabrata %A Huber, Marcus %B Journal of Physics A: Mathematical and Theoretical %V 48 %P 505302 %G eng %U http://stacks.iop.org/1751-8121/48/i=50/a=505302?key=crossref.2e93a28de5494676a0b866fa95ccebfd %R 10.1088/1751-8113/48/50/505302 %0 Journal Article %J Communications in Mathematical Physics %D 2014 %T Relative Entropy and Squashed Entanglement %A Ke Li %A Winter, Andreas %B Communications in Mathematical Physics %V 326 %P 63-80 %8 2/2014 %N 1 %! Commun. Math. Phys. %R 10.1007/s00220-013-1871-2 %0 Journal Article %J Physical Review A %D 2013 %T Routing quantum information in spin chains %A Paganelli, Simone %A Lorenzo, Salvatore %A Apollaro, Tony J. G. %A Plastina, Francesco %A Giorgi, Gian Luca %B Physical Review A %V 87 %8 6/2013 %N 6 %! Phys. Rev. A %R 10.1103/PhysRevA.87.062309 %0 Journal Article %J Physica Scripta %D 2010 %T Recycling of qubits %A P Rapcan %A John Calsamiglia %A Muñoz-Tapia, Ramon %A Bagan, Emilio %A V Buzek %X We consider a finite number, N, of qubits that encode a pure single qubit state SU(2) covariantly. Given the N-qubit state has already been measured optimally to estimate the single-qubit state, we analyse the maximum information obtainable by a second, and subsequent observers ignorant of important details of the previous measurements. We quantify the information acquired by each observer as a function of N and of the number of independent observers that in succession have independently measured the same ensemble of qubits before him. %B Physica Scripta %V T140 %P 014059 %U http://iopscience.iop.org/1402-4896/2010/T140/014059?fromSearchPage=true %R 10.1088/0031-8949/2010/T140/014059 %0 Journal Article %J arXiv %D 2007 %T Recycling of quantum information: Multiple observations of quantum systems %A Rapcan, Peter %A John Calsamiglia %A Muñoz-Tapia, Ramon %A Bagan, Emili %A Bużek, Vladimir %X Given a finite number of copies of an unknown qubit state that have already been measured optimally, can one still extract any information about the original unknown state? We give a positive answer to this question and quantify the information obtainable by a given observer as a function of the number of copies in the ensemble, and of the number of independent observers that, one after the other, have independently measured the same ensemble of qubits before him. The optimality of the protocol is proven and extensions to other states and encodings are also studied. According to the general lore, the state after a measurement has no information about the state before the measurement. Our results manifestly show that this statement has to be taken with a grain of salt, specially in situations where the quantum states encode confidential information. %B arXiv %8 08/2007 %G eng %U http://arxiv.org/abs/0708.1086 %0 Journal Article %J Physical Review A (Atomic, Molecular, and Optical Physics) %D 2006 %T Relative states, quantum axes, and quantum references %A Bagan, Emili %A Iblisdir, Sofyan %A Muñoz-Tapia, Ramon %K quantum theory %B Physical Review A (Atomic, Molecular, and Optical Physics) %V 73 %P 022341–6 %8 02/2006 %G eng %U http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PLRAAN000073000002022341000001&idtype=cvips&gifs=yes %R 10.1103/PhysRevA.73.022341