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We propose a scheme for recovering quantum states from a single observable, corresponding to a single setup, by adding a known ancilla state, introducing mixing between degrees of freedom, and utilizing structure in the states.
Multiple photon absorption processes typically have a nonlinear dependence on the amplitude of the incident optical field. On the other hand, quantum technologies rely on single photon events. It has therefore been of great technical difficulty to achieve nonlinear devices using single photons. This is due to the small cross-section of absorption in room temperature devices, with multi-photon absorption...
We show that prior knowledge that a quantum state is close to a pure state enables a direct and efficient measurement of the density matrix representing the state, using the weak measurements methodology.
By introducing concepts of beam shaping from nonlinear optics into quantum mechanics, we show how interference of electrons wavefunctions can exactly balance the nonlinear self-repulsion of an electron-beam, creating nonspreading shape-preserving propagation in free-space.
We show that prior information, such as that a quantum state is sparse in a known mathematical basis, enables algorithmic reconstruction of an initial three-photon state from two-photon coincidence measurements, thereby achieving quantum super-resolution.
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