Titel: Description of two qubit entanglement space in terms of polynomial invariants: A challenge for computer algebra
Startdatum: 02 Mai
Startzeit: 17:15
Stoppzeit: 18:30Uhr
Prof. Dr. Vladimir Gerdt, Joint Institute for Nuclear Research, Dubna, Russia 
Ort: Seminarraum 1403

The entanglement of qubits (quantum bits) provided by their quantum correlations is the main

resource of quantum computation and quantum information processes, e.g., superdense coding,

teleportation and cryptography. By this reason a qualitative and quantative characterization

of entanglement is a topical research problem. We consider computational aspects of

characterising the entanglement space of pure states of a few qubits and qutrits in terms

of hyperdeterminants. Then we analyse two qubit mixed states via the polynomial invariants

of local unitary group $SU(2)\times SU(2)$. Although in the literature a number of computer algebra

based algorithms has been designed for construction of the ring of invariant polynomials,

the underlying computations related to two qubits are too hard for those algorithms. In this

context we restrict ourselves with a subset of the two qubit states containing so-called

$X$-states and investigate its invariant ring.