# Observables can be tailored to change the entanglement of any pure state

## Abstract

We show that, for a finite-dimensional Hilbert space, there exist observables that induce a tensor product structure such that the entanglement properties of any pure state can be tailored. In particular, we provide an explicit, finite method for constructing observables in an unstructured d-dimensional system so that an arbitrary known pure state has any Schmidt decomposition with respect to an induced bipartite tensor product structure. In effect, this article demonstrates that, in a finite-dimensional Hilbert space, entanglement properties can always be shifted from the state to the observables and all pure states are equivalent as entanglement resources in the ideal case of complete control of observables.

- Authors:

- Department of Physics, American University, 4400 Massachusetts Ave., NW, Washington, DC 20016-8058 (United States)
- Institut fuer Quantenphysik, Universitaet Ulm, Albert-Einstein-Allee 11, D-89081 Ulm (Germany)

- Publication Date:

- OSTI Identifier:
- 22038609

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. A

- Additional Journal Information:
- Journal Volume: 84; Journal Issue: 1; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; HILBERT SPACE; PURE STATES; QUANTUM ENTANGLEMENT; TENSORS

### Citation Formats

```
Harshman, N. L., and Ranade, Kedar S.
```*Observables can be tailored to change the entanglement of any pure state*. United States: N. p., 2011.
Web. doi:10.1103/PHYSREVA.84.012303.

```
Harshman, N. L., & Ranade, Kedar S.
```*Observables can be tailored to change the entanglement of any pure state*. United States. doi:10.1103/PHYSREVA.84.012303.

```
Harshman, N. L., and Ranade, Kedar S. Fri .
"Observables can be tailored to change the entanglement of any pure state". United States. doi:10.1103/PHYSREVA.84.012303.
```

```
@article{osti_22038609,
```

title = {Observables can be tailored to change the entanglement of any pure state},

author = {Harshman, N. L. and Ranade, Kedar S.},

abstractNote = {We show that, for a finite-dimensional Hilbert space, there exist observables that induce a tensor product structure such that the entanglement properties of any pure state can be tailored. In particular, we provide an explicit, finite method for constructing observables in an unstructured d-dimensional system so that an arbitrary known pure state has any Schmidt decomposition with respect to an induced bipartite tensor product structure. In effect, this article demonstrates that, in a finite-dimensional Hilbert space, entanglement properties can always be shifted from the state to the observables and all pure states are equivalent as entanglement resources in the ideal case of complete control of observables.},

doi = {10.1103/PHYSREVA.84.012303},

journal = {Physical Review. A},

issn = {1050-2947},

number = 1,

volume = 84,

place = {United States},

year = {2011},

month = {7}

}

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