The optimal N qubit states featuring highest sensitivity to small misalignment of Cartesian reference frames are found using the quantum Cramér-Rao bound. It is shown that the optimal states are supported on the symmetric subspace and hence are mathematically equivalent to a single spin J = N / 2. Majorana representation of spin states is used to reveal a beautiful connection between the states optimal for aligning reference frames and the platonic solids.
Creating miniature chip scale implementations of optical quantum information protocols is a dream for many in the quantum optics community. This is largely because of the promise of stability and scalability. Here we present a monolithically integratable chip architecture upon which is built a photonic device primitive called a Bragg reflection waveguide (BRW). Implemented in gallium arsenide, we show that, via the process of spontaneous parametric down conversion, the BRW is capable of directly producing polarization entangled photons without additional path difference compensation, spectral filtering or post-selection. After splitting the twin-photons immediately after they emerge from the chip, we perform a variety of correlation tests on the photon pairs and show non-classical behaviour in their polarization. Combined with the BRW's versatile architecture our results signify the BRW design as a serious contender on which to build large scale implementations of optical quantum processing devices.
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