Entanglement transfer via Chiral Quantum Walk on a Triangular Chain

Abstract

We investigate the chiral quantum walk (CQW) for entanglement transfer on a triangular chain. We specifically consider two and three site Bell and W type entanglement cases, respectively. Using concurrence as quantum entanglement measure, together with the Bures distance and trace distance as the measures of the fidelity of the state transfer, we evaluate the success of the entanglement transfer. We compare the entangled state transfer time and quality in CQW against continuous-time quantum random walk. Furthermore, how the chain length and back-scattering at the end of the chain influence the entanglement transfer are pointed out.

Controlled transport in chiral quantum walks on graphs

“…The Y-junction graph, in which the phases on the edge-weights can not be gauged away as in Section 2 due to the loop nature, can bring novel phenomena in quantum walks such as directed currents [38], non-reciprocal transmission [35], and quantum transport enhancement [39]. It was paid close attention recently both in theories [16,21,27,39] and experiments [36,[40][41][42][43]. The Y-junction graph can be realized in experiments by high-dimensional photonic quantum states, multiple concatenated interferometers, or dimension-dependent losses [37].…”

“…the fact Ξ(θ) = N 2 + O(1) has been used above and phase β is defined by β ≡ f (k 0 , 0) − f (k 0 , ω). The above equation indicates that main contributions of the summations in (27) come from terms around q, p = N k 0 π , since they decay to zero very fast when the integer q or p moves away. In the same spirit, we learn that around q, p = N k 0 π , one has Moreover, by Taylor expansion of the spectra around q, p → N k 0 π , we obtain e it(Ep−ǫq) ≈ e it•2 sin k 0…”

“…In the past decade, the chiral quantum walk has attracted lots of attentions [22][23][24][25][26]. Research has shown that chirality can lead to novel physical phenomena [16,27], inspiring further exploration both theoretically [19,[28][29][30][31][32][33][34][35] and experiments [36][37][38]. In the presence of chirality, asymmetric and non-reciprocal transports were experimentally demonstrated in quantum circuits [22], quantum optics [23], and optical waveguides [26].…”

“…Asymmetric spin transport [24] and steady state transport [25] were proposed to emerge in chiral spin and atomic chains. On graphs, completely suppressed flow and fast entanglement transfer have been proposed [16,27]. In particular, it was demonstrated in [39] that the transport efficiency in quantum walks on graphs could be greatly enhanced by controlling the chirality, and even the direction of transport can be controlled.…”