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A First-Principles Thermodynamic Uncertainty Relation for Shortcuts to Adiabaticity
Guillermo Ezequiel Perna1,2, Federico Centrone3, Esteban Calzetta1,2
1Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Ciudad de Buenos Aires CP 1428, Argentina.
Entropy (Basel, Switzerland)
|May 26, 2026
Summary
Implementing quantum time-dependent protocols faces limitations when using quantum clocks. A new study reveals a thermodynamic uncertainty tradeoff linking precision to purity loss, crucial for quantum control precision.
Area of Science:
- Quantum mechanics
- Quantum information science
- Quantum thermodynamics
Background:
- Time-dependent Hamiltonian protocols are essential for controlling quantum systems.
- Traditionally, 'time' is an external classical parameter, but using a quantum clock introduces fundamental limitations.
- Shortcuts-to-adiabaticity (STA) offer faster control but are sensitive to implementation details.
Purpose of the Study:
- To investigate the fundamental limitations of implementing time-dependent Hamiltonian protocols using a quantum clock.
- To analyze the impact of a minimal clock degree of freedom on the system's dynamics and achievable precision.
- To establish a quantitative relationship between control precision and state purity loss.
Main Methods:
- Studied a parametric harmonic oscillator controlled via an STA schedule.
- Coupled the oscillator to a minimal quantum clock degree of freedom.
- Traced out the clock to derive the effective reduced dynamics.
- Computed energetic deviation, fluctuations, fidelity, and purity loss in a noise-dominated regime for vacuum and coherent states.
Main Results:
- Tracing out the quantum clock leads to a reduced dynamics described by a mixture of unitary Gaussian trajectories.
- In the noise-dominated regime, energetic deviation, fidelity, and purity loss were quantified.
- A thermodynamic-uncertainty-type tradeoff was identified, connecting precision to irreducible purity loss.
Conclusions:
- The precision of quantum control protocols using quantum clocks is fundamentally limited by the clock's precision and protocol sensitivity.
- This limitation manifests as an irreducible loss of quantum state purity.
- The findings are crucial for understanding and optimizing quantum control strategies in realistic noisy quantum systems.
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