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Weak values of a quantum observable and the cross-Wigner distribution
Maurice A de Gosson1, Serge M de Gosson
1University of Vienna, Faculty of Mathematics, NuHAG, A-1090 Vienna, Austria.
Physics Letters. A
|February 3, 2012
Summary
This study uses Wigner formalism to analyze quantum weak values, revealing they arise from the interference of past and future wavefunctions. This approach connects quantum mechanics to radar theory via the cross-Wigner transform.
Area of Science:
- Quantum mechanics
- Quantum information theory
- Time-frequency analysis
Background:
- Weak values offer unique insights into quantum systems.
- The Wigner formalism provides a phase-space representation of quantum mechanics.
- Connections between quantum mechanics and classical signal processing are increasingly explored.
Purpose of the Study:
- To investigate quantum weak values using the Wigner formalism.
- To explore the relationship between weak values and the cross-Wigner transform.
- To provide a new perspective on the physical interpretation of weak values.
Main Methods:
- Utilizing the Wigner formalism to study quantum observables.
- Employing the cross-Wigner transform, also known as the cross-ambiguity function.
- Expressing weak values in terms of a complex probability distribution.
Main Results:
- The cross-Wigner transform is identified as a key tool for analyzing weak values.
- Weak values are successfully expressed using a complex probability distribution.
- The study provides a framework for understanding weak values as arising from wavefunction interference.
Conclusions:
- The Wigner formalism offers a powerful lens for understanding quantum weak values.
- The cross-Wigner transform provides a bridge between quantum weak values and classical signal processing concepts.
- The findings support the conjecture that weak values result from the interference of past and future quantum states.
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