The roles of quantum correlations, entanglement, discord, and dissonance needed for performing unambiguous quantum state discrimination assisted by an auxiliary system are studied. In general, this procedure for conclusive recognition between two nonorthogonal states relies on the availability of entanglement and discord. However, we find that there exist special cases for which the procedure can be successfully achieved without entanglement. In particular, we show that the optimal case for discriminating between two nonorthogonal states prepared with equal a priori probabilities does not require entanglement but quantum dissonance only.

Quantum teleportation of qudits is revisited. In particular, we analyze the case where the quantum channel corresponds to a non-maximally entangled state and show that the success of the protocol is directly related to the problem of distinguishing non-orthogonal quantum states. The teleportation channel can be seen as a coherent superposition of two channels, one of them being a maximally entangled state thus, leading to perfect teleportation and the other, corresponding to a non-maximally entangled state living in a subspace of the d-dimensional Hilbert space. The second channel leads to a teleported state with reduced fidelity. We calculate the average fidelity of the process and show its optimality.

We study the problem of driving a known initial quantum state onto a known pure state without using a unitary evolution. This task can be achieved by means of von Neumann measurement processes, introducing N observables which are consecutively measured in order to approach the state of the system to the target state. We proved that the probability of projecting onto the target state can be increased meaningfully by adding suitable observables to the process, that is, it converges to 1 when N increases. We also discuss a physical implementation of this scheme.

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We find the allowed complex overlaps for N equidistant pure quantum states. The accessible overlaps define a petal-shaped area on the Argand plane. Each point inside the petal represents a set of N linearly independent pure states and each point on its contour represents a set of N linearly dependent pure states. We find the optimal probabilities of success of discriminating unambiguously in which of the N equidistant states the system is. We show that the phase of the involved overlap plays an important role in the probability of success. For a fixed overlap modulus, the success probability is highest for the set of states with an overlap with phase equal to zero. In this case, if the process fails, then the information about the prepared state is lost. For states with a phase different from zero, the information could be obtained with an error-minimizing measurement protocol.

We study entanglement swapping through nonmaximally entangled states. The combination of the standard protocol with an optimal scheme for quantum state discrimination leads to a reliable protocol for the conclusive probabilistic generation of maximally entangled states. A possible setup based on cold trapped ions is proposed.

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