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Trade-Off Between Work and Correlations in Quantum Thermodynamics

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Thermodynamics in the Quantum Regime

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 195))

Abstract

Quantum thermodynamics and quantum information are two frameworks for employing quantum mechanical systems for practical tasks, exploiting genuine quantum features to obtain advantages with respect to classical implementations. While appearing disconnected at first, the main resources of these frameworks, work and correlations, have a complicated yet interesting relationship that we examine here. We review the role of correlations in quantum thermodynamics, with a particular focus on the conversion of work into correlations. We provide new insights into the fundamental work cost of correlations and the existence of optimally correlating unitaries, and discuss relevant open problems.

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Notes

  1. 1.

    Or, more generally, out-of-equilibrium states from which energy can be extracted.

  2. 2.

    We use units where \(\hbar =k_{{{B}}}=1\) throughout.

  3. 3.

    This is one of the most widely used measures of correlations in the context of thermodynamics, which arises quite naturally, due to being a linear function of the von Neumann entropies of the subsystems, and thus directly related to thermodynamical potentials. See also the subsequent discussion.

  4. 4.

    See, e.g., [17] for a pedagogical introduction to entanglement detection via conditional entropies and mutual information.

  5. 5.

    For simplicity here we could consider finite-dimensional systems.

  6. 6.

    Note that the final state need not be entangled.

  7. 7.

    Here, local refers to the collections of subsystems \(A_{1}, \ldots , A_{N}\) and \(B_{1}, \ldots , B_{N}\) for N copies of \(\rho _{{{AB}}}\).

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Acknowledgements

We are grateful to Faraj Bakhshinezhad, Felix Binder, and Felix Pollock for helpful comments and suggestions. We thank Rick Sanchez for moral support. We acknowledge support from the Austrian Science Fund (FWF) through the START project Y879-N27, the Lise-Meitner project M 2462-N27, the project P 31339-N27, and the joint Czech-Austrian project MultiQUEST (I 3053-N27 and GF17-33780L).

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Authors and Affiliations

  1. Institute for Quantum Optics and Quantum Information - IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090, Vienna, Austria

    Giuseppe Vitagliano, Claude Klöckl, Marcus Huber & Nicolai Friis

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  1. Giuseppe Vitagliano
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Correspondence to Giuseppe Vitagliano .

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Editors and Affiliations

  1. School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore

    Felix Binder

  2. School of Mathematical Sciences, University of Nottingham, Nottingham, UK

    Luis A. Correa

  3. ICFO: Institut de Ciencies Fotoniques, Barcelona Institute of Science and Technology, Castelldefels, Spain

    Christian Gogolin

  4. CEMPS, Physics and Astronomy, University of Exeter, Exeter, UK

    Janet Anders

  5. School of Mathematical Sciences, University of Nottingham, Nottingham, UK

    Gerardo Adesso

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Vitagliano, G., Klöckl, C., Huber, M., Friis, N. (2018). Trade-Off Between Work and Correlations in Quantum Thermodynamics. In: Binder, F., Correa, L., Gogolin, C., Anders, J., Adesso, G. (eds) Thermodynamics in the Quantum Regime. Fundamental Theories of Physics, vol 195. Springer, Cham. https://doi.org/10.1007/978-3-319-99046-0_30

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