Quantum Walks Assisted Bidirectional Remote State Preparation

Abstract

We present a scheme for bidirectional remote state preparation (BRSP) using quantum walks on two independent one-dimensional lattices and two independent cycles with two and four vertices, employing nearest-neighbor jumps with coin outcomes. The protocol is implemented in two distinct ways: one without the involvement of a controller and the other assisted by a controller . In this approach, the quantum walk dynamics generate entanglement during the remote state preparation process, thereby eliminating the need for any pre-shared initial entanglement between the communicating parties. Finally, we show that the bidirectional remote state preparation schemes based on quantum walks on a two-vertex and four-vertex system exhibit consistent behavior under the respective uncontrolled and controlled configurations.

Figures (5)

• Figure 1: The quantum walk on a one dimensional line. If the coin outcome is $0$, the walker move towards right (from $i$ to $i+1$). If the coin outcome is $1$, the walker moves towards left (from $i$ to $i-1$).
• Figure 2: Circuit diagram for uncontrolled bidirectional remote state preparation using quantum walks.
• Figure 3: Two vertex complete graph with one coin.
• Figure 4: A cycle with four vertices (4-cycle).
• Figure 5: Circuit diagram for controlled bidirectional remote state preparation using quantum walks.