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New quantum uncertainty relations for multiple observables in open systems were derived. These multidimensional bounds, accounting for quantum coherence, offer tighter constraints than single-observable relations.

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Area of Science:

  • Quantum Thermodynamics
  • Nonequilibrium Statistical Mechanics
  • Quantum Information Theory

Background:

  • Classical thermodynamic (TUR) and kinetic (KUR) uncertainty relations bound fluctuations in nonequilibrium systems.
  • Violations of classical bounds in open quantum systems necessitate quantum versions accounting for coherence.
  • Existing quantum relations often focus on single observables.

Purpose of the Study:

  • To derive multidimensional kinetic and thermodynamic uncertainty relations for multiple observables in open quantum systems.
  • To investigate the role of quantum coherence and correlations in these bounds.
  • To identify quantum signatures of correlations beyond classical stochastic dynamics.

Main Methods:

  • Development of multidimensional KUR and TUR for Markovian open quantum systems.
  • Utilizing a multiparameter quantum metrology approach centered on the Fisher information matrix.
  • Analysis of correlations between multiple observables.

Main Results:

  • Derived tighter multidimensional quantum uncertainty bounds by incorporating correlations between observables.
  • Identified an off-diagonal Fisher information matrix element as a unique quantum signature of correlations, absent in classical dynamics.
  • Demonstrated saturation of the multidimensional quantum KUR bound in specific systems (driven qubit, three-level maser) under perfect correlation.

Conclusions:

  • Multidimensional quantum uncertainty relations provide enhanced constraints on fluctuations in open quantum systems.
  • Quantum coherence and inter-observable correlations play a crucial role in defining these tighter bounds.
  • The derived framework offers a new perspective on quantum correlations and their signatures in nonequilibrium dynamics.