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Optics Letters

Transition from quantum-to-classical random walk distributions with spin–orbit modes

V. S. Lamego, G. T. C. Cruz, Dennis Lima, Saif M. Al-Kuwari, J. A. O. Huguenin

Published Nov 7, 2024• 3 citations
Publisher

Abstract

Quantum walks (QW) offer a speed-up advantage over random walks in quantum search applications. We present an experimental study of the transition from quantum-to-classical random walk using an emulation of the decoherence process for polarization qubits that exploits maximally non-separable spin-orbit modes of an intense laser beam for the first, to the best of our knowledge, time. We are able to continuously control the input polarization mode in an all-optical quantum walk circuit to observe transitions associated with quantum, quantum stochastic, and classical random walk distributions. The results are in agreement with theoretical expectations.

DOI
10.1364/ol.537273

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Quantum walks (QW) offer a speed-up advantage over random walks in quantum search applications. We present an experimental study of the transition from quantum-to-classical random walk using an emulation of the decoherence process for polarization qubits that exploits maximally non-separable spin-orbit modes of an intense laser beam for the first, to the best of our knowledge, time. We are able to continuously control the input polarization mode in an all-optical quantum walk circuit to observe transitions associated with quantum, quantum stochastic, and classical random walk distributions. The results are in agreement with theoretical expectations.
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The possibility of fine-tuning the couplings between optical modes is a key requirement in photonic circuits for quantum simulations. In these architectures, emulating the long-time evolution of particles across large lattices requires sophisticated setups that are often intrinsically lossy. Here we report ultra-long photonic quantum walks across several hundred optical modes, obtained by propagating a light beam through very few closely stacked liquid-crystal metasurfaces. By exploiting spin–orbit effects, these implement space-dependent polarization transformations that mix circularly polarized optical modes carrying quantized transverse momentum. As each metasurface implements long-range couplings between distant modes, by using only a few of them we simulate quantum walks up to 320 discrete steps without any optical amplification, far beyond state-of-the-art experiments. To showcase the potential of this method, we experimentally demonstrate that in the long time limit a quantum walk affected by dynamical disorder generates maximal entanglement between two system partitions. Our platform grants experimental access to large-scale unitary evolutions while keeping optical losses at a minimum, thereby paving the way to massive multi-photon multi-mode quantum simulations.
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Abstract We translate the quantum teleportation protocol into a sequence of coherent operations involving three degrees of freedom of a classical laser beam. The protocol, which we demonstrate experimentally, transfers the polarization state of the input beam to the transverse mode of the output beam. The role of quantum entanglement is played by a non-separable mode describing the path and transverse degrees of freedom. Our protocol illustrates the possibility of new optical applications based on this intriguing classical analogue of quantum entanglement.
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