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Three-qubit pure-state canonical forms

A Acín1, A Andrianov1,2, E Jané1 and R Tarrach1

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In this paper we analyse the canonical forms into which any pure three-qubit state can be cast. The minimal forms, i.e. the ones with the minimal number of product states built from local bases, are also presented and lead to a complete classification of pure three-qubit states. This classification is related to the values of the polynomial invariants under local unitary transformations by a one-to-one correspondence.


PACS

03.67.Lx Quantum computation architectures and implementations

02.30.Gp Special functions

03.65.Ud Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.)

MSC

81P68 Quantum computation and quantum cryptography (See also 68Q05, 94A60)

15A21 Canonical forms, reductions, classification

Subjects

Mathematical physics

Computational physics

Quantum information and quantum mechanics

Dates

Issue 35 (7 September 2001)

Received 4 October 2000, in final form 8 May 2001

Published 24 August 2001



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