Entanglement measures and monotones
- Event time: 11:30am
- Event date: 12th April 2015
- Speaker: Peter Jarvis (School of Mathematics and Physics University of Tasmania)
- Location: Room 2511, James Clerk Maxwell Building (JCMB) James Clerk Maxwell Building Peter Guthrie Tait Road Edinburgh EH9 3FD GB
In quantum physics, the non-intuitive property of nonlocality -- non-independence of measurements carried out on separated subsystems, due to their correlated joint state -- is commonly attributed to 'entanglement'. There is a hunt on to quantify this mysterious entity (after all, one day we may tax it...).
The talk will introduce and exemplify entangled states (wavefunctions), their local unitary invariants, and the notion of entanglement monotones (optimal measures of entanglement). An interesting paper of Oreshkov and Brun* will be described, formulating differential criteria for monotones (via constraint conditions imposed on their partial derivatives with respect to the wavefunction components).
An key case study illustrating all this will be for 2 qubit mixed states. There is a specific inhomogeneous combination of local unitary invariants, which fulfils the Oreshkov-Brun conditions. However, it actually owes its existence in turn, to a cameo appearance of the Lorentz group, in the guise of SL(2,C), the so-called SLOCC (stochastic local operations and classical communication) invariance group.
If there is time, some generalizations will be mentioned: in the quantum case, for qutrits, and in the case of stochastic systems, for probability models in mathematical phylogenetics.
* [Phys. Rev. A 73, 042314 (2006); erratum Phys. Rev. A 76, 059905 (2007)]
This is a roughly weekly series of didactical blackboard talks focussing on some theoretical aspect of Condensed Matter, Biological, and Statistical Physics..