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Related Concept Videos

Quantum Numbers02:43

Quantum Numbers

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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.
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The Quantum-Mechanical Model of an Atom02:45

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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.
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The de Broglie Wavelength02:32

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In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
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Atomic Nuclei: Nuclear Spin State Overview01:03

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NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of...
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The Pauli Exclusion Principle03:06

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The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
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Free Energy Changes for Nonstandard States03:25

Free Energy Changes for Nonstandard States

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The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 1 bar; concentrations other than 1 M) is related to the standard free energy change according to this equation:
 
where R is the gas constant (8.314 J/K·mol), T is the absolute temperature in kelvin, and Q is the reaction quotient. This equation may be used to predict the spontaneity of a process under any given set of conditions.
Reaction Quotient...
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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
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Pseudomagic Quantum States.

Andi Gu1, Lorenzo Leone2,3, Soumik Ghosh4

  • 1Department of Physics, Harvard University, 17 Oxford Street, Cambridge, Massachusetts 02138, USA.

Physical Review Letters
|June 10, 2024
PubMed
Summary
This summary is machine-generated.

We introduce pseudomagic quantum states that appear computationally simple but are complex. These states reveal that quantum magic is a hidden property, not always apparent to observers with limited computational power.

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Area of Science:

  • Quantum Information Science
  • Quantum Computing Theory

Background:

  • Nonstabilizerness quantifies the nonclassical nature of quantum states, crucial for quantum advantage.
  • Low nonstabilizerness in quantum states limits potential quantum computational advantage.

Purpose of the Study:

  • Introduce "pseudomagic" ensembles of quantum states.
  • Investigate the relationship between pseudomagic and pseudoentanglement.
  • Explore applications in quantum scrambling, state synthesis, property testing, and cryptography.

Main Methods:

  • Define and analyze pseudomagic ensembles.
  • Compare pseudomagic with pseudoentanglement.
  • Examine computational indistinguishability from the perspective of bounded observers.

Main Results:

  • Pseudomagic states are computationally indistinguishable from high nonstabilizerness states despite having low nonstabilizerness.
  • Pseudomagic does not follow from nor imply pseudoentanglement.
  • Identified states from nonscrambling unitaries that are indistinguishable from scrambled states.

Conclusions:

  • Nonstabilizerness is a "hide-able" characteristic of quantum states.
  • Findings offer new insights into quantum scrambling and computational complexity.
  • Demonstrate the physical significance of quantities measurable by computationally bounded observers.