We derive an exact computable formula for fidelity deviation in quantum teleportation with an arbitrary state of two qubits. As an application, we obtain the condition for universality: the condition that all input states are teleported equally well and provide a necessary and sufficient condition for a state to be both useful and universal for quantum teleportation. We illustrate these results with examples from well-known classes of two-qubit states. * Electronic address: a.

Recently, it has been shown that at most two observers (Bobs) can sequentially demonstrate bipartite nonlocality with a spatially separated single observer (Alice) invoking a scenario where an entangled system of two spin-1 2 particles are shared between a single Alice in one wing and several Bobs on the other wing, who act sequentially and independently of each other [Phys. Rev. Lett. 114, 250401 (2015)]. This has been probed through the quantum violations of CHSH inequality, i. e., when each observer performs two dichotomic measurements.In the present study we investigate how many Bobs can sequentially demonstrate bipartite nonlocality with a single Alice in the above scenario when the number of measurement settings per observer is increased. It is shown that at most two Bobs can exhibit bipartite nonlocality with a single Alice using local realist inequalities with three as well as four dichotomic measurements per observer. We then conjecture that the above feature remains unchanged contingent upon using local realist inequalities with n dichotomic measurements per observer, where n is arbitrary. We further present the robustness of bipartite nonlocality sharing in the above scenario against the entanglement and mixedness of the shared state. arXiv:1811.04813v2 [quant-ph]

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Quantum teleportation with a two-qubit state can be suitably characterized in terms of maximal fidelity and fidelity deviation, where the former is the maximal value of the average fidelity achievable within the standard protocol and local unitary operations, and the latter is the standard deviation of fidelity over all input states. In this paper, we characterize the twoqubit states that are optimal for quantum teleportation for a given linear entropy, maximum mean value of the Bell-CHSH observable, and concurrence, respectively, where the optimal states are defined as those states that, for given value of the state property under consideration, achieve the largest maximal fidelity and also exhibit zero fidelity deviation. We find that for a given linear entropy or Bell-CHSH violation, the largest maximal fidelity states are optimal, but for a given concurrence, the optimal states form a strict subset of the largest maximal fidelity states.

We study information-disturbance trade-off in generalized entanglement swapping protocols wherein starting from Bell pairs (1, 2) and (3, 4), one performs an arbitrary joint measurement on (2, 3), so that (1, 4) now becomes correlated. We obtain trade-off inequalities between information gain in correlations of (1, 4) and residual information in correlations of (1, 2) and (3, 4) respectively and argue that information contained in correlations (information) is conserved if each inequality is an equality. We show that information is conserved for a maximally entangled measurement but is not conserved for any other complete orthogonal measurement and Bell measurement mixed with white noise. However, rather surprisingly, we find that information is conserved for rank-two Bell diagonal measurements, although such measurements do not conserve entanglement. We also show that a separable measurement on (2, 3) can conserve information, even if, as in our example, the post-measurement states of all three pairs (1, 2), (3, 4), and (1, 4) become separable. This implies correlations from an entangled pair can be transferred to separable pairs in nontrivial ways so that no information is lost in the process.