High-dimensional Bell-like states are necessary for increasing the channel capacity of the quantum protocol. However, their preparation and measurement are still huge challenges, especially for the latter. Here, we prepare an initial eight-dimensional Bell-like state based on hyperentanglement of spin and orbital angular momentum (OAM) of the first and the third orders. We design simple unitary operations to produce eight Bell-like states, which can be distinguished completely in theory among each other. We propose and illustrate a multiple projective measurement scheme composed of only linear optical elements and experimentally demonstrate that all the eight hyperentangled Bell-like states can be completely distinguished by our scheme. Our idea of manipulating the eight Bell-like states is beneficial to achieve the 3-bit channel capacity of quantum protocol, opening the door for extending applications of OAM states in future quantum information technology.
Besides a linear momentum, optical fields also carry angular momentum (AM), which has two intrinsic components: one is spin angular momentum related to the polarization state and the other is orbital angular momentum (OAM) caused by the helical phase due to the existence of a topological azimuthal charge. The two AM components of the optical field may not be independent of each other, especially if spin-to-orbit conversion (STOC) under high focusing creates a spin-dependent optical vortex in the longitudinal field. However, it would be very exciting to experimentally manifest and control the local OAM density. Here, we present a strategy for achieving STOC via a radial intensity gradient. The linearly varying radial phase provides an effective way to control the local AM density, which induces a counterintuitive orbital motion of the isotropic microparticles in optical tweezers without intrinsic OAM. Our work not only provides fundamental insights into the STOC of light, but could also have applications in optical micromanipulation.
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