We show that the entanglement between the internal (spin) and external (position) degrees of freedom of a qubit in a random (dynamically disordered) one-dimensional discrete time quantum random walk (QRW) achieves its maximal possible value asymptotically in the number of steps, outperforming the entanglement attained by using ordered QRW. The disorder is modeled by introducing an extra random aspect to QRW, a classical coin that randomly dictates which quantum coin drives the system's time evolution. We also show that maximal entanglement is achieved independently of the initial state of the walker, study the number of steps the system must move to be within a small fixed neighborhood of its asymptotic limit, and propose two experiments where these ideas can be tested.

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.

We show that using a slightly modified XX model for a spin-1/2 chain, one can transmit almost perfectly a maximally entangled two-qubit state from one end of the chain to the other one. This is accomplished without external fields or modulation of the coupling constants among the qubits. We also show that this strategy works for any size of the chain and is relatively robust to imperfections in the coupling constants among the qubits belonging to the chain. Actually, under certain scenarios of small disorder, we obtain better results than those predicted by the optimal ordered and noiseless case.

We investigate how robust is the modified XX spin-1/2 chain of [R. G. Rigolin, Phys. Lett. A 382, 2586 (2018)] in transmitting entanglement when several types of disorder and noise are present. First, we consider how deviations about the optimal settings that lead to almost perfect transmission of a maximally entangled two-qubit state affect the entanglement reaching the other side of the chain. Those deviations are modeled by static, dynamic, and fluctuating disorder. We then study how spurious or undesired interactions and external magnetic fields diminish the entanglement transmitted through the chain. For chains of the order of hundreds of qubits, we show for all types of disorder and noise here studied that the system is not appreciably affected when we have weak disorder (deviations of less than 1% about the optimal settings) and that for moderate disorder it still beats the standard and ordered XX model when deployed to accomplish the same task. IntroductionAn important tool in the practical implementation of quantum computation and communication tasks is the reliable transmission of quantum states from one location to another [1]. Quantum information, or equivalently a quantum state, can be sent from one party (Alice) to another (Bob) in at least three ways, namely, via direct transmission, via the quantum teleportation protocol [2], and via spin chains [3]. This last strategy, where Alice and Bob are connected by a spin chain through which they can send quantum states to each

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