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The principle of superposition is an intriguing feature of Quantum Mechanics, which is regularly exploited at various instances. A recent work [PRL textbf{116}, 110403 (2016)] shows that the fundamentals of Quantum Mechanics restrict the superposition of two arbitrary pure states of a quantum system, even though it is possible to superpose two quantum states with partial prior knowledge. The prior knowledge imposes geometrical constraints on the choice of input pure states. We discuss an experimentally feasible protocol to superpose multiple pure states of a $d$ dimensional quantum system and carry out an explicit experimental realization to superpose two single-qubit pure states on a two-qubit NMR quantum information processor.
The indistinguishability of non-orthogonal pure states lies at the heart of quantum information processing. Although the indistinguishability reflects the impossibility of measuring complementary physical quantities by a single measurement, we demons
We provide a detailed analysis of the question: how many measurement settings or outcomes are needed in order to identify a quantum system which is constrained by prior information? We show that if the prior information restricts the system to a set
We formulate an algorithm to lower bound the fidelity between quantum many-body states only from partial information, such as the one accessible by few-body observables. Our method is especially tailored to permutationally invariant states, but it gi
We propose a learning method for estimating unknown pure quantum states. The basic idea of our method is to learn a unitary operation $hat{U}$ that transforms a given unknown state $|psi_taurangle$ to a known fiducial state $|frangle$. Then, after co
Quantum teleportation provides a disembodied way to transfer an unknown quantum state from one quantum system to another. However, all teleportation experiments to date are limited to cases where the target quantum system contains no prior quantum in