Discord and entanglement of two-particle quantum walk on cycle graphs

Rodriguez, J. P. J.; Li, Zhonghua; Wang, Jingbo

doi:10.1007/s11128-014-0859-y

Cited by 8 publications

(4 citation statements)

References 19 publications

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“…It is clear from the result (18) that none of the original degrees of freedom {S 1 , S 2 , X 1 , X 2 } factorizes for t > 0. On the other hand, the two-spin state (19) depends only on the relative coordinate, so that the state associated with the center of mass must factorize. This can be proved as follows.…”

Section: B Two Walkersmentioning

confidence: 99%

“…For instances involving two quantum walkers [16], the production of nonclassical features-hereafter referred to generically as quantumnesses-becomes even more sophisticated. Different partitions exist and entanglement can be found between the subsystems (position-spin of one particle with position-spin of another particle) [17,18], the spins [19], and the positions [20]. Incidentally, it is precisely the presence of interaction-and entanglement-between the walkers that makes it possible to solve, for example, a wider range of graph isomorphism problems when compared to noninteracting walkers [21].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: B Two Walkersmentioning

confidence: 99%

Section: Introductionmentioning

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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“…Most papers addressing interacting quantum walks employs the phase interaction [21,22,25], which is different from the one based on the HPP model. The evolution operator based on the phase interaction is defined as…”

Section: Interacting Quantum Walk With Hpp Collision Rulesmentioning

confidence: 99%

“…Two-particle quantum walks were applied to the graph isomorphism problem [16,17], and also to show that an interacting quantum walk dynamics might lead to the formation of a stable compound state [18]. In these references, as well as in others [17,[19][20][21][22], the interaction is described by an operation that changes the relative phase between the walkers if they are on the same node.…”

Section: Introductionmentioning

confidence: 99%

Multiparticle quantum walk with a gaslike interaction

2019

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We analyze the dynamics of multiparticle discrete-time quantum walk on the two-dimensional lattice, with an interaction inspired on a classical model for gas collision, called HPP model. In this classical model, the direction of motion changes only when the particles collide head-on, preserving momentum and energy. In our quantum model, the dynamics is driven by the usual quantum-walk evolution operator if the particles are on different nodes, and is driven by the HPP rules if the particles are in the same node, linearly extended for superpositions. Using this new form of evolution operator, we numerically analyze three physical quantities for the two-walker case: The probability distribution of the position of one walker, the standard deviation of the position of one walker, and the entanglement between the walkers as a function of the number of steps. The numerical analysis implies that the entanglement between the walkers as a function of the number of steps initially increases and quickly tends to a constant value, which depends on the initial condition. We compare the results obtained using the HPP interaction with the equivalent ones using the phase interaction, which is based on an evolution operator that inverts the sign of the coin operator if the walkers are in the same position. arXiv:1906.07293v1 [quant-ph]

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Two Quantum Coins Sharing a Walker

Yang

Han

et al. 2018

Int J Theor Phys

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Discord and entanglement of two-particle quantum walk on cycle graphs

Cited by 8 publications

References 19 publications

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

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

Multiparticle quantum walk with a gaslike interaction

Two Quantum Coins Sharing a Walker

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