Polynomial invariants of four qubits

By Jean-Gabriel Luque, Jean-Yves Thibon. 2002

182 citations recorded by the source corpus.

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){sup 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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/8a9471e4195a379c2c14c54350366eb95ca05f01

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Ingemar Bengtsson
2. Giorgio Ottaviani
3. Karol Zyczkowski

In Atomic and Molecular Physics, and Optics

1. D. Dahanayake
2. Ingemar Bengtsson
3. W. Rubens
4. H. Ebrahim
5. Karol Zyczkowski
6. M. Duff
7. L. Borsten

Citations in the corpus

• Induction for secant varieties of Segre varieties (2006, background): “made several appearances in the recent physics literature (see for example [ LT ] and the literature quoted therein).”
• Geometry of Quantum States: Index (2007, background): “Polynomial invariants are known for four [590, 628] and five qubits [629], although the results for the latter are partial only.”
• Black Holes, Qubits and Octonions (2008, background): “For M-theory The STU black hole entropy is described by the 2× 2× 2 hyperdeterminant, but there is a much richer mathematical structure behind the theory of more general hyperdeterminants [24] which also enters the classification of entanglement invariants [18, 106, 69, 227].”