  Unlocking the mystery of the strange metal state has become the focal point
of high T$_{c}$ research, not because of its importance for superconductivity,
but because it appears to represent a truly novel phase of matter dubbed
`quantum supreme matter'. Detected originally through high magnetic field,
transport experiments, signatures of this phase have now been uncovered with a
variety of probes. Our high resolution optical data of the low T$_{c}$ cuprate
superconductor, Bi$_{2-x}$Pb$_{x}$Sr$_{2-y}$La$_{y}$CuO$_{6+\delta}$ allows us
to probe this phase over a large energy and temperature window. We demonstrate
that the optical signatures of the strange metal phase persist throughout the
phase diagram. The strange metal signatures in the optical conductivity are
two-fold, (i): a low energy Drude response with Drude width on the order of
temperature and (ii): a high energy conformal tail with doping dependent
power-law exponent. While the Drude weight evolves monotonously throughout the
entire doping range studied, the spectral weight contained in the high energy
conformal tail appears to be doping and temperature independent. Our analysis
further shows that the temperature dependence of the optical conductivity is
completely determined by the Drude parameters. Our results indicate that there
is no critical doping level inside the superconducting dome where the carrier
density starts to change drastically and that the previously observed 'return
to normalcy' is a consequence of the increasing importance of the Drude
component relative to the conformal tail with doping. Importantly, both the
doping and temperature dependence of the resistivity are largely determined by
the Drude width.
