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Optimizing Quantum Measurements by Partitioning Multisets of Observables.
O Veltheim1, E Keski-Vakkuri1,2,3
1University of Helsinki, Department of Physics, P.O. Box 64, FIN-00014 , Finland.
Physical Review Letters
|February 10, 2025
Summary
This study introduces a multiset approach for quantum tomography, minimizing measurements by considering repetitions. This method, linked to graph coloring, offers significant improvements in measurement efficiency.
Area of Science:
- Quantum Information Science
- Quantum Measurement Theory
Background:
- Quantum tomography reconstructs quantum states from measurements.
- Current methods often involve redundant measurements of observables.
Purpose of the Study:
- To develop a more efficient measurement scheme for quantum tomography.
- To minimize the total number of measurements required.
Main Methods:
- Reformulating the problem as a graph theoretic multicoloring problem.
- Utilizing a multiset of observables, accounting for necessary repetitions.
- Applying greedy coloring algorithms for practical implementation.
Main Results:
- The multiset method provides a theoretical upper bound of quadratic improvement in measurement efficiency.
- Demonstrated asymptotically quadratic improvement using greedy coloring algorithms.
- The approach is achievable even for NP-hard optimal coloring problems.
Conclusions:
- A multiset approach to quantum tomography significantly enhances measurement efficiency.
- Graph theory provides a powerful framework for optimizing quantum measurement schemes.
- Practical algorithms offer substantial gains, approaching theoretical limits.
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