  We investigate whether future measurements of high redshift standard candles
(HzSCs) will be a powerful probe of dark energy, when compared to other types
of planned dark energy measurements. Active galactic nuclei and gamma ray
bursts have both been proposed as potential HzSC candidates. Due to their high
luminosity, they can be used to probe unexplored regions in the expansion
history of the universe. Information from these regions can help constrain the
properties of dark energy, and in particular, whether it varies over time.
  We consider both linear and piecewise parameterizations of the dark energy
equation of state, $w(z)$, and assess the optimal redshift distribution a
high-redshift standard-candle survey could take to constrain these models.
  The more general the form of the dark energy equation of state $w(z)$ being
tested, the more useful high-redshift standard candles become. For a linear
parameterization of $w(z)$, HzSCs give only small improvements over planned
supernova and baryon acoustic oscillation measurements; a wide redshift range
with many low redshift points is optimal to constrain this linear model.
However to constrain a general, and thus potentially more informative, form of
$w(z)$, having many HzSCs can significantly improve limits on the nature of
dark energy.
