Quantum Information Theory

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Quantum Thermodynamics

We study thermodynamics both at the quantum scale and otherwise, and from both a foundational and information-theoretic perspective.

Thermodynamics is a highly successful macroscopic theory that is widely used across the natural sciences and for the construction of everyday devices, from car engines and fridges to power plants and solar cells. A key feature is its independence from the specific physics of the system it describes, so that it can be indiscriminately applied to gases, magnets and quantum many-body systems alike.

Members of our group pursue several directions of research in this field, including

  • the axiomatic foundations of thermodynamics
  • the interface between information theory and thermodynamics
  • processes away from ideal thermodynamic limits of equilibrium, reversibility, control
  • the limits imposed on thermodynamics by the imperfect nature of quantum clocks and vice-versa
  • thermodynamic properties of many-body systems

Processes away from ideal thermodynamic limits  

An important line of research is into processes that take place away from the ideal thermodynamic limits of reversibility, equilibrium, unbounded thermal machines, and infinite thermal baths. It has been shown that imperfect thermalisation is sufficient to achieve optimal processes [1]. We can also consider the limits to cooling quantum systems using only finite-sized thermal machines and determine, for instance, cooling bounds applicable to any paradigm of quantum thermodynamics [2]. Another idealisation to get rid of is that of perfect control and timing, which is fundamentally impossible for truly quantum mechanical operations. We have shown that using good-enough quantum clocks, one can have the quantum back-reaction small enough to maintain the validity of thermodynamic laws at the quantum scale [3]. The converse direction of research is also of interest, that of the limits to quantum clocks from thermodynamics [4].

References

  1. Elisa Bäumer, Martí Perarnau-Llobet, Philipp Kammerlander, Henrik Wilming and Renato Renner. Imperfect thermalizations allow for optimal thermodynamic processes. Quantum 3, 153 (2019). external pagedoi: 10.22331/q-2019-06-24-153
  2. Fabien Clivaz, Ralph Silva, Géraldine Haack, Jonatan Bohr Brask, Nicolas Brunner and Marcus Huber. Unifying paradigms of quantum refrigeration: a universal and attainable bound on cooling. Phys. Rev. Lett. 123, 170605 (2019). external pagedoi: 10.1103/PhysRevLett.123.170605 external pagearXiv:1903.04970
  3. Mischa P. Woods and Michał Horodecki. The resource theoretic paradigm of quantum thermodynamics with control. external pagearXiv:1912.05562
  4. Paul Erker, Mark T. Mitchison, Ralph Silva, Mischa P. Woods, Nicolas Brunner and Marcus Huber. Autonomous quantum clocks: does thermodynamics limit our ability to measure time? Phys. Rev. X 7, 031022 (2017). external pagedoi: 10.1103/PhysRevX.7.031022 
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Work fluctuations during thermodynamic processes

A further cornerstone of thermodynamics research is to characterise the fluctuations in work during thermodynamic processes. We have investigated unique limitations on doing so for quantum coherent processes [1], and introduced novel methods of measuring work fluctuations that capture quantum interference phenomena [2]. In addition, we studied the use of catalysts to bypass fluctuation theorems on work extraction [3] and fundamental lower bounds to the work required for quantum processes [4].

The tools of information theory can also be put to use in thermodynamics, which has proved very fruitful. Our group has done research on the connection between the notions of thermodynamic and information entropies [5], uniquely quantum information-processing tasks with a thermodynamic work cost [6], the thermodynamic capacity of quantum channels [7], and the generalisation of thermodynamic laws in the presence of multiple conserved charges [8].

Members of the group are also engaged in research into the behaviour of quantum many-body systems and their connection to thermodynamics and quantum information theory. This includes exploring the role that entanglement has in thermodynamic properties, such as for how well they equilibrate [9] or fail to do so [10], and how to interpret the 'area law of entanglement' from an information-theoretic point of view [11]. We also showed, using resource theories, how thermodynamic potentials arise in many-body systems [12].

Finally, from a foundational perspective, one can re-examine the axioms that serve as the building blocks of thermodynamics [13]. This is important for the application of thermodynamics to systems where the microscopic physics is not yet fully understood, such as black holes. It might also lead to new insights into established axioms, for example, into the zeroth law of thermodynamics, which we showed to be a consequence of the first and second laws rather than an independent postulate [14]. Conversely, we can use thermodynamics itself as a template for more general resource theories, with their own sets of laws, free states, and notions of adiabatic and isothermal transformations [15].

