Entangling power of disordered quantum walks

Abstract

We investigate how the introduction of different types of disorder affects the generation of entanglement between the internal (spin) and external (position) degrees of freedom in one-dimensional quantum random walks (QRW ). Disorder is modeled by adding another random feature to QRW , i.e., the quantum coin that drives the system's evolution is randomly chosen at each position and/or at each time step, giving rise to either dynamic, fluctuating, or static disorder. The first one is position-independent, with every lattice site having the same coin at a given time, the second has time and position dependent randomness, while the third one is time-independent. We show for several levels of disorder that dynamic disorder is the most powerful entanglement generator, followed closely by fluctuating disorder. Static disorder is the less efficient entangler, being almost always less efficient than the ordered case. Also, dynamic and fluctuating disorder lead to maximally entangled states asymptotically in time for any initial condition while static disorder has no asymptotic limit and, similarly to the ordered case, has a long time behavior highly sensitive to the initial conditions.

Robust and efficient transport of two-qubit entanglement via disordered spin chains

“…Following Ref. [54,55], we also assume that when dealing with time dependent disorder, the Hamiltonian changes with time only a finite number of times and after the same period τ .…”

Weak Disorder Enhancing the Production of Entanglement in Quantum Walks

“…Ordered QW and SDD QW have distinct characteristics regarding their entanglement generation. While the ordered QW reach a maximal entanglement for specific initial states [13][14][15][16][17], the SDD QW always achieve the maximal entanglement, but for distinct time rates depending on the initial state [25][26][27]. Since the entanglement generation of ordered QW and the rate of entanglement production in a disordered context are both sensitive to their initial conditions, in order to properly compare them and observe their general features, we perform the simulations to obtain the average entanglement using Eq.…”

“…Therefore, a controlled way to decrease the amount of disorder can be reached by introducing a probability to have one coin instead of the other. Once a random choice between Hadamard and Fourier coins has a better efficiency to achieve high entanglement rates than the one among infinite possibilities of coins [25,26] or with two other coins [27], then from this point, we will just deal with the first kind of disorder. Let us consider WDD 2 QW with a probability p(t) ∈ [0, 1] to obtain a Fourier coin, where for p = 0 we have a Hadamard QW, for p = 0.5 we recover SDD 2 QW and for p = 1 we have a Fourier QW.…”

“…When the QW start from the local state, ADO 2 in QW (∆t = 100) exceeds WDD 2 QW with p = 12% and SDD 2 QW, while from the Gaussian state, WDD 2 QW with p = 3% defeats ADO 2 in QW (∆t = 100) and SDD 2 QW, in both cases over almost the whole evolution on time. Moreover, we add an ordered simulation with one Fourier coin every 33 steps, which gives 3% of Fourier coins over all the steps, in order to emphasize the need of disorder to achieve maximal entanglement [25,26].…”

Asymptotic entanglement in quantum walks from delocalized initial states

“…For a QW starting from a local state, the maximal entanglement is reached asymptotically and only for few specific initial spin states [10,11,12,13] and also for two walkers [14]. The maximal entanglement is also achieved regardless of the initial state through the introduction of a dynamic disorder along the QW, such as a random quantum coin in each time step [15,16]. There are few papers about delocalized initial conditions in QW showing a rich variety of spreading behavior highly dependent of the quantum coin [17,18] and their entanglement content [19,20,21].…”