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A combination of a finite number of linear independent states forms superposition in a way that cannot be conceived classically. Here, using the tools of resource theory of superposition, we give the conditions for a class of superposition state transformations. These conditions strictly depend on the scalar products of the basis states and reduce to the well-known majorization condition for quantum coherence in the limit of orthonormal basis. To further superposition-free transformations of $d$-dimensional systems, we provide superposition-free operators for a deterministic transformation of superposition states. The linear independence of a finite number of basis states requires a relation between the scalar products of these states. With this information in hand, we determine the maximal superposition states which are valid over a certain range of scalar products. Notably, we show that, for $d\geq3$, scalar products of the pure superposition-free states have a greater place in seeking maximally resourceful states. Various explicit examples illustrate our findings., Comment: 14 pages, 1 figure and 1 table

The states of three-qubit systems split into two inequivalent types of genuine tripartite entanglement, namely the Greenberger-Horne-Zeilinger (GHZ) type and the $W$ type. A state belonging to one of these classes can be stochastically transformed only into a state within the same class by local operations and classical communications. We provide local quantum operations, consisting of the most general two-outcome measurement operators, for the deterministic transformations of three-qubit pure states in which the initial and the target states are in the same class. We explore these transformations, originally having standard GHZ and standard $W$ states, under the local measurement operations carried out by a single party and $p$ ($p=2,3$) parties (successively). We find a notable result that the standard GHZ state cannot be deterministically transformed to a GHZ-type state in which all its bipartite entanglements are nonzero, i.e., a transformation can be achieved with unit probability when the target state has at least one vanishing bipartite concurrence., Comment: 9 pages, 4 figures. Published version!

We present an optimal probabilistic protocol to distill quantum coherence. Inspired by a specific entanglement distillation protocol, our main result yields a strictly incoherent operation that produces one of a family of maximally coherent states of variable dimension from any pure quantum state. We also expand this protocol to the case where it is possible, for some initial states, to avert any waste of resources as far as the output states are concerned, by exploiting an additional transformation into a suitable intermediate state. These results provide practical schemes for efficient quantum resource manipulation., Comment: 5 pages, 2 figures

It is well known that the majorization condition is the necessary and sufficient condition for the deterministic transformations of both pure bipartite entangled states by local operations and coherent states under incoherent operations. In this paper, we present two explicit protocols for these transformations. We first present a permutation-based protocol which provides a method for the single-step transformation of $d$-dimensional coherent states. We also obtain generalized solutions of this protocol for some special cases of $d$-level systems. Then, we present an alternative protocol where we use $d'$-level ($d'$ $<$ $d$) subspace solutions of the permutation-based protocol to achieve the complete transformation as a sequence of coherent-state transformations. We show that these two protocols also provide solutions for deterministic transformations of pure bipartite entangled states., Comment: 16 pages, 8 figures

We propose an explicit protocol for the deterministic transformations of bipartite pure states in any dimension using deterministic transformations in lower dimensions. As an example, explicit solutions for the deterministic transformations of $3\otimes 3$ pure states by a single measurement are obtained, and an explicit protocol for the deterministic transformations of $n\otimes n$ pure states by three-outcome measurements is presented., Comment: 11 pages, published version

It is well known that quantum states that can be transformed into each other by local unitary transformations are equal from the information theoretic point of view. This defines equivalence classes of states and allows one to write any state with the minimal number of parameters called the canonical form of the state. We define the equivalence classes of local measurements such that local operations which transform states from one equivalence class into another with the same probability are equivalent. This equivalence relation allows one to write the operators with the minimal number of parameters, which we call canonical operators, and hence the use of the canonical operators simplifies the optimal manipulation of quantum states. We use the canonical local operators for the concentration of three-qubit Greenberger-Horne-Zeilinger states and obtain the optimal concentration protocols in terms of the unitary invariants of quantum states, namely, the bipartite concurrences and the three-tangle., Comment: 15 pages, published version

Some of the asymmetric three qubit $W$ states are used for perfect teleportation, superdense coding and quantum information splitting. We present the protocols for the optimal distillation of the asymmetric as well as the symmetric $W$ states from a single copy of any three qubit $W$ class pure state., Comment: 10 pages