# Entanglement of assistance and multipartite state distillation

## Abstract

We find that the asymptotic entanglement of assistance of a general bipartite mixed state is equal to the smaller of its two local entropies. Our protocol gives rise to the asymptotically optimal Einstein-Podolsky-Rosen (EPR) pair distillation procedure for a given tripartite pure state, and we show that it actually yields EPR and Greenberger-Horne-Zeilinger (GHZ) states; in fact, under a restricted class of protocols, which we call ''one-way broadcasting,'' the GHZ rate is shown to be optimal. This result implies a capacity theorem for quantum channels where the environment helps transmission by broadcasting the outcome of an optimally chosen measurement. We discuss generalizations to m parties and show (for m=4) that the maximal amount of entanglement that can be localized between two parties is given by the smallest entropy of a group of parties of which the one party is a member, but not the other. This gives an explicit expression for the asymptotic localizable entanglement and shows that any nontrivial ground state of a spin system can be used as a perfect quantum repeater if many copies are available in parallel. Finally, we provide evidence that any unital channel is asymptotically equivalent to a mixture of unitaries and any generalmore »

- Authors:

- IBM T. J. Watson Research Center, Yorktown Heights, New York 10598 (United States)
- Institute for Quantum Information, Caltech 107-81, Pasadena, California 91125 (United States)
- (Germany)
- Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW (United Kingdom)

- Publication Date:

- OSTI Identifier:
- 20786469

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 72; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.72.052317; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; CAPACITY; ENTROPY; GROUND STATES; MIXED STATE; MIXTURES; QUANTUM ENTANGLEMENT; QUANTUM MECHANICS; SPIN

### Citation Formats

```
Smolin, John A., Verstraete, Frank, Max-Planck-Institut fuer Quantenoptik, Hans-Kopfermann-Str.1, 85748 Garching, and Winter, Andreas.
```*Entanglement of assistance and multipartite state distillation*. United States: N. p., 2005.
Web. doi:10.1103/PHYSREVA.72.0.

```
Smolin, John A., Verstraete, Frank, Max-Planck-Institut fuer Quantenoptik, Hans-Kopfermann-Str.1, 85748 Garching, & Winter, Andreas.
```*Entanglement of assistance and multipartite state distillation*. United States. doi:10.1103/PHYSREVA.72.0.

```
Smolin, John A., Verstraete, Frank, Max-Planck-Institut fuer Quantenoptik, Hans-Kopfermann-Str.1, 85748 Garching, and Winter, Andreas. Tue .
"Entanglement of assistance and multipartite state distillation". United States.
doi:10.1103/PHYSREVA.72.0.
```

```
@article{osti_20786469,
```

title = {Entanglement of assistance and multipartite state distillation},

author = {Smolin, John A. and Verstraete, Frank and Max-Planck-Institut fuer Quantenoptik, Hans-Kopfermann-Str.1, 85748 Garching and Winter, Andreas},

abstractNote = {We find that the asymptotic entanglement of assistance of a general bipartite mixed state is equal to the smaller of its two local entropies. Our protocol gives rise to the asymptotically optimal Einstein-Podolsky-Rosen (EPR) pair distillation procedure for a given tripartite pure state, and we show that it actually yields EPR and Greenberger-Horne-Zeilinger (GHZ) states; in fact, under a restricted class of protocols, which we call ''one-way broadcasting,'' the GHZ rate is shown to be optimal. This result implies a capacity theorem for quantum channels where the environment helps transmission by broadcasting the outcome of an optimally chosen measurement. We discuss generalizations to m parties and show (for m=4) that the maximal amount of entanglement that can be localized between two parties is given by the smallest entropy of a group of parties of which the one party is a member, but not the other. This gives an explicit expression for the asymptotic localizable entanglement and shows that any nontrivial ground state of a spin system can be used as a perfect quantum repeater if many copies are available in parallel. Finally, we provide evidence that any unital channel is asymptotically equivalent to a mixture of unitaries and any general channel to a mixture of partial isometries.},

doi = {10.1103/PHYSREVA.72.0},

journal = {Physical Review. A},

number = 5,

volume = 72,

place = {United States},

year = {Tue Nov 15 00:00:00 EST 2005},

month = {Tue Nov 15 00:00:00 EST 2005}

}