Research On Entanglement Entropy In Quantum Walks

Quantum entanglement is an important resource in quantum informatics.Therefore,study of quantum entanglement has become a hot spot of current research.Previous studies have shown that there is entanglement between the coin and walker in standard quantum walks.The entanglement can be quantified by Von Neumann Entropy.We study quantum entanglement correlation based on quantum walks.The following work has been done in this paper:(1)We study the entanglement between the coin and walker in quantum walks with positiondependent evolutionary operations.The probability of returning to the origin position and the position variance change with the evolution steps quasi-periodically.Therefore,such quantum walks are called quasi-periodic evolutionary quantum walks.The entanglement quantification in the quasi-periodic evolution quantum walks is discussed and analyzed in this paper.The coin-walker entanglement is quantified by the von Neumann entropy of the coin.Through numerical calculations,it is found that the entanglement entropy depends on the initial state,the number of evolution steps,and the parameters of evolution operators.When the suitable coin operations are selected,the entanglement entropy changes in the quasi-period pattern.The maximal entanglement state can be obtained when the proper parameters of evolution operators,the number of evolution steps are selected for the given initial state.We discuss the entanglement metric of quantum walks under a specific initial condition In the process of quantum walks,for the initial state of a specific system,the final state and entanglement entropy after each step of evolution operation are calculated,and the numerical results show that the maximal entanglement state can be obtained after 1 step of evolution operation for the quantum walks under the specific initial conditions.Among the 20 evolutionary steps,there are 10 steps that can obtain the maximum entangled state.(2)We propose an optical system in which the polarization states M and V of a photon represent the states 0 and 1 of a coin.The experimental scheme of expandable quantum walk is realized by using ring structure and time multiplexing technology.The walker's position is represented at different times by the photon reaching the detector(APD).The final state of the coin can be obtained by counting the number of photons with different projection bases.