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We produce and holographically measure entangled qudits encoded in transverse spatial modes of single photons. With the novel use of a quantum state tomography method that only requires two-state superpositions, we achieve the most complete characterisation of entangled qutrits to date. Ideally, entangled qutrits provide better security than qubits in quantum bit-commitment: we model the sensitivity of this to mixture and show experimentally and theoretically that qutrits with even a small amount of decoherence cannot offer increased security over qubits. PACS numbers: 42.50.Dv, 03.65.Wj, 03.67.Dd, 03.67.Mn Many two-level quantum systems, or qubits, have been used to encode information [1]; using d-level systems, or qudits, enables access to larger Hilbert spaces, which can provide significant improvements over qubits such as increased channel capacity in quantum communication [2]. When entangled, qutrits (d=3) provide the best known levels of security in quantum bit-commitment and coinflipping protocols, which cannot be matched using qubitbased systems [3]. The ability to completely characterise entangled qudits is critical for applications. This is only possible using quantum state tomography [4,5].Entangled qudits have been realised in few physical systems, and only indirect measurements have been made of the quantum states of these systems. Qutrit entanglement has been generated between the arrival times of correlated photon pairs, where fringe measurements were used to infer features such as fidelities with specific entangled states and to estimate a potential Bell violation [6]. It is also possible to encode qudits in the transverse spatial modes of a photon, Fig. 1. There have been measurements demonstrating, but again not quantifying, spatial mode entanglement in parametric downconversion [7], including fringe measurements [8,9] and the violation of a two-qutrit Bell inequality [10,11].Here, we use quantum state tomography to completely characterise entangled, photonic qudits (both d = 2 and 3) encoded in transverse spatial modes, measuring the amount of entanglement and the degree of mixture. We show how to use the qutrit system in a quantum bitcommitment protocol and investigate the experimental requirements for achieving the best known security [3]. To illustrate these results, we first introduce and demonstrate two conceptually distinct ways of encoding information in transverse spatial modes, which differ in the behaviour of superposition states. This work constitutes the most complete characterisation of spatially-encoded qubits and qutrits and the first quantitative measurement of entangled qutrit states.The Gaussian spatial modes are a complete basis for describing the paraxial propagation of light [13]. Two orthonormal mode families are shown in Fig. 1(a): the Hermite-Gauss (HG rs ) and Laguerre-Gauss-Vortex (LGV pl ). These modes are self-similar under propagation; modes of the same order experience the same propagation-dependent phase shift, the Gouy phase shift. We define degenerate qudits...

We report on precision measurements of the elastic cross section for electron-proton scattering performed in Hall C at Jefferson Lab. The measurements were made at 28 distinct kinematic settings covering a range in momentum transfer of 0.4 < Q 2 < 5.5 (GeV/c) 2 . These measurements represent a significant contribution to the world's cross section data set in the Q 2 range where a large discrepancy currently exists between the ratio of electric to magnetic proton form factors extracted from previous cross section measurements and that recently measured via polarization transfer in Hall A at Jefferson Lab. This data set shows good agreement with previous cross section measurements, indicating that if a here-to-fore unknown systematic error does exist in the cross section measurements then it is intrinsic to all such measurements.

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