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Resource Theory of Coherence Based on Positive-Operator-Valued Measures
Felix Bischof1, Hermann Kampermann1, Dagmar Bruß1
1Institut für Theoretische Physik III, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany.
Physical Review Letters
|October 2, 2019
Summary
This study generalizes quantum coherence theory to arbitrary quantum measurements (POVMs). It introduces new coherence measures and operations, extending standard quantum information resource theories.
Area of Science:
- Quantum Information Science
- Quantum Measurement Theory
Background:
- Quantum coherence is essential for quantum information processing.
- Standard coherence theory relies on incoherent states diagonal in a fixed basis, linked to von Neumann measurements.
Purpose of the Study:
- To generalize the resource theory of coherence beyond standard bases.
- To incorporate arbitrary quantum measurements, specifically Positive-Operator-Valued Measures (POVMs).
Main Methods:
- Development of POVM-based coherence measures and operations.
- Utilizing semidefinite programming for state interconversion characterization.
- Analytical derivations for specific cases, such as the qubit trine POVM.
Main Results:
- Established POVM-incoherent operations and coherence measures.
- Demonstrated consistency with standard theory for von Neumann measurements.
- Characterized resource state interconversion using semidefinite programming.
Conclusions:
- The generalized framework expands the scope of quantum coherence resource theories.
- POVMs provide a more general foundation for studying quantum coherence.
- The framework offers new tools for analyzing quantum states and operations.
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