References

  1. Martí Perarnau-Llobet, Elisa Bäumer, Karen V. Hovhannisyan, Marcus Huber and Antonio Acín. No-go theorem for the characterisation of work fluctuations in coherent quantum systems. Phys. Rev. Lett. 118, 070601 (2017). external pagedoi: 10.1103/PhysRevLett.118.070601 external pagearXiv:1606.08368
  2. Elisa Bäumer, Matteo Lostaglio, Martí Perarnau-Llobet and Rui Sampaio. Fluctuating work in coherent quantum systems: proposals and limitations. In: Binder F., Correa L., Gogolin C., Anders J., Adesso G. (eds) Thermodynamics in the Quantum Regime. Fundamental Theories of Physics, vol. 195 (2018). external pagedoi: 10.1007/978-3-319-99046-0_11 external pagearXiv:1805.10096
  3. Paul Boes, Rodrigo Gallego, Nelly H. Y. Ng, Jens Eisert and Henrik Wilming. By-passing fluctuation theorems. Quantum 4, 231 (2020). external pagedoi: 10.22331/q-2020-02-20-231
  4. Philippe Faist and Renato Renner. Fundamental work cost of quantum processes. Phys. Rev. X 8, 021011 (2018). external pagedoi: 10.1103/PhysRevX.8.021011
  5. Mirjam Weilenmann, Lea Krämer, Philippe Faist and Renato Renner. Axiomatic relation between thermodynamic and information-theoretic entropies. Phys. Rev. Lett. 117, 260601 (2016). external pagedoi: 10.1103/PhysRevLett.117.260601 external pagearXiv:1501.06920
  6. Philipp Kammerlander and Janet Anders. Coherence and measurement in quantum thermodynamics. Sci. Rep. 6, 22174 (2016). external pagedoi: 10.1038/srep22174
  7. Philippe Faist, Mario Berta and Fernando Brandão. Thermodynamic capacity of quantum processes. Phys. Rev. Lett. 122, 200601 (2019). external pagedoi: 10.1103/PhysRevLett.122.200601 external pagearXiv:1807.05610
  8. Nicole Yunger Halpern, Philippe Faist, Jonathan Oppenheim and Andreas Winter. Microcanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charges. Nat. Commun. 7, 12051 (2016). external pagedoi: 10.1038/ncomms12051
  9. Henrik Wilming, Marcel Goihl, Ingo Roth and Jens Eisert. Entanglement-ergodic quantum systems equilibrate exponentially well. Phys. Rev. Lett. 123, 200604 (2019). external pagedoi: 10.1103/PhysRevLett.123.200604 external pagearXiv:1802.02052
  10. Álvaro M. Alhambra, Anurag Anshu, Henrik Wilming. Revivals imply quantum many-body scars. Phys. Rev. B 101, 205107 (2020). external pagedoi:10.1103/PhysRevB.101.205107 external pagearXiv:1911.05637
  11. Henrik Wilming and Jens Eisert. Single-shot holographic compression from the area law. Phys. Rev. Lett. 122, 190501 (2019). external pagedoi: 10.1103/PhysRevLett.122.190501 external pagearXiv:1809.10156
  12. Philippe Faist, Takahiro Sagawa, Kohtaro Kato, Hiroshi Nagaoka and Fernando G. S. L. Brandão. Macroscopic thermodynamic reversibility in quantum many-body systems. Phys. Rev. Lett. 123, 250601 (2019). external pagedoi: 10.1103/PhysRevLett.123.250601 external pagearXiv:1907.05651
  13. Philipp Kammerlander and Renato Renner. Tangible phenomenological thermodynamics. external pagearXiv:2002.08968
  14. Philipp Kammerlander and Renato Renner. The zeroth law of thermodynamics is redundant. external pagearXiv:1804.09726
  15. Carlo Sparaciari, Lidia del Rio, Carlo Maria Scandolo, Philippe Faist and Jonathan Oppenheim. The first law of general quantum resource theories. Quantum 4, 259 (2020). external pagedoi: 10.22331/q-2020-04-30-259

Further reading

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