Fundamental Limitations for Measurements in Quantum Many-Body Systems

Area of Science:

• Quantum physics
• Quantum many-body systems
• Quantum simulation

Background:

• Dynamical measurement schemes are crucial for studying quantum many-body systems.
• Quantum simulation advances necessitate efficient measurement techniques.

Purpose of the Study:

• To determine the efficiency of implementing generic quantum measurements.
• To investigate if experimentally realizable measurements can be extended via time evolution.

Main Methods:

• Considered two time evolution scenarios: unitary circuits and controlled Hamiltonians.
• Constructed ϵ-packings for manifolds of observables with identical spectra.
• Compared cardinalities of ϵ-packings and ϵ-coverings for quantum circuits and unitary time-evolution operators.

Main Results:

• The time to achieve a specific measurement accuracy generally scales exponentially with system size.
• This exponential scaling represents a fundamental limitation for generic measurements.

Conclusions:

• Generic quantum measurements are not efficiently implementable in large quantum systems.
• Time evolution, whether via unitary circuits or controlled Hamiltonians, does not overcome this fundamental limitation.