For a noisy quantum channel, a quantum error correcting code exists if and only if the joint higher rank numerical ranges associated with the error operators of the channel is non-empty. In this paper, geometric properties of the joint higher rank numerical ranges are obtained and their implications to quantum computing are discussed. It is shown that if the dimension of the underlying Hilbert ...

Associated with every commuting m-tuples of operators on a complex Hilbert space X is its Aluthge transform. In this paper we show that and transform have the same joint essential spectrum. Further, it shown spectrum contained in numerical range

background:  the glenohumeral joint becomes dislocated more than any other major joint because it maintains a wide range of motion and its stability is inherently weak. the most common complication following acute initial shoulder dislocation is recurrent dislocation or chronic instability. imbalance of strength and range of motion in individuals with anterior dislocation can be a contributing ...

In this note, a generalization of higher rank numerical range isintroduced and some of its properties are investigated