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Related Experiment Video

Updated: Nov 26, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

From Quantum Probabilities to Quantum Amplitudes.

Sofia Martínez-Garaot¹, Marisa Pons², Dmitri Sokolovski^1,3

¹Departamento de Química-Física, Universidad del País Vasco, UPV/EHU, 48940 Leioa, Spain.

Entropy (Basel, Switzerland)

|December 11, 2020

Summary

This summary is machine-generated.

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.

Keywords:

Pauli problem quantum measurements quantum particle’s past transition amplitudes weak measurements

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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.