Zero transfer in continuous-time quantum walks

Abstract

In this paper we show how using complex valued edge weights in a graph can completely suppress the flow of probability amplitude in a continuous time quantum walk to specific vertices of the graph when the edge weights, graph topology and initial state of the quantum walk satisfy certain conditions. The conditions presented in this paper are derived from the so-called chiral quantum walk, a variant of the continuous time quantum walk which incorporates directional bias with respect to site transfer probabilities between vertices of a graph by using complex edge weights. We examine the necessity to break the time reversal symmetry in order to achieve zero transfer in continuous time quantum walks. We also consider the effect of decoherence on zero transfer and suggest that this phenomena may be used to detect decoherence in the system.

Controlled transport in chiral quantum walks on graphs

“…The Y-junction graph, in which the phases on the edge-weights cannot 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].…”

“…where σ = e i 2π 3 and |χ νη ⟩ is the ηth eigenstate of the effective chain Hamiltonian Ĥν eff in (16). Starting from an initial wave package on the first chain with wave function |ψ 0 ⟩ = n ϕ 0 n |1, n⟩ = P 1 |χ 0 ⟩, the time evolution can be easily computed by…”

“…Traditionally, the limit of Green's function is computed perturbatively by summing series of the free Green's function. However, here we compute finite time Green's function directly, based on the exact solvability of the effective chain Hamiltonians in (16).…”

“…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.…”