  One of largest uncertainties in nuclear physics is the relation between the
pressure and density of supranuclear matter: the equation of state. Some of
this uncertainty may be removed through future gravitational wave observations
of neutron star binaries by extracting the tidal deformabilities (or Love
numbers) of neutron stars. Previous studies showed that only a certain
combination of the individual deformabilities of each body (chirp tidal
deformability) can be measured with second-generation gravitational wave
interferometers, such as Adv. LIGO, due to correlations between the individual
deformabilities. To overcome this, we search for approximately universal (or
equation-of-state independent) relations between two combinations of the
individual tidal deformabilities, such that once one of them has been measured,
the other can be automatically obtained and the individual ones decoupled
through these relations. We find an approximately universal relation between
the symmetric and the anti-symmetric combination of the individual tidal
deformabilities that is equation-of-state-insensitive to $20\%$ for binaries
with masses less than $1.7M_\odot$. We show that these relations can be used to
eliminate a combination of the tidal parameters from the list of model
parameters, thus breaking degeneracies and improving the accuracy in parameter
estimation. A simple study shows that the universal relations can improve the
accuracy in the extraction of the symmetric combination of tidal parameters by
as much as an order of magnitude, making the overall accuracy in the extraction
of this parameter slightly better than that of the chirp tidal deformability.
These new universal relations and the improved measurement accuracy on tidal
parameters not only are important to astrophysics and nuclear physics, but also
impact our ability to probe extreme gravity with gravitational waves and
cosmology.
