A pseudo-unitary quasiperiodic quantum walk model exhibits a novel mobility edge sharply dividing metallic and insulating phases plus a second transition unique to discrete time, with PT-symmetry breaking quantified by spectral winding number.
Two-particle bosonic-fermionic quantum walk via 3D integrated photonics
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abstract
Quantum walk represents one of the most promising resources for the simulation of physical quantum systems, and has also emerged as an alternative to the standard circuit model for quantum computing. Up to now the experimental implementations have been restricted to single particle quantum walk, while very recently the quantum walks of two identical photons have been reported. Here, for the first time, we investigate how the particle statistics, either bosonic or fermionic, influences a two-particle discrete quantum walk. Such experiment has been realized by adopting two-photon entangled states and integrated photonic circuits. The polarization entanglement was exploited to simulate the bunching-antibunching feature of non interacting bosons and fermions. To this scope a novel three-dimensional geometry for the waveguide circuit is introduced, which allows accurate polarization independent behaviour, maintaining a remarkable control on both phase and balancement.
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Sufficient conditions are proven for zero velocity in position-dependent 1D quantum walks via an a priori velocity bound depending on sparse site sequences and local coin parameters, with extensions to random cases and CMV matrices.
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Mobility edges in pseudo-unitary quasiperiodic quantum walks
A pseudo-unitary quasiperiodic quantum walk model exhibits a novel mobility edge sharply dividing metallic and insulating phases plus a second transition unique to discrete time, with PT-symmetry breaking quantified by spectral winding number.
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Absence of Ballistic Transport in Quantum Walks with Asymptotically Reflecting Sites
Sufficient conditions are proven for zero velocity in position-dependent 1D quantum walks via an a priori velocity bound depending on sparse site sequences and local coin parameters, with extensions to random cases and CMV matrices.