# Topology of the three-qubit space of entanglement types

## Abstract

The three-qubit space of entanglement types is the orbit space of the local unitary action on the space of three-qubit pure states and, hence, describes the types of entanglement that a system of three qubits can achieve. We show that this orbit space is homeomorphic to a certain subspace of R{sup 6}, which we describe completely. We give a topologically based classification of three-qubit entanglement types, and we argue that the nontrivial topology of the three-qubit space of entanglement types forbids the existence of standard states with the convenient properties of two-qubit standard states.

- Authors:

- Department of Physics, Lebanon Valley College, Annville, Pennsylvania 17003 (United States)

- Publication Date:

- OSTI Identifier:
- 20786476

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 72; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.72.052324; (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; DATA TRANSMISSION; QUANTUM COMPUTERS; QUANTUM ENTANGLEMENT; QUANTUM MECHANICS; QUBITS; SPACE; TOPOLOGY

### Citation Formats

```
Walck, Scott N., Glasbrenner, James K., Lochman, Matthew H., and Hilbert, Shawn A.
```*Topology of the three-qubit space of entanglement types*. United States: N. p., 2005.
Web. doi:10.1103/PHYSREVA.72.0.

```
Walck, Scott N., Glasbrenner, James K., Lochman, Matthew H., & Hilbert, Shawn A.
```*Topology of the three-qubit space of entanglement types*. United States. doi:10.1103/PHYSREVA.72.0.

```
Walck, Scott N., Glasbrenner, James K., Lochman, Matthew H., and Hilbert, Shawn A. Tue .
"Topology of the three-qubit space of entanglement types". United States.
doi:10.1103/PHYSREVA.72.0.
```

```
@article{osti_20786476,
```

title = {Topology of the three-qubit space of entanglement types},

author = {Walck, Scott N. and Glasbrenner, James K. and Lochman, Matthew H. and Hilbert, Shawn A.},

abstractNote = {The three-qubit space of entanglement types is the orbit space of the local unitary action on the space of three-qubit pure states and, hence, describes the types of entanglement that a system of three qubits can achieve. We show that this orbit space is homeomorphic to a certain subspace of R{sup 6}, which we describe completely. We give a topologically based classification of three-qubit entanglement types, and we argue that the nontrivial topology of the three-qubit space of entanglement types forbids the existence of standard states with the convenient properties of two-qubit standard states.},

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}

}

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