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Related Experiment Video

Updated: May 9, 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

Private quantum subsystems.

Tomas Jochym-O'Connor1, David W Kribs, Raymond Laflamme

  • 1Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.

Physical Review Letters
|August 6, 2013
PubMed
Summary
This summary is machine-generated.

We explore private quantum codes, focusing on quantum subsystems and subspaces. Our findings show private subsystems can exist independently of private subspaces, challenging previous assumptions in quantum error correction.

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Last Updated: May 9, 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 Theory
  • Quantum Error Correction
  • Quantum Cryptography

Background:

  • Private quantum codes protect quantum information within specific subsystems or subspaces.
  • Existing theory often links private codes with quantum error-correcting codes through complementarity.
  • The general structure of private quantum codes requires further investigation.

Purpose of the Study:

  • To investigate the most general definition of private quantum codes.
  • To develop testable conditions for the existence of private quantum subsystems.
  • To explore the relationship between private subsystems and private subspaces in quantum channels.

Main Methods:

  • Deriving conditions for private quantum subsystems using Kraus operators.
  • Analyzing quantum channels to identify scenarios where private subsystems exist.
  • Investigating the complementarity between private subsystems and operator quantum error-correcting codes.

Main Results:

  • Established testable conditions for private quantum subsystems, analogous to Knill-Laflamme conditions.
  • Demonstrated the existence of private subsystems in many quantum channels, even without private subspaces.
  • Discovered the first examples of private subsystems not complemented by quantum error-correcting codes.

Conclusions:

  • The complementarity between private codes and quantum error-correcting codes does not hold universally for private quantum subsystems.
  • Private quantum subsystems represent a more general concept than previously understood.
  • New theoretical frameworks are needed to fully characterize general private quantum codes.