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S Padua - One of the best experts on this subject based on the ideXlab platform.
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implementing Positive Operator valued measurement elements in photonic circuits for performing minimum quantum state tomography of path qudits
Physical Review A, 2019Co-Authors: W R Cardoso, D F Barros, M R Barros, S PaduaAbstract:Manipulation of qudits in optical tables is a difficult and nonscalable task. The use of integrated optical circuits opens new possibilities for the generation, manipulation, and characterization of high dimensional states besides the ease of transmission of these states through an optical fiber. In this work we propose photonic circuits to perform minimum quantum state tomography of path qudits and show how to determine all the constituents parameters of these circuits (beam splitters and phase shifters). Our strategies were based on the symmetries of the involved POVMs (Positive Operator-valued measures) suggested for minimum tomography and allowed us to obtain interferometers smaller than those obtained by other already known methods. The calculations of the transmittances and reflectivities of the beam splitters were made using the definition of probability Operators in extended Hilbert spaces and the application of Naimark's theorem. The employment of equidistant states for the definition of the POVM elements allowed us to develop a recipe applicable to the tomography of qudits of any dimension, generalizing our scheme.
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minimum tomography of two entangled qutrits using local measurements of one qutrit symmetric informationally complete Positive Operator valued measure
Physical Review A, 2013Co-Authors: W M Pimenta, B Marques, Thiago O Maciel, Reinaldo O Vianna, A Delgado, C Saavedra, S PaduaAbstract:An experimental demonstration of two-qutrit state tomography via one-qutrit symmetric informationally complete Positive Operator-valued measure (SIC-POVM) is presented. A two-qutrit state is encoded in the transversal paths of a spontaneous parametric down-converted photon pair. A spatial light modulator allows us to implement the necessary 81 POVM elements to reconstruct the state. The quality of the reconstruction is evaluated by comparing independent measurements with the predicted results calculated with the reconstructed state. Entanglement in the system is calculated via negativity and generalized robustness from the two-qutrit reconstructed density Operator.
Gelo Noel Tabia - One of the best experts on this subject based on the ideXlab platform.
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experimental scheme for qubit and qutrit symmetric informationally complete Positive Operator valued measurements using multiport devices
Physical Review A, 2012Co-Authors: Gelo Noel TabiaAbstract:It is crucial for various quantum information processing tasks that the state of a quantum system can be determined reliably and efficiently from general quantum measurements. One important class of measurements for this purpose is symmetric informationally complete Positive Operator-valued measurements (SIC-POVMs). SIC-POVMs have the advantage of providing an unbiased estimator for the quantum state with the minimal number of outcomes needed for full tomography. By virtue of Naimark's dilation theorem, any POVM can always be realized with a suitable coupling between the system and an auxiliary system and by performing a projective measurement on the joint system. In practice, finding the appropriate coupling is rather non-trivial. Here we propose an experimental design for directly implementing SIC-POVMs using multiport devices and path-encoded qubits and qutrits, the utility of which has recently been demonstrated by several experimental groups around the world. Furthermore, we describe how these multiports can be attained in practice with an integrated photonic system composed of nested linear optical elements.
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experimental characterization of qutrits using symmetric informationally complete Positive Operator valued measurements
Physical Review A, 2011Co-Authors: Z E D Medendorp, F A Torresruiz, Lynden K Shalm, Gelo Noel Tabia, Christopher A Fuchs, Aephraim M SteinbergAbstract:Generalized quantum measurements [also known as Positive Operator-valued measures (POVMs)] are of great importance in quantum information and quantum foundations but are often difficult to perform. We present an experimental approach which can in principle be used to perform arbitrary POVMs in a linear-optical context. One of the most interesting POVMs, the symmetric informationally complete (SIC) POVM, is the most compact set of measurements that can be used to fully describe a quantum state. We use our technique to carry out the first experimental characterization of the state of a qutrit using SIC POVMs. Because of the highly symmetric nature of this measurement, such a representation has the unique property that it permits all other measurement outcomes to be predicted by a simple extension of the classical Bayesian sum rule, making no use of complex amplitudes or Hilbert-space Operators. We demonstrate this approach on several qutrit states encoded in single photons.
Aephraim M Steinberg - One of the best experts on this subject based on the ideXlab platform.
