Test-Measured Rényi Divergences

One possibility of defining a quantum Rényi $\alpha $ -divergence two states is to optimize the classical their post-measurement probability distributions over all possible measurements (measured divergence), and maybe regularize these quantities multiple copies (regularized measured -divergence). A key observation behind theorem for strong converse exponent asymptotic binary state discrimination that regularized coincides with sandwiched when >1$ . Moreover, it also follows from same achieve this, sufficient consider 2-outcome (tests) any number (this somewhat surprising, as achieving notation="LaTeX">$n$ might require measurement outcomes diverges in , general). In view seems natural expect < 1$ ; however, we show this not case. fact, even commuting (classical case) quantity attainable using general strictly smaller than (which unique case). case shows above “regularized test-measured” extension divergence sharp contrast