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From Quantum Probabilities to Quantum Amplitudes
Sofia Martínez-Garaot1, Marisa Pons2, Dmitri Sokolovski1,3
1Departamento de Química-Física, Universidad del País Vasco, UPV/EHU, 48940 Leioa, Spain.
Entropy (Basel, Switzerland)
|December 11, 2020
Summary
Researchers can now recover quantum system path amplitudes using three measurements. This method, unlike the Pauli problem, utilizes unique interference from three-step histories and fuzzy intermediate measurements for accurate reconstruction.
Area of Science:
- Quantum mechanics
- Quantum information theory
- Quantum state reconstruction
Background:
- The Pauli problem, reconstructing quantum states from measurements, typically involves two steps: preparation and measurement.
- Existing methods for state reconstruction are limited in scope and complexity.
Purpose of the Study:
- To generalize the Pauli problem by recovering Feynman's transition amplitudes from at least three consecutive measurements.
- To explore the potential of three-step quantum histories and interference for amplitude recovery.
Main Methods:
- Analyzing quantum systems with pre- and post-selected histories involving at least three measurements.
- Exploiting unique quantum interference patterns arising from three-step histories.
- Utilizing 'fuzzy' or weak intermediate measurements to enable path amplitude recovery.
Main Results:
- Demonstrated that three-step histories exhibit interference effects not present in two-step processes.
- Showed that fuzzy intermediate measurements allow for the successful recovery of path amplitudes.
- Analyzed the specific case of a two-level quantum system in detail.
Conclusions:
- The proposed method extends quantum state reconstruction beyond the limitations of the Pauli problem.
- Fuzzy measurements in three-step quantum histories offer a novel pathway to reconstruct transition amplitudes.
- The recovered path amplitudes have potential applications in understanding and manipulating quantum systems.
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