# Resource cost results for one-way entanglement distillation and state merging of compound and arbitrarily varying quantum sources

## Abstract

We consider one-way quantum state merging and entanglement distillation under compound and arbitrarily varying source models. Regarding quantum compound sources, where the source is memoryless, but the source state an unknown member of a certain set of density matrices, we continue investigations begun in the work of Bjelaković et al. [“Universal quantum state merging,” J. Math. Phys. 54, 032204 (2013)] and determine the classical as well as entanglement cost of state merging. We further investigate quantum state merging and entanglement distillation protocols for arbitrarily varying quantum sources (AVQS). In the AVQS model, the source state is assumed to vary in an arbitrary manner for each source output due to environmental fluctuations or adversarial manipulation. We determine the one-way entanglement distillation capacity for AVQS, where we invoke the famous robustification and elimination techniques introduced by Ahlswede. Regarding quantum state merging for AVQS we show by example that the robustification and elimination based approach generally leads to suboptimal entanglement as well as classical communication rates.

- Authors:

- Lehrstuhl für Theoretische Informationstechnik, Technische Universität München, 80290 München (Germany)

- Publication Date:

- OSTI Identifier:
- 22306026

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 8; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMMUNICATIONS; DENSITY MATRIX; QUANTUM ENTANGLEMENT; QUANTUM MECHANICS; QUANTUM STATES

### Citation Formats

```
Boche, H., E-mail: boche@tum.de, and Janßen, G., E-mail: gisbert.janssen@tum.de.
```*Resource cost results for one-way entanglement distillation and state merging of compound and arbitrarily varying quantum sources*. United States: N. p., 2014.
Web. doi:10.1063/1.4893635.

```
Boche, H., E-mail: boche@tum.de, & Janßen, G., E-mail: gisbert.janssen@tum.de.
```*Resource cost results for one-way entanglement distillation and state merging of compound and arbitrarily varying quantum sources*. United States. doi:10.1063/1.4893635.

```
Boche, H., E-mail: boche@tum.de, and Janßen, G., E-mail: gisbert.janssen@tum.de. Fri .
"Resource cost results for one-way entanglement distillation and state merging of compound and arbitrarily varying quantum sources". United States.
doi:10.1063/1.4893635.
```

```
@article{osti_22306026,
```

title = {Resource cost results for one-way entanglement distillation and state merging of compound and arbitrarily varying quantum sources},

author = {Boche, H., E-mail: boche@tum.de and Janßen, G., E-mail: gisbert.janssen@tum.de},

abstractNote = {We consider one-way quantum state merging and entanglement distillation under compound and arbitrarily varying source models. Regarding quantum compound sources, where the source is memoryless, but the source state an unknown member of a certain set of density matrices, we continue investigations begun in the work of Bjelaković et al. [“Universal quantum state merging,” J. Math. Phys. 54, 032204 (2013)] and determine the classical as well as entanglement cost of state merging. We further investigate quantum state merging and entanglement distillation protocols for arbitrarily varying quantum sources (AVQS). In the AVQS model, the source state is assumed to vary in an arbitrary manner for each source output due to environmental fluctuations or adversarial manipulation. We determine the one-way entanglement distillation capacity for AVQS, where we invoke the famous robustification and elimination techniques introduced by Ahlswede. Regarding quantum state merging for AVQS we show by example that the robustification and elimination based approach generally leads to suboptimal entanglement as well as classical communication rates.},

doi = {10.1063/1.4893635},

journal = {Journal of Mathematical Physics},

number = 8,

volume = 55,

place = {United States},

year = {Fri Aug 01 00:00:00 EDT 2014},

month = {Fri Aug 01 00:00:00 EDT 2014}

}