Polynomial invariants of four qubits

被引：147

作者：

Luque, JG ^{[1
]}

Thibon, JY ^{[1
]}

机构：

[1] Univ Marne La Vallee, Inst Gaspard Monge, F-77454 Marne La Vallee, France

来源：

PHYSICAL REVIEW A | 2003年 / 67卷 / 04期

关键词：

D O I：

10.1103/PhysRevA.67.042303

中图分类号：

O43 [光学];

学科分类号：

070207 ; 0803 ;

摘要：

We describe explicitly the algebra of polynomial functions on the Hilbert space of four-qubit states that are invariant under the group SL(2,C)(4) of stochastic local quantum operations assisted by classical communication. From this description, we obtain a closed formula for the hyperdeterminant in terms of low degree invariants.

引用

页数：5

共 50 条

[1] On polynomial invariants of several qubits
Dokovic, D. Z.
Osterloh, A.
JOURNAL OF MATHEMATICAL PHYSICS, 2009, 50 (03)
[2] On the ring of local polynomial invariants for a pair of entangled qubits
Gerdt V.
Khvedelidze A.
Palii Y.
Journal of Mathematical Sciences, 2010, 168 (3) : 368 - 378
[3] SLOCC polynomial invariants of degree 6 for even n qubits
Li, Xiangrong
Li, Dafa
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2013, 46 (13)
[4] On polynomial invariants of several qubits (vol 50, 033509, 2009)
Dokovic, Dragomir Z.
Osterloh, Andreas
JOURNAL OF MATHEMATICAL PHYSICS, 2012, 53 (04)
[5] Polynomial invariants of four-dimensional orthogonal groups
Chu, H
COMMUNICATIONS IN ALGEBRA, 2001, 29 (03) : 1153 - 1164
[6] Polynomial invariants of degree 4 for even-n qubits and their applications in entanglement classification
Li, Xiangrong
Li, Dafa
PHYSICAL REVIEW A, 2013, 88 (02):
[7] POLYNOMIAL INVARIANTS ARE POLYNOMIAL
Bar-Natan, Dror
MATHEMATICAL RESEARCH LETTERS, 1995, 2 (03) : 231 - 238
[8] Polynomial invariants for discrimination and classification of four-qubit entanglement
Viehmann, Oliver
Eltschka, Christopher
Siewert, Jens
PHYSICAL REVIEW A, 2011, 83 (05):
[9] Algebraic invariants of five qubits
Luque, JG
Thibon, JY
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2006, 39 (02): : 371 - 377
[10] ON THE GEOMETRY AND INVARIANTS OF QUBITS, QUARTITS AND OCTITS
Planat, M.
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 2011, 8 (02) : 303 - 313

← 1 2 3 4 5 →