On the units of bipartite entanglement: is sixteen ounces of entanglement always equal to one pound?

In a good physical theory dimensionless quantities, such as the ratio m(p)/ m(e), of the mass of the proton to the mass of the electron, do not depend on the system of units being used. This paper demonstrates that one widely used method for defining measures of entanglement violates this principle. Specifically, in this approach dimensionless ratios E(rho)/E(sigma) of enta nglement measures may depend on what state is chosen as the basic unit of e ntanglement. This observation leads us to suggest three novel approaches to the quantification of entanglement. These approaches lead to unit-free def initions for the entanglement of formation and the distillable entanglement , and suggest natural measures of entanglement for multipartite systems. We also show that the behaviour of one of these novel measures, the entanglem ent of computation, is related to some open problems in computational compl exity.