**A frameness measure for mixed states** - Borzumehr Toloui Semnani

Almost all states and operations in the lab involve some degree of mixedness, so it is necessary to extend the results of the newly developed reference frame (RF) resource theories to include mixed states. We will go over different ways of extending measures of frameness to mixed states, and point out some of the differences between entanglement and quantum RFs that need to be taken into account for defining "frameness of formation".
The frameness of formation denotes the average resource cost of generating a mixed state. The cost is measured in terms of standard resource states, called refbits, that are chosen as units of frameness. We will produce explicit results for a qubit's frameness of formation under the group U(1) associated with phases. In order to determine the exact value of this frameness measure, we develop a novel technique that generalizes Wootter's idea for entanglement of formation to RF resource theories. We introduce "concurrence of frameness" as a generalization of the concurrence measure to quantum RFs, and determine the concurrence of a resource state explicitly. Finally, the cost of preparing a resource is expressed as a simple function of this concurrence.