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Compatibility of Generalized Noisy Qubit Measurements
1University of Vienna, Faculty of Physics, Vienna Center for Quantum Science and Technology (VCQ), Boltzmanngasse 5, 1090 Vienna, Austria and Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria.
Physical Review Letters
|July 12, 2024
Summary
Adding white noise to quantum measurements can make incompatible measurements compatible. This study finds the critical noise level where all qubit measurements, including positive operator-valued measures (POVMs), become jointly measurable, impacting quantum steering and nonlocality.
Area of Science:
- Quantum mechanics
- Quantum information theory
- Quantum foundations
Background:
- Quantum measurements are generally incompatible, meaning they cannot be performed simultaneously without disturbing the system.
- Noise can affect the compatibility of quantum measurements.
Purpose of the Study:
- To determine the critical noise level at which all qubit measurements become compatible.
- To investigate the impact of noise-induced compatibility on quantum steering and Bell nonlocality.
Main Methods:
- Analysis of white noise effects on measurement incompatibility.
- Derivation of the critical visibility threshold for joint measurability of all positive operator-valued measures (POVMs) on qubits.
- Application of these findings to two-qubit Werner states.
Main Results:
- Identified the critical visibility for achieving joint measurability of all qubit POVMs under white noise.
- Developed a tight local hidden state model for two-qubit Werner states with visibility 1/2.
- Established the exact steering bound for these states.
- Provided an improved local hidden variable model.
Conclusions:
- White noise can render incompatible quantum measurements compatible.
- POVMs do not offer an advantage over projective measurements for demonstrating quantum steering with two-qubit Werner states at visibility 1/2.
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