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Quantum Numbers

Quantum Numbers

It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.

The Quantum-Mechanical Model of an Atom

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.

Short-distance Transport of Resources

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Short-distance transport refers to transport that occurs over a distance of just 2-3 cells, crossing the plasma membrane in the process. Small uncharged molecules, such as oxygen, carbon dioxide, and water, can diffuse across the plasma membrane on their own. In contrast, ions and larger molecules require the assistance of transport proteins due to their charge or size. Transport across membranes also occurs within individual cells, playing a variety of essential roles for the plant as a whole.

Quantifying Work

Quantifying Work

As a system undergoes a change, its internal energy can change, and energy can be transferred from the system to the surroundings, or from the surroundings to the system.

Xylem and Transpiration-driven Transport of Resources

Xylem and Transpiration-driven Transport of Resources

The xylem of vascular plants distributes water and dissolved minerals that are taken up by the roots to the rest of the plant. The cells that transport xylem sap are dead upon maturity, and the movement of xylem sap is a passive process.

Quantifying Heat

Quantifying Heat

Thermal Energy Microscopically, thermal energy is the kinetic energy associated with the random motion of atoms and molecules. Temperature is a quantitative measure of “hot” or “cold”, which depends on the amount of thermal energy. When the atoms and molecules in an object are moving or vibrating quickly, they have a higher average kinetic energy (KE) (or higher thermal energy), and the object is perceived as “hot”, or it is described as being at a higher temperature. When the...

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Related Experiment Video

Updated: Jan 26, 2026

Gradient Echo Quantum Memory in Warm Atomic Vapor

Gradient Echo Quantum Memory in Warm Atomic Vapor

Published on: November 11, 2013

Quantifying Quantum Resources with Conic Programming.

Roope Uola^1,2, Tristan Kraft^1,3, Jiangwei Shang⁴

¹Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Str. 3, D-57068 Siegen, Germany.

Physical Review Letters

|April 24, 2019

Summary

This summary is machine-generated.

Resource theories quantify quantum resources like entanglement and coherence. This study shows robustness measures quantify outperformance in discrimination tasks using conic programming.

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Area of Science:

Quantum Information Science
Quantum Physics
Quantum Computation

Background:

Resource theories formalize quantum resources such as entanglement, asymmetry, coherence, and measurement incompatibility.
These theories enable the quantification and manipulation of these quantum resources.
A key question is whether a given quantum state or measurement can outperform resource-free counterparts in specific tasks.

Purpose of the Study:

To establish a general framework for quantifying quantum resource outperformance.
To demonstrate the connection between robustness measures and task-specific outperformance.
To provide a unified approach for analyzing various quantum resources.

Main Methods:

Utilizing conic programming to analyze resource measures.
Proving that general robustness measures act as quantifiers of outperformance.
Applying the developed technique to diverse quantum information processing scenarios.

Main Results:

Demonstrated that any general robustness measure quantifies outperformance in a discrimination task.
Established a formal link between robustness and the ability to excel in specific quantum tasks.
Showcased the applicability of the method to joint measurability, simulable POVMs, and state assemblages.

Conclusions:

Robustness measures provide a universal way to quantify the advantage of quantum states or measurements in specific tasks.
The conic programming approach offers a powerful tool for resource quantification in quantum information.
This work unifies the understanding of various quantum resources through the lens of task-based outperformance.