We present an experimental proof-of-principle for the generation and detection of pure two-qubit states which have been encoded in degrees of freedom that are common to both classical-light beams and single photons. Our protocol requires performing polarization tomography on a single qubit from a qubit pair. The degree of entanglement in the qubit pair is measured by concurrence, which can be directly extracted from intensity measurements-or photon counting-entering single-qubit polarization tomography. Entangled qubit pairs are basic units in schemes devised to implement quantum information processes such as quantum communication, quantum cryptography, etc., as well as in schemes designed to address foundational issues of quantum mechanics. The exploitation of entanglement is one of the most challenging goals of quantum information technologies. There are good reasons to believe that entanglement plays a key role in the advantage that quantum circuits would have over classical circuits [1]. Entanglement is however difficult to characterize experimentally. So-called entanglement witnesses are state specific, in the sense that they are tailored to detecting some types of entanglement while they are blind to others. Alternatively, one can rely on entanglement measures, which are designed to be state independent. A prominent example is concurrence, which is defined for any pure, bipartite state Φ as C(Φ) = | Φ|(σ y ⊗ σ y)|Φ * |, where σ y is the Pauli matrix and |Φ * the complex-conjugate of |Φ in the computational basis of the tensor-product space to which Φ belongs. Now, confronted with this measure, the experimentalist sees no obvious way to implement it directly in the laboratory. To begin with, complex conjugation is an unphysical operation, because it does not conserve positive-definiteness. Thus, the only way to obtain C(Φ) from measurements seems to be by means of full tomographic determination of state Φ, which is experimentally demanding and prone to inaccuracies. The evaluation of C(Φ), which nonlinearly depends on the parameters fixing Φ, can then be too inaccurate. Back in 2005, Mintert et al. [2] found a way out of the

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The wave equation of electromagnetism, the Helmholtz equation, has the same form as the Schrödinger equation, and so optical waves can be used to study quantum mechanical problems. The electromagnetic wave solutions for non-diffracting beams lead to the two-dimensional Helmholtz equation. When expressed in elliptical coordinates the solution of the angular part is the same as the Schrödinger equation for the simple pendulum. The resulting optical eigenmodes, Mathieu modes, have an optical Fourier transform with a spatial intensity distribution that is proportional to the quantum mechanical probability for the pendulum. Comparison of Fourier intensities of eigenmodes are in excellent agreement with calculated quantum mechanical probabilities of pendulum stationary states. We further investigate wave-packet superpositions of a few modes and show that they mimic the libration and the nonlinear rotation of the classical pendulum, including revivals due to the quantized nature of superpositions. The ability to ‘dial a wavefunction’ with the optical modes allows the exploration of important aspects of quantum wave-mechanics and the pendulum that may not be possible with other physical systems.

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