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Area of Science:

  • Quantum Information Science
  • Theoretical Physics
  • Mathematical Physics

Background:

  • Analogue Hamiltonian simulation is a key quantum computing application with experimental success.
  • Duality in physics relates seemingly different theories.
  • Current Hamiltonian simulation definitions don't cover all physical dualities.

Purpose of the Study:

  • Generalize the definition of duality in physics.
  • Develop a framework applicable to all dualities, including those transforming strong and weak interactions.
  • Characterize dual maps on operators and states.

Main Methods:

  • Introduced a generalized definition of duality.
  • Characterized dual maps for operators and states.
  • Proved duality equivalence via observables, partition functions, and entropies.
  • Extended results on entropy-preserving maps to include an additive constant.

Main Results:

  • A generalized duality definition is established, encompassing strong-weak interaction transformations.
  • Equivalence of duality is proven for observables, partition functions, and entropies.
  • A new class of maps preserving entropy up to an additive constant is introduced.
  • These maps decompose into unitary and antiunitary components.

Conclusions:

  • The generalized duality framework broadens the applicability of Hamiltonian simulations.
  • The characterization of dual maps provides new tools for theoretical physics.
  • The mathematical properties of entropy-preserving maps offer independent interest.