Bound on trace distance based on superfidelity
  We provide a bound for the trace distance between two quantum states. The lower bound is based on the superfidelity, which provides the upper bound on quantum fidelity. One of the advantages of the presented bound is that it can be estimated using a simple measurement procedure. We also compare this bound with the one provided in terms of fidelity. 
Zbigniew Pucha{\l}a, Jaros{\l}aw Adam Miszczak