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We examine the problem of finding the minimum number of Pauli measurements needed to uniquely determine an arbitrary $n$-qubit pure state among all quantum states. We show that only $11$ Pauli measurements are needed to determine an arbitrary two-qubit pure state compared to the full quantum state tomography with $16$ measurements, and only $31$ Pauli measurements are needed to determine an arbitrary three-qubit pure state compared to the full quantum state tomography with $64$ measurements. We demonstrate that our protocol is robust under depolarizing error with simulated random pure states. We experimentally test the protocol on two- and three-qubit systems with nuclear magnetic resonance techniques. We show that the pure state tomography protocol saves us a number of measurements without considerable loss of fidelity. We compare our protocol with same-size sets of randomly selected Pauli operators and find that our selected set of Pauli measurements significantly outperforms those random sampling sets. As a direct application, our scheme can also be used to reduce the number of settings needed for pure-state tomography in quantum optical systems.
Estimation of quantum states and measurements is crucial for the implementation of quantum information protocols. The standard method for each is quantum tomography. However, quantum tomography suffers from systematic errors caused by imperfect knowl
We describe a technique for self consistently characterizing both the quantum state of a single qubit system, and the positive-operator-valued measure (POVM) that describes measurements on the system. The method works with only ten measurements. We a
Tomography of a quantum state is usually based on positive operator-valued measure (POVM) and on their experimental statistics. Among the available reconstructions, the maximum-likelihood (MaxLike) technique is an efficient one. We propose an extensi
We investigate quantum state tomography (QST) for pure states and quantum process tomography (QPT) for unitary channels via $adaptive$ measurements. For a quantum system with a $d$-dimensional Hilbert space, we first propose an adaptive protocol wher
The standard method of measuring quantum wavefunction is the technique of {it indirect} quantum state tomography. Owing to conceptual novelty and possible advantages, an alternative {it direct} scheme was proposed and demonstrated recently in quantum