# An upper bound on the second order asymptotic expansion for the quantum communication cost of state redistribution

## Abstract

State redistribution is the protocol in which given an arbitrary tripartite quantum state, with two of the subsystems initially being with Alice and one being with Bob, the goal is for Alice to send one of her subsystems to Bob, possibly with the help of prior shared entanglement. We derive an upper bound on the second order asymptotic expansion for the quantum communication cost of achieving state redistribution with a given finite accuracy. In proving our result, we also obtain an upper bound on the quantum communication cost of this protocol in the one-shot setting, by using the protocol of coherent state merging as a primitive.

- Authors:

- Statistical Laboratory, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
- Centre for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology Sydney, NSW 2007 (Australia)
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT (United Kingdom)
- (Singapore)

- Publication Date:

- OSTI Identifier:
- 22596838

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Physics

- Additional Journal Information:
- Journal Volume: 57; Journal Issue: 5; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANNIHILATION OPERATORS; EIGENSTATES; QUANTUM ENTANGLEMENT; QUANTUM INFORMATION; QUANTUM STATES

### Citation Formats

```
Datta, Nilanjana, E-mail: n.datta@statslab.cam.ac.uk, Hsieh, Min-Hsiu, E-mail: Min-Hsiu.Hsieh@uts.edu.au, Oppenheim, Jonathan, E-mail: j.oppenheim@ucl.ac.uk, and Department of Computer Science and Centre for Quantum Technologies, National University of Singapore, Singapore 119615.
```*An upper bound on the second order asymptotic expansion for the quantum communication cost of state redistribution*. United States: N. p., 2016.
Web. doi:10.1063/1.4949571.

```
Datta, Nilanjana, E-mail: n.datta@statslab.cam.ac.uk, Hsieh, Min-Hsiu, E-mail: Min-Hsiu.Hsieh@uts.edu.au, Oppenheim, Jonathan, E-mail: j.oppenheim@ucl.ac.uk, & Department of Computer Science and Centre for Quantum Technologies, National University of Singapore, Singapore 119615.
```*An upper bound on the second order asymptotic expansion for the quantum communication cost of state redistribution*. United States. doi:10.1063/1.4949571.

```
Datta, Nilanjana, E-mail: n.datta@statslab.cam.ac.uk, Hsieh, Min-Hsiu, E-mail: Min-Hsiu.Hsieh@uts.edu.au, Oppenheim, Jonathan, E-mail: j.oppenheim@ucl.ac.uk, and Department of Computer Science and Centre for Quantum Technologies, National University of Singapore, Singapore 119615. Sun .
"An upper bound on the second order asymptotic expansion for the quantum communication cost of state redistribution". United States. doi:10.1063/1.4949571.
```

```
@article{osti_22596838,
```

title = {An upper bound on the second order asymptotic expansion for the quantum communication cost of state redistribution},

author = {Datta, Nilanjana, E-mail: n.datta@statslab.cam.ac.uk and Hsieh, Min-Hsiu, E-mail: Min-Hsiu.Hsieh@uts.edu.au and Oppenheim, Jonathan, E-mail: j.oppenheim@ucl.ac.uk and Department of Computer Science and Centre for Quantum Technologies, National University of Singapore, Singapore 119615},

abstractNote = {State redistribution is the protocol in which given an arbitrary tripartite quantum state, with two of the subsystems initially being with Alice and one being with Bob, the goal is for Alice to send one of her subsystems to Bob, possibly with the help of prior shared entanglement. We derive an upper bound on the second order asymptotic expansion for the quantum communication cost of achieving state redistribution with a given finite accuracy. In proving our result, we also obtain an upper bound on the quantum communication cost of this protocol in the one-shot setting, by using the protocol of coherent state merging as a primitive.},

doi = {10.1063/1.4949571},

journal = {Journal of Mathematical Physics},

issn = {0022-2488},

number = 5,

volume = 57,

place = {United States},

year = {2016},

month = {5}

}

DOI: 10.1063/1.4949571

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