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Generation and Coherent Control of Pulsed Quantum Frequency Combs

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Phase-space quantum Wiener-Khintchine theorem.

Ainara Álvarez-Marcos, Alfredo Luis

|September 15, 2022

Summary

This summary is machine-generated.

We developed a quantum Wiener-Khintchine theorem for phase-space displacement detection. This quantum ruler approach reveals a universal link between measurement resolution and coherence for quantum states.

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Area of Science:

Quantum optics
Quantum information theory
Phase-space quantum mechanics

Background:

The classical Wiener-Khintchine theorem relates a signal's autocorrelation function to its power spectral density.
Extending classical optical theorems to the quantum realm is crucial for understanding quantum measurement and information transfer.
Phase-space representations offer a powerful tool for analyzing quantum states and dynamics.

Purpose of the Study:

To derive a quantum mechanical analogue of the classical-optics Wiener-Khintchine theorem.
To introduce a phase-space-based quantum mutual coherence function incorporating detector effects.
To establish a fundamental relationship between measurement resolution and coherence in quantum detection.

Main Methods:

Derivation of a quantum Wiener-Khintchine theorem using a quantum ruler for phase-space displacement detection.
Introduction and analysis of a phase-space quantum mutual coherence function.
Application of the derived framework to specific quantum states, including Gaussian and number states.

Main Results:

A quantum version of the Wiener-Khintchine theorem is established for phase-space measurements.
A novel quantum mutual coherence function is defined, accounting for detector contributions.
An universal equality connecting measurement resolution and coherence is derived.

Conclusions:

The study provides a quantum framework for analyzing phase-space measurements, analogous to classical spectral analysis.
The derived equality offers new insights into the trade-offs between measurement precision and quantum coherence.
The findings are demonstrated to be applicable to important quantum states, validating the theoretical framework.