Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Finite de Finetti theorem for infinite-dimensional systems.

Christian D'Cruz1, Tobias J Osborne, Rüdiger Schack

  • 1Department of Mathematics, Royal Holloway, University of London, United Kingdom. C.H.D-Cruz@rhul.ac.uk

Physical Review Letters
|May 16, 2007
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Simulation of a Rohksar-Kivelson ladder on a NISQ device.

Scientific reports·2024
Same author

When will Two Agents Agree on a Quantum Measurement Outcome? Intersubjective Agreement in QBism.

International journal of theoretical physics·2024
Same author

Reviving product states in the disordered Heisenberg chain.

Nature communications·2023
Same author

On the renormalization group fixed point of the two-dimensional Ising model at criticality.

Scientific reports·2023
Same author

Critical Lattice Model for a Haagerup Conformal Field Theory.

Physical review letters·2022
Same author

Training deep quantum neural networks.

Nature communications·2020
Same journal

Erratum: Bacterial Turbulence at Compressible Fluid Interfaces [Phys. Rev. Lett. 136, 138301 (2026)].

Physical review letters·2026
Same journal

Unveiling Light-Quark Yukawa Flavor Structure via Dihadron Fragmentation at Lepton Colliders.

Physical review letters·2026
Same journal

Adaptable Route to Fast Coherent State Transport via Bang-Bang-Bang Protocols.

Physical review letters·2026
Same journal

Topological Transition and Emergence of Elasticity of Dislocation in Skyrmion Lattice: Beyond Kittel's Magnetic-Polar Analogy.

Physical review letters·2026
Same journal

Pound-Drever-Hall Method for Superconducting-Qubit Readout.

Physical review letters·2026
Same journal

Coupling a ^{73}Ge Nuclear Spin to an Electrostatically Defined Quantum Dot in Silicon.

Physical review letters·2026
See all related articles

We proved a de Finetti representation theorem for quantum systems with infinite-dimensional subsystems. Finitely exchangeable states approach mixtures of pure power states as subsystem count increases.

Area of Science:

  • Quantum Information Theory
  • Mathematical Physics
  • Quantum Many-Body Systems

Background:

  • De Finetti's theorem is fundamental in probability and statistical mechanics, relating exchangeability to statistical independence.
  • Extending de Finetti's theorem to quantum systems is crucial for understanding quantum entanglement and correlations.
  • Infinite-dimensional quantum systems present unique challenges due to their continuous nature.

Purpose of the Study:

  • To formulate and prove a de Finetti representation theorem for finitely exchangeable states in quantum systems with infinite-dimensional subsystems.
  • To characterize these states and their asymptotic behavior as the number of subsystems increases.
  • To provide an alternative characterization for the specific family of quantum states considered.

Main Methods:

Related Experiment Videos

  • Formulation of a de Finetti-type theorem tailored for quantum states.
  • Utilizing partial trace operations on pure states from a specific family of symmetric subspaces.
  • Mathematical analysis of the asymptotic behavior of these states for large numbers of subsystems.

Main Results:

  • A de Finetti representation theorem is established for finitely exchangeable quantum states with k infinite-dimensional subsystems.
  • These states are shown to converge to mixtures of pure power states as the number of subsystems (n) grows.
  • An equivalent characterization for the family of quantum state subsets {Cn} is provided.

Conclusions:

  • The study successfully extends de Finetti's theorem to a complex quantum setting.
  • The results offer insights into the statistical properties and emergent behavior of large quantum systems.
  • The findings contribute to a deeper understanding of quantum exchangeability and state characterization.