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The Quantum-Mechanical Model of an Atom02:45

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. Schrödinger...
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Norton's Theorem01:14

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Second Uniqueness Theorem01:16

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Related Experiment Video

Updated: Jul 16, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Verifier-initiated quantum message-authentication via quantum zero-knowledge proofs.

Wusheng Wang1, Masahito Hayashi2,3,4

  • 1Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya, 464-8602, Aichi, Japan.

Nature Communications
|July 14, 2026
PubMed
Summary

We introduce verifier-initiated quantum digital signatures (VIQDS) for scalable quantum systems. This approach reduces overhead by allowing on-demand authentication, enhancing security and privacy without computational assumptions.

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Last Updated: Jul 16, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Area of Science:

  • Quantum Information Science
  • Cryptography
  • Computer Science

Background:

  • Scalable quantum systems require efficient authentication methods.
  • Existing quantum signature schemes are often signer-initiated, leading to unnecessary overhead.
  • On-demand authentication is crucial for sporadic verification needs in distributed systems.

Purpose of the Study:

  • To introduce verifier-initiated quantum digital signatures (VIQDS) for on-demand authentication.
  • To reduce communication and storage overhead in quantum authentication workflows.
  • To enhance security and privacy in quantum signature schemes.

Main Methods:

  • Leveraging quantum zero-knowledge techniques for secure verification.
  • Developing a general conversion principle from quantum proofs to VIQDS.
  • Implementing a concrete VIQDS protocol using elementary qubit platforms.

Main Results:

  • Demonstrated a verifier-initiated approach to quantum digital signatures.
  • Achieved information-theoretic security against forgery.
  • Ensured privacy against curious verifiers without computational hardness assumptions.

Conclusions:

  • VIQDS offers a practical and efficient solution for on-demand authentication in quantum systems.
  • The proposed method enhances security and privacy while minimizing resource utilization.
  • This work provides a foundation for future secure and scalable quantum communication infrastructures.