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experimental characterization of qutrits using symmetric informationally complete Positive Operator valued measurements
Physical Review A, 2011Co-Authors: Z E D Medendorp, F A Torresruiz, Lynden K Shalm, Gelo Noel Tabia, Christopher A Fuchs, Aephraim M SteinbergAbstract:Generalized quantum measurements [also known as Positive Operator-valued measures (POVMs)] are of great importance in quantum information and quantum foundations but are often difficult to perform. We present an experimental approach which can in principle be used to perform arbitrary POVMs in a linear-optical context. One of the most interesting POVMs, the symmetric informationally complete (SIC) POVM, is the most compact set of measurements that can be used to fully describe a quantum state. We use our technique to carry out the first experimental characterization of the state of a qutrit using SIC POVMs. Because of the highly symmetric nature of this measurement, such a representation has the unique property that it permits all other measurement outcomes to be predicted by a simple extension of the classical Bayesian sum rule, making no use of complex amplitudes or Hilbert-space Operators. We demonstrate this approach on several qutrit states encoded in single photons.
Robert W Boyd - One of the best experts on this subject based on the ideXlab platform.
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experimental realization of quantum tomography of photonic qudits via symmetric informationally complete Positive Operator valued measures
Physical Review X, 2015Co-Authors: Nicolas Bent, Hammam Qassim, Asad A Tahir, Denis Sych, Gerd Leuchs, L L Sanchezsoto, Ebrahim Karimi, Robert W BoydAbstract:Symmetric informationally complete Positive Operator-valued measures provide efficient quantum state tomography in any finite dimension. In this work, we implement state tomography using symmetric informationally complete Positive Operator-valued measures for both pure and mixed photonic qudit states in Hilbert spaces of orbital angular momentum, including spaces whose dimension is not power of a prime. Fidelities of reconstruction within the range of 0.81-0.96 are obtained for both pure and mixed states. These results are relevant to high-dimensional quantum information and computation experiments, especially to those where a complete set of mutually unbiased bases is unknown.
Todd A Brun - One of the best experts on this subject based on the ideXlab platform.
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qubit Positive Operator valued measurements by destructive weak measurements
Physical Review A, 2019Co-Authors: Yihsiang Chen, Todd A BrunAbstract:Many quantum measurements, such as photodetection, can be destructive. In photodetection, when the detector ``clicks'' a photon has been absorbed and destroyed. Yet the lack of a click also gives information about the presence or absence of a photon. In monitoring the emission of photons from a source, one decomposes the strong measurement into a series of weak measurements, which describe the evolution of the state during the measurement process. Motivated by this example of destructive photon detection, a simple model of destructive weak measurements using qubits was studied in earlier work by the authors. It has shown that the model can achieve any Positive-Operator-valued measurement (POVM) with commuting POVM elements including projective measurements. In this paper, we use a different approach for decomposing any POVM into a series of weak measurements. The process involves three steps: randomly choose, with certain probabilities, a set of linearly independent POVM elements; perform that POVM by a series of destructive weak measurements; and output the result of the series of weak measurements with certain probabilities. The probabilities of the outcomes from this process agree with those from the original POVM, and hence this model of destructive weak measurements can perform any qubit POVM.
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decomposing qubit Positive Operator valued measurements into continuous destructive weak measurements
Physical Review A, 2018Co-Authors: Yihsiang Chen, Todd A BrunAbstract:It has been shown that any generalized measurement can be decomposed into a sequence of weak measurements corresponding to a stochastic process. However, the weak measurements may require almost arbitrary unitaries, which are unlikely to be realized by any real measurement device. Furthermore, many measurement processes are destructive, like photon counting procedures that terminate once all photons are consumed. One cannot expect to have full control of the evolution of a state under such destructive measurements, and the possible unitaries allow only a limited set of weak measurements. In this paper, we consider a qubit model of destructive weak measurements, which is a toy version of an optical cavity, in which the state of an electromagnetic field mode inside the cavity leaks out and is measured destructively while the vacuum state $|0\ensuremath{\rangle}$ leaks into the cavity. At long times, the state of the qubit inevitably evolves to be $|0\ensuremath{\rangle}$, and the only available control is the choice of measurement on the external ancilla system. Surprisingly, this very limited model can still perform an arbitrary projective measurement on the qubit in any basis, where the probability of getting an outcome satisfies the usual Born rule. Combining this method with probabilistic postprocessing, the result can be extended to any generalized measurement with commuting Positive-Operator-valued measurement (POVM) elements. This implies, among other results, that any two-outcome POVM on a qubit can be decomposed into a sequence of destructive weak measurements by this restricted measurement device.