Connecting velocity and entanglement in quantum walks

Orthey, Alexandre C.; Amorim, Edgard P. M.

doi:10.1103/physreva.99.032320

Cited by 15 publications

(10 citation statements)

References 37 publications

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“…The second main characteristic is the entanglement between spin and position, which also has a strong dependence on the initial state and used quantum coin. The initial qubits which lead to the maximal entanglement necessarily also lead to a symmetrical probability distribution regardless of the initial position state [18]. At the same time, while there are only two particular initial qubits over one position (local state) which lead the quantum walk to asymptotically time-evolve to the maximal entanglement condition, when a quantum walk starts from a delocalized state, there are infinite available initial qubits to reach this condition [19].…”

Section: Resultsmentioning

confidence: 99%

Trojan Quantum Walks

Ghizoni

Amorim

2019

Braz J Phys

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We investigate the transport properties and entanglement between spin and position of one-dimensional quantum walks starting from a qubit over position states following a delta-like (local state) and Gaussian (delocalized state) distributions. We find out that if the initial state is delocalized enough and a NOT gate reflects this state backwards, then the interference pattern extinguishes the position dispersion without preventing the propagation of the state. This effect allows the creation of a Trojan wave packet, a non-spreading and non-stationary double-peak quantum state.Keywords Spreading · Entanglement · Gaussian states · Quantum walks 1 IntroductionFrom the epic poem Iliad, the term "Trojan" was used to name a group of asteroids which share the Jupiter's orbit around the Sun. The center of mass of the Trojan asteroids is steady relative to Jupiter, once they are trapped on stable Lagrange regions (L 4 and L 5 ) of this celestial mechanical system [1]. In the quantum-mechanical context, Trojan wave packets have non-spreading and nonstationary behavior and they have been observed as a localized Rydberg electron over a circular orbit with dispersion suppressed by external fields [2,3].Quantum walks are the quantum analogue of the classical random walks [4]. The quantum walker is a spin-1/2 particle positioned over discrete positions in a one-dimensional lattice. The quantum walk state is composed by a tensor product between the internal (spin) and external (position) degrees of freedom. The time

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Section: Resultsmentioning

confidence: 99%

Trojan Quantum Walks

Ghizoni

Amorim

2019

Braz J Phys

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“…In this work, by introducing a Gaussian model, which proved to be quite accurate for delocalized walkers (σ 0 ≫ 1), we were able to conduct a profound analysis of the quantumnesses dynamics in a two-walker system. Previous studies [33,34,41,[53][54][55][56][57] allow us to optimistically speculate upon the applicability of our model even to scenarios involving more localized states.…”

Section: Discussionmentioning

confidence: 80%

“…[48]. On the other hand, EPR steering and Bell nonlocality become distinguishable when at least three measurements are allowed per site, in which case the following EPR steering quantifier can be derived for the general twoqubit state (34):…”

Section: B Epr Steeringmentioning

confidence: 99%

Nonlocality, quantum correlations, and violations of classical realism in the dynamics of two noninteracting quantum walkers

Orthey

Angelo

2019

Phys. Rev. A

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That quantum correlations can be generated over time between the spin and the position of a quantum walker is indisputable. The creation of bipartite entanglement has also been reported for two-walker systems. In this scenario, however, since the global state lies in a fourpartite Hilbert space, the question arises as to whether genuine multipartite entanglement may develop in time. Also, since the spatial degrees of freedom can be viewed as a noisy channel for the two-spin part, one may wonder how other nonclassical aspects (quantumnesses), such as Bell nonlocality, Einstein-Podolsky-Rosen steering, quantum discord, and symmetrical quantum discord, evolve in time during the walk. The scarcity of such a broader investigation is possibly due to computational difficulties associated with the recursive nature of quantum walks. Here, we work around this issue by introducing a simplified Gaussian model which proves to be very accurate within a given domain and powerful for the analytical studies. Then, for an instance involving two noninteracting quantum walkers, whose spins start in the singlet state, we quantify the aforementioned quantumnesses as a function of time, and evaluate violations of both realism and related aspects of locality. In addition, we analyze situations in which the initial two-spin state is affected by white noise. The typical scenario found is such that while genuine fourpatite entanglement increases over time, all the investigated quantumnesses vanish (suddenly or asymptotically) except realism-based nonlocality. Moreover, realism is prevented for all finite times.

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“…Quantum walks are a promising framework to implement a variety of quantum tasks, such as quantum search algorithms [7,8] and universal quantum computation [9,10]. A rich dynamical behavior can be engineered in a quantum walk, ranging from diffusive to ballistic transport [11][12][13][14][15][16][17][18], and many physical systems can be used to experimentally build a quantum walk [19,20].…”

Section: The Protocol's Platformmentioning

confidence: 99%

Quantum Corralling

Vieira,

Rigolin,

Amorim

2021

Preprint

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We propose a robust and efficient way to store and transport quantum information via onedimensional discrete time quantum walks. We show how to attain an effective dispersionless wave packet evolution using only two types of local unitary operators (quantum coins or gates), properly engineered to act at predetermined times and at specific lattice sites during the system's time evolution. In particular, we show that a qubit initially localized about a Gaussian distribution can be almost perfectly confined during arbitrary long times or sent and latter recovered at arbitrary distances using only Hadamard and σx gates.

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Connecting velocity and entanglement in quantum walks

Cited by 15 publications

References 37 publications

Trojan Quantum Walks

Trojan Quantum Walks

Nonlocality, quantum correlations, and violations of classical realism in the dynamics of two noninteracting quantum walkers

Quantum Corralling

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