The paper proves that trace distance, geometric, and fidelity-based quantities are valid quantum-state texture measures, and that l1-norm, relative entropy, and robustness are not suitable.
How- ever, for trace distance, we have Ttr(σα ) = 3 −α 4 , Ttr(τα ) = 1 4 (1 −α + √ α2 + 2α + 5)
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Quantifying quantum-state texture
The paper proves that trace distance, geometric, and fidelity-based quantities are valid quantum-state texture measures, and that l1-norm, relative entropy, and robustness are not suitable.