Generation of hybrid maximally entangled states in a one-dimensional quantum walk

Abstract

We study the generation of hybrid entanglement in a one-dimensional quantum walk. In particular, we explore the preparation of maximally entangled states between position and spin degrees of freedom. We address it as an optimization problem, where the cost function is the Schmidt norm. We then benchmark the algorithm and compare the generation of entanglement between the Hadamard quantum walk, the random quantum walk and the optimal quantum walk. Finally, we discuss an experimental scheme with a photonic quantum walk in the orbital angular momentum of light. The experimental measurement of entanglement can be achieved with weak values measurements.

Universal and optimal coin sequences for high entanglement generation in 1D discrete time quantum walks

“…Our work therefore extends existing results that either achieve state independent entanglement only in the asymptotic limit of an infinite quantum walk [25] or that can achieve maximal entanglement in a short sequence, but not independently of the initial state [29,30]. Furthermore, the RL scheme we have presented can be useful in a variety of other, experimentally relevant settings.…”

“…However, the large number of steps this strategy requires makes the scheme unrealistic for current experiments. As a possible solution, the optimization of the coin operator sequence was suggested and it was shown that this can reduce the number of steps to less than 10 [29,30]. However, the entanglement that can be generated by optimising is highly dependent on the initial state and requires potentially the full set of possible coin operators to be realized experimentally.…”

Negative correlations can play a positive role in disordered quantum walks

“…Entanglement in QWs has been addressed earlier with the introduction of modifications—relatively to the standard QW—either in the coin operator 14 , 15 , 21 , 26 – 29 , 29 – 34 , 55 or in the step operator 17 , 18 , 35 , 36 . Nevertheless, the model we have introduced is able to combine the set of properties we obtained: (1) for weak disorder strength, , and assuming systems with either negative or positive correlation, , [eg, Fig.…”

Generating highly entangled states via discrete-time quantum walks with Parrondo sequences

“…Hybrid entanglement as the name suggests is the entanglement between different degrees of freedom like polarization, orbital angular momentum, time-bin energy, or spatial mode. If these degrees of freedom belong to the same particle, more information can be encoded at the single-particle level, which can help to reduce the required resources [24]. Photonic hybrid entangled states can be advantageous in optical quantum networks as it enables a more flexible network with each photon being transmitted through the more suited channel [25].…”

“…Gratsea, et. al., suggested the optimization of the coin operator sequence using a basin-hopping algorithm [24]. It was shown that maximal entanglement is achieved in just 10 steps.…”