Emily and Brian win URA award!

The Quantum Euler relation will be probed in different contexts to find optimal measurements where the quantum Euler relation becomes tight. The existing quantum Euler relation will be extended to generalized measurements, POVMs, which stands for positive operator-valued measures. POVMs are measures that are semi-definite, positive operators on a Hilbert space. These measurements are a generalization of projective measurements. The main goal of this theoretical research project is to find optimal quantum measurements for the quantum Euler relation. The von Neumann entropy, quantum discord, ergotropy, which is the maximum quantity of work that can be extracted from a quantum system, expectation values, and mutual information are all quantities that will be examined either analytically or numerically.  

            Physical models in higher dimensional states and different master equations are two scenarios in which the tightness of the quantum Euler relation will be explored. In the original paper, a collective dissipation model with particular X-state density matrices was used with a two-qubit system coupled to a thermal bath with an inverse temperature. This collective dissipation model will be used in higher dimensions and with different master equations to find optimal measurements for the quantum Euler relation.