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The first law of general quantum resource theories

Sparaciari, Carlo and del Rio, Lidia and Scandolo, Carlo Maria and Faist, Philippe and Oppenheim, Jonathan (2018) The first law of general quantum resource theories. . (Submitted)

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We extend the tools of quantum resource theories to scenarios in which multiple quantities (or resources) are present, and their interplay governs the evolution of the physical systems. We derive conditions for the interconversion of these resources, which generalise the first law of thermodynamics. We study reversibility conditions for multi-resource theories, and find that the relative entropy distances from the invariant sets of the theory play a fundamental role in the quantification of the resources. The first law for general multi-resource theories is a single relation which links the change in the properties of the system during a state transformation and the weighted sum of the resources exchanged. In fact, this law can be seen as relating the change in the relative entropy from different sets of states. In contrast to typical single-resource theories, the notion of free states and invariant sets of states become distinct in light of multiple constraints. Additionally, generalisations of the Helmholtz free energy, and of adiabatic and isothermal transformations, emerge. We thus have a set of laws for general quantum resource theories, which generalise the laws of thermodynamics. We first test this approach on thermodynamics with multiple conservation laws, and then apply it to the theory of local operations under energetic restrictions.

Item Type:Report or Paper (Discussion Paper)
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Additional Information:We thank the anonymous TQC referees for feedbacks, and Tobias Fritz for detailed comments on a previous version of this manuscript, CS is supported by the EPSRC (grant number EP/L015242/1). LdR acknowledges support from the Swiss National Science Foundation through SNSF project No. 200020 165843 and through the National Centre of Competence in Research Quantum Science and Technology (QSIT), and from the FQXi grant Physics of the observer. CMS is supported by the Engineering and Physical Sciences Research Council (EPSRC) through the doctoral training grant 1652538, and by Oxford-Google DeepMind graduate scholarship. CMS would like to thank the Department of Physics and Astronomy at UCL for their hospitality. PhF acknowledges support from the Swiss National Science Foundation (SNSF) through the Early PostDoc.Mobility Fellowship No. P2EZP2 165239 hosted by the Institute for Quantum Information and Matter (IQIM) at Caltech, from the IQIM which is a National Science Foundation (NSF) Physics Frontiers Center (NSF Grant PHY − 1733907), and from the Department of Energy Award DE − SC0018407. JO is supported by the Royal Society, and by an EPSRC Established Career Fellowship. We thank the COST Network MP1209 in Quantum Thermodynamics.
Group:IQIM, Institute for Quantum Information and Matter
Funding AgencyGrant Number
Swiss National Science Foundation (SNSF)P2EZP2 165239
NSF Physics Frontiers CenterPHY−1733907
Department of Energy (DOE)DE−SC0018407
Engineering and Physical Sciences Research Council (EPSRC)EP/L015242/1
Swiss National Science Foundation (SNSF)200020 165843
Foundational Questions Institute (FQXI)UNSPECIFIED
Engineering and Physical Sciences Research Council (EPSRC)652538
Oxford-Google DeepMind graduate scholarshipUNSPECIFIED
Record Number:CaltechAUTHORS:20190211-154327639
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92841
Deposited By: Bonnie Leung
Deposited On:15 Feb 2019 21:35
Last Modified:03 Oct 2019 20:48

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