Closed timelike curves and the second law of thermodynamics

Małgorzata Bartkiewicz, Andrzej Grudka, Ryszard Horodecki, Justyna Łodyga, and Jacek Wychowaniec
Phys. Rev. A 99, 022304 – Published 5 February 2019

Abstract

One out of many emerging implications from solutions of Einstein's general relativity equations are closed timelike curves (CTCs), which are trajectories through space-time that allow for time travel to the past without exceeding the speed of light. Two main quantum models of computation with the use of CTCs were introduced by Deutsch (D-CTC) and by Bennett and Schumacher (P-CTC). Unlike the classical theory in which CTCs lead to logical paradoxes, the quantum D-CTC model provides a solution that is logically consistent due to the self-consistency condition imposed on the evolving system, whereas the quantum P-CTC model chooses such a solution through postselection. Both models are nonequivalent and imply nonstandard phenomena in the field of quantum computation and quantum mechanics. In this paper, we study the implications of these two models on the second law of thermodynamics—the fundamental principle which states that in an isolated system the entropy never decreases. In particular, we construct CTC-based quantum circuits which lead to a decrease in entropy.

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  • Received 16 November 2018

DOI:https://doi.org/10.1103/PhysRevA.99.022304

©2019 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyGravitation, Cosmology & AstrophysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Małgorzata Bartkiewicz1, Andrzej Grudka1, Ryszard Horodecki2, Justyna Łodyga1, and Jacek Wychowaniec3,4

  • 1Faculty of Physics, Adam Mickiewicz University, 61-614 Poznań, Poland
  • 2Institute of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, 80-308 Gdańsk, Poland and National Quantum Information Centre of Gdańsk, 81-824 Sopot, Poland
  • 3School of Materials, The University of Manchester, Oxford Road, M13 9PL Manchester, United Kingdom
  • 4Manchester Institute of Biotechnology, The University of Manchester, 131 Princess Street, M1 7DN Manchester, United Kingdom

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Issue

Vol. 99, Iss. 2 — February 2019

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