Cohomology in algebra, geometry, physicsand statistics

Classification of four qubit and rebit states

Speaker’s name:

Willem de Graaf

Speaker’s affiliation:

University of Trento

Place:

ZOOM meeting

Date:

Wednesday, 11. May 2022 - 13:30 to 14:30

Abstract:

We consider the problem of classifying the orbits of SL(2, C) ^4 on the space

C^2 ⊗ C^2 ⊗ C^2 ⊗ C^2. In quantum information theory this is known as the

classification of four qubit states under SLOCC operations. We approach

the problem by constructing the representation via a symmetric pair of max-

imal rank. This makes it possible to apply the theory of θ-representations

developed by Vinberg in the 70’s. The orbits are devided into three types:

nilpotent, semisimple and mixed. The orbits of each type are classified sep-

arately. We also obtain the stabilizers of representatives of the orbits. The

talk will end with some comments on the same problem over R, known as

the classification of four rebit states. This is joint work with Heiko Dietrich,

Alessio Marrani and Marcos Origlia.

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We open ZOOM at 13.15 for virtual cafe and close at 15.00.

Join Zoom Meeting

https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09

Meeting ID: 995 9841 3922

Passcode: Galois

C^2 ⊗ C^2 ⊗ C^2 ⊗ C^2. In quantum information theory this is known as the

classification of four qubit states under SLOCC operations. We approach

the problem by constructing the representation via a symmetric pair of max-

imal rank. This makes it possible to apply the theory of θ-representations

developed by Vinberg in the 70’s. The orbits are devided into three types:

nilpotent, semisimple and mixed. The orbits of each type are classified sep-

arately. We also obtain the stabilizers of representatives of the orbits. The

talk will end with some comments on the same problem over R, known as

the classification of four rebit states. This is joint work with Heiko Dietrich,

Alessio Marrani and Marcos Origlia.

--------------------------------------------------------------------------------------------------------------------------------------------------

We open ZOOM at 13.15 for virtual cafe and close at 15.00.

Join Zoom Meeting

https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09

Meeting ID: 995 9841 3922

Passcode: Galois