A Finite de Finetti Theorem for Infinite-Dimensional Systems

Abstract

We formulate and prove a de Finetti representation theorem for finitely exchangeable states of a quantum system consisting of k infinite-dimensional subsystems. The theorem is valid for states that can be written as the partial trace of a pure state chosen from a family of subsets C_n of the full symmetric subspace for $n$ subsystems. We show that such states become arbitrarily close to mixtures of pure power states as n increases. We give a second equivalent characterization of the family C_n.

4 pages, 2 figures

References in corpus (9)

• Experimental long-lived entanglement of two macroscopic objects
• Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
• Unknown Quantum States and Operations, a Bayesian View
• Atom--Molecule Coherence in a Bose-Einstein Condensate
• An information-theoretic security proof for QKD protocols
• Unknown Quantum States: The Quantum de Finetti Representation
• A de Finetti representation for finite symmetric quantum states
• A de Finetti Representation Theorem for Quantum Process Tomography
• Entanglement purification of unknown quantum states

Cited by in corpus (9)

• A de Finetti representation theorem for infinite dimensional quantum systems and applications to quantum cryptography
• Symmetry implies independence
• Schur-Weyl Duality for the Clifford Group with Applications: Property Testing, a Robust Hudson Theorem, and de Finetti Representations
• Security of continuous-variable QKD: exploiting symmetries in phase space
• $SU(p,q)$ coherent states and a Gaussian de Finetti theorem
• Client-friendly continuous-variable blind and verifiable quantum computing
• A quantum de Finetti theorem in phase space representation
• Apply current exponential de Finetti theorem to realistic quantum key distribution
• On Exchangeable Continuous Variable Systems