Abstract If A is in the p -Schatten class on {R}ⁿ, 1 p 4n/ (2n-1), then the quantum translates of A are linearly independent. Moreover, there exists a nonzero operator in the p -Schatten class on {R}ⁿ, p>4n/ (2n-1), whose quantum translates are linearly dependent.
Mansi Mishra (Mon,) studied this question.