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Title: 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:
; ; ;  [1]
  1. 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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