Experimental characterization of qutrits using symmetric informationally complete positive operator-valued measurements

Medendorp, Zachari; Torres-Ruiz, F. A.; Shalm, Lynden K.; Tabia, Gelo Noel; Fuchs, Christopher A.; Steinberg, Aephraim M.

doi:10.1103/physreva.83.051801

Cited by 83 publications

(62 citation statements)

References 19 publications

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“…Informally, 2-designs are sets of quantum states whose projectors span the vector space of operators as uniformly as possible; more precisely, the ensemble's second moments are equal to those of the uniform Haar ensemble over pure states. Common examples of 2-designs include mutually unbiased bases [36] and symmetric informationally complete measurements [37,38], and there is strong theoretical [36] and experimental [39] evidence that 2-designs are optimal for state tomography. Our results here are the first experimental evidence that 2-designs are optimal for QPT (see theory in Refs.…”

Section: Quantum Process Tomographymentioning

confidence: 99%

Optimizing the Choice of Spin-Squeezed States for Detecting and Characterizing Quantum Processes

et al. 2014

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Quantum metrology uses quantum states with no classical counterpart to measure a physical quantity with extraordinary sensitivity or precision. Most such schemes characterize a dynamical process by probing it with a specially designed quantum state. The success of such a scheme usually relies on the process belonging to a particular one-parameter family. If this assumption is violated, or if the goal is to measure more than one parameter, a different quantum state may perform better. In the most extreme case, we know nothing about the process and wish to learn everything. This requires quantum process tomography, which demands an informationally complete set of probe states. It is very convenient if this set is group covarianti.e., each element is generated by applying an element of the quantum system's natural symmetry group to a single fixed fiducial state. In this paper, we consider metrology with 2-photon ("biphoton") states and report experimental studies of different states' sensitivity to small, unknown collective SUð2Þ rotations ["SUð2Þ jitter"]. Maximally entangled N00N states are the most sensitive detectors of such a rotation, yet they are also among the worst at fully characterizing an a priori unknown process. We identify (and confirm experimentally) the best SUð2Þ-covariant set for process tomography; these states are all less entangled than the N00N state, and are characterized by the fact that they form a 2-design.

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Section: Quantum Process Tomographymentioning

confidence: 99%

Optimizing the Choice of Spin-Squeezed States for Detecting and Characterizing Quantum Processes

et al. 2014

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“…We also remark on how the optical multiport scheme for qutrit SIC-POVMs compares to the Medendorp experiment [12]. In the Medendorp scheme, photons are sent into an optical storage loop and the SIC-POVM is performed by weakly coupled partially polarizing beam splitters (PPBS), with a full measurement completed after the signal makes 3 rounds.…”

Section: Discussionmentioning

confidence: 99%

“…A practical approach for direct implementation of qutrit SIC-POVMs using linear optical elements was demonstrated by Medendorp et al [12], where the qutrit was encoded in polarizations states of a photon with two spatial modes. The photons propagated inside a storage loop containing a calcite beam displacer for performing the shift X gate and three liquid crystal wave plates for performing phase Z gates.…”

Section: Introductionmentioning

confidence: 99%

Experimental scheme for qubit and qutrit symmetric informationally complete positive operator-valued measurements using multiport devices

Tabia

2012

Phys. Rev. A

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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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“…In contrast to the major theoretical progress all experiments and even proposals for experiments implementing SIC POMs have been limited to the very basic quantum system, the two-level system (qubit) [10,11], with the exception of the recent experiment by Medendorp et al [12] where a SIC POM for a three-level system was approximated. This is, in part, due to the fact that there is no systematic procedure for implementing SIC POMs in higher dimensions, in a simple experimental set-up.…”

Section: Introductionmentioning

confidence: 99%

Symmetric minimal quantum tomography by successive measurements

2012

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We consider the implementation of a symmetric informationally complete probability-operator measurement (SIC POM) in the Hilbert space of a d-level system by a two-step measurement process: a diagonal-operator measurement with high-rank outcomes, followed by a rank-1 measurement in a basis chosen in accordance with the result of the first measurement. We find that any HeisenbergWeyl group-covariant SIC POM can be realized by such a sequence where the second measurement is simply a measurement in the Fourier basis, independent of the result of the first measurement. Furthermore, at least for the particular cases studied, of dimension 2, 3, 4, and 8, this scheme reveals an unexpected operational relation between mutually unbiased bases and SIC POMs; the former are used to construct the latter. As a laboratory application of the two-step measurement process, we propose feasible optical experiments that would realize SIC POMs in various dimensions.

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Experimental characterization of qutrits using symmetric informationally complete positive operator-valued measurements

Cited by 83 publications

References 19 publications

Optimizing the Choice of Spin-Squeezed States for Detecting and Characterizing Quantum Processes

Optimizing the Choice of Spin-Squeezed States for Detecting and Characterizing Quantum Processes

Experimental scheme for qubit and qutrit symmetric informationally complete positive operator-valued measurements using multiport devices

Symmetric minimal quantum tomography by successive measurements

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