# 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 vertical bar {psi}><{psi} vertical bar chosen from a family of subsets (C{sub 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{sub n})

- Authors:

- Department of Mathematics, Royal Holloway, University of London (United Kingdom)

- Publication Date:

- OSTI Identifier:
- 20951243

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review Letters; Journal Volume: 98; Journal Issue: 16; Other Information: DOI: 10.1103/PhysRevLett.98.160406; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ENERGY LEVELS; MANY-DIMENSIONAL CALCULATIONS; QUANTUM FIELD THEORY; QUANTUM MECHANICS; SET THEORY

### Citation Formats

```
D'Cruz, Christian, Osborne, Tobias J., and Schack, Ruediger.
```*Finite de Finetti Theorem for Infinite-Dimensional Systems*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVLETT.98.160406.

```
D'Cruz, Christian, Osborne, Tobias J., & Schack, Ruediger.
```*Finite de Finetti Theorem for Infinite-Dimensional Systems*. United States. doi:10.1103/PHYSREVLETT.98.160406.

```
D'Cruz, Christian, Osborne, Tobias J., and Schack, Ruediger. Fri .
"Finite de Finetti Theorem for Infinite-Dimensional Systems". United States.
doi:10.1103/PHYSREVLETT.98.160406.
```

```
@article{osti_20951243,
```

title = {Finite de Finetti Theorem for Infinite-Dimensional Systems},

author = {D'Cruz, Christian and Osborne, Tobias J. and Schack, Ruediger},

abstractNote = {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 vertical bar {psi}><{psi} vertical bar chosen from a family of subsets (C{sub 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{sub n})},

doi = {10.1103/PHYSREVLETT.98.160406},

journal = {Physical Review Letters},

number = 16,

volume = 98,

place = {United States},

year = {Fri Apr 20 00:00:00 EDT 2007},

month = {Fri Apr 20 00:00:00 EDT 2007}

}

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