  We present Atacama Large Millimeter/submillimeter Array (ALMA) observations
of the binary Class 0 protostellar system BHR 71 IRS1 and IRS2 as part of the
Early Planet Formation in Embedded Disks (eDisk) ALMA Large Program. We
describe the $^{12}$CO ($J$=2--1), $^{13}$CO ($J$=2--1), C$^{18}$O ($J$=2--1),
H$_2$CO ($J=3_{2,1}$--$2_{2,0}$), and SiO ($J$=5--4) molecular lines along with
the 1.3 mm continuum at high spatial resolution ($\sim$0.08" or $\sim$5 au).
Dust continuum emission is detected toward BHR 71 IRS1 and IRS2, with a central
compact component and extended continuum emission. The compact components are
smooth and show no sign of substructures such as spirals, rings or gaps.
However, there is a brightness asymmetry along the minor axis of the presumed
disk in IRS1, possibly indicative of an inclined geometrically and optically
thick disk-like component. Using a position-velocity diagram analysis of the
C$^{18}$O line, clear Keplerian motions were not detected toward either source.
If Keplerian rotationally-supported disks are present, they are likely deeply
embedded in their envelope. However, we can set upper limits of the central
protostellar mass of 0.46 M$_\odot$ and 0.26 M$_\odot$ for BHR 71 IRS1 and BHR
71 IRS2, respectively. Outflows traced by $^{12}$CO and SiO are detected in
both sources. The outflows can be divided into two components, a wide-angle
outflow and a jet. In IRS1, the jet exhibits a double helical structure,
reflecting the removal of angular momentum from the system. In IRS2, the jet is
very collimated and shows a chain of knots, suggesting episodic accretion
events.
