Thermodynamics Cost of Creating Correlations

Marcus Huber^a,b, Martí Perarnau-LLobet^b, Karen V. Hovhannisyan^b, Paul Skrzypczyk^b, Claude Klöckl^a, Nicolas Brunner^c, and Antonio Acín^b,d

^aDepartament de Física, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain

^bICFO-Institut de Ciències Fotòniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain

^cDépartement de Physique Théorique, Université de Genève, 1211 Genève, Switzerland

^dICREA-Institució Catalana de Recerca i Estudis Avançats, Lluis Companys 23, 08010 Barcelona, Spain

We investigate the fundamental limitations imposed by thermodynamics for creating correlations. Considering a collection of initially uncorrelated thermal quantum systems, we ask how much classical and quantum correlations can be obtained via a cyclic Hamiltonian process. We derive bounds on both the mutual information and entanglement of formation, as a function of the temperature of the systems and the available energy; and we discuss explicit protocols that can saturate such bounds. We also characterize the maximal temperature that allows for the creation of entanglement. In the multipartite

case, we consider several types of entanglement, in particular genuine multipartite and bipartite entanglement. We find an (almost) linear scaling between the number of subsystems and the maximal temperature required to generate (multipartite) entanglement. That is, both bipartite and genuine multipartite entanglement can be created at arbitrary high temperatures if we have enough copies of the system. This approach may find applications, e.g. in quantum information processing, for physical platforms in which thermodynamical considerations cannot be ignored. This work is based on [1], and it is embedded on the recent interest on finding connections between quantum information and thermodynamics (see, for example, [2-4]).

[1] arXiv:1404.2169[quant-ph] (2014).

[2] L. Del Rio, J. Aberg, R. Renner, O. Dahlsten, and V. Vedral, Nature 474, 61 (2011).

[3] F.G.S.L. Brandao \emph{et al.}, Phys. Rev. Lett. 111, 250404 (2013).

[4]K.V. Hovhannisyan, M. Perarnau-Llobet, M. Huber, and A. Acín, Phys. Rev. Lett. 111, 240401 (2013).