Steered discrete-time quantum walks for engineering of quantum states
- URL: http://arxiv.org/abs/2205.04872v2
- Date: Sun, 22 May 2022 17:31:35 GMT
- Title: Steered discrete-time quantum walks for engineering of quantum states
- Authors: Gururaj Kadiri
- Abstract summary: We analyze the strengths and limitations of steered discrete time quantum walks in generating quantum states of bipartite quantum systems.
We show that not all quantum states in the composite space are accessible through quantum walks, even under the most generalized definition of a quantum step.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We analyze the strengths and limitations of steered discrete time quantum
walks in generating quantum states of bipartite quantum systems comprising of a
qubit coupled to a qudit system. We demonstrate that not all quantum states in
the composite space are accessible through quantum walks, even under the most
generalized definition of a quantum step, leading to a bifurcation of the
composite Hilbert space into "walk-accessible states" and the
"walk-inaccessible states". We give an algorithm for generating any
walk-accessible state from a simple-to-realize product state, in a minimal
number of walk steps, all of unit step size. We further give a prescription
towards constructing minimal quantum walks between any pair of such
walk-accessible states. Linear optics has been a popular physical system for
implementing coin-based quantum walks, where the composite space is built up of
spin and orbital angular momenta of light beams. We establish that in such an
implementation, all normalized quantum states are "walk-accessible".
Furthermore, any generalized quantum step can be implemented upto a global
phase using a single q-plate and a pair of homogeneous waveplates. We then give
a quantum walk based scheme for realizing arbitrary vector beams, using only
q-plates and waveplates.
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