Locally unextendible non-maximally entangled basis

We introduce the concept of the locally unextendible non-maximally entangled basis (LUNMEB) in Hd⊗Hd. It is shown that such a basis consists of d orthogonal vectors for a non-maximally entangled state. However, there can be a maximum of (d - 1)2 orthogonal vectors for non-maximally entangled state if it is maximally entangled in (d- 1) dimensional subspace. Such a basis plays an important role in determining the number of classical bits that one can send in a superdense coding protocol using a nonmaximally entangled state as a resource. By constructing appropriate POVM operators, we find that the number of classical bits one can transmit using a non-maximally entangled state as a resource is (1+p0d/d-1) log d, where p0 is the smallest Schmidt coefficient. However, when the state is maximally entangled in its subspace then one can send up to 2 log(d-1) bits. We also find that for d = 3, former may be more suitable for the superdense coding.