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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 thesystem of units being used. This paper demonstrates that one widely used methodfor defining measures of entanglement violates this principle. Specifically, inthis approach dimensionless ratios E(rho) / E(sigma) of entanglement measuresmay depend on what state is chosen as the basic unit of entanglement. Thisobservation leads us to suggest three novel approaches to the quantification ofentanglement. These approaches lead to unit-free definitions for theentanglement of formation and the distillable entanglement, and suggest naturalmeasures of entanglement for multipartite systems. We also show that thebehaviour of one of these novel measures, the entanglement of computation, isrelated to some open problems in computational complexity.Comment: 6 page

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