## Quantum Entanglement and the Correlation Numerical Range(Joint work with Eli Bashwinger and Mohammad Javaheri) |

**Professor Jon Bannon**

Siena

October 13, 2015

5:00 pm

Bailey Hall 207

Refreshments will be served in Bailey Hall 204 4:45pm

Abstract: One of the fundamental open problems of quantum information theory (Tsirelson's problem) roughly asks whether the quantum correlations between two separated systems described by quantum mechanics agree with those described by quantum field theory. If the answer is 'yes', then certain known estimates of the Bell inequalities describing quantum entanglement are known to be tight, whereas if the answer is 'no', then there must exist quantum correlations that cannot be described using finite-dimensional approximations. Tsirelson's problem is essentially equivalent to a question about a certain generalized numerical range for matrices. The three-dimensional version of this equivalent problem originally required sophisticated computational algebraic geometry to solve, but our recent solution to an elegant related problem posed by Don Hadwin and Deguang Han yields a reasonably easy "bare-hands" solution of the three-dimensional case. We discuss this elegant related problem and the bare-hands solution, and if there is time left over we can discuss what our findings point to regarding quantum correlations.

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