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Thermodynamic Capacity of Quantum Processes.

Philippe Faist1, Mario Berta2, Fernando Brandão1,3

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We introduce a thermodynamic resource theory for quantum processes, defining a "thermodynamic capacity" to quantify their value. This theory becomes reversible in the macroscopic limit, mirroring classical thermodynamics.

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Area of Science:

  • Quantum Thermodynamics
  • Quantum Information Theory
  • Statistical Mechanics

Background:

  • Classical thermodynamics uses free energy to characterize reversible state transformations in the macroscopic limit.
  • Quantum channels, which describe quantum information processing, lack a similar universally reversible characterization.

Purpose of the Study:

  • To develop a thermodynamic resource theory for quantum processes that is reversible in the macroscopic limit.
  • To identify a single-letter, additive quantity characterizing the thermodynamic value of quantum channels.

Main Methods:

  • Formulating a resource theory for quantum channels based on thermodynamic principles.
  • Defining and analyzing the 'thermodynamic capacity' of a quantum channel.
  • Developing asymptotically optimal constructions for universal quantum process implementations.

Main Results:

  • A novel thermodynamic resource theory for quantum processes is presented, which becomes reversible in the macroscopic limit.
  • The 'thermodynamic capacity' is identified as a unique, single-letter, additive quantity quantifying the thermodynamic value of a quantum channel.
  • The work cost to simulate quantum processes is shown to equal the difference in their thermodynamic capacities.

Conclusions:

  • The thermodynamic capacity provides a fundamental measure for quantum channels, analogous to free energy in classical thermodynamics.
  • The results offer a generalized notion of quantum typical subspaces and an operational interpretation for channel entropy differences.
  • This work bridges quantum information theory and thermodynamics, with implications for quantum Shannon theory.