Entanglement dynamics of two-particle quantum walks

Carson, G. R.; Loke, T.; Wang, Jingbo

doi:10.1007/s11128-015-1047-4

Cited by 18 publications

(11 citation statements)

References 25 publications

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“…Similar behaviors for the fidelity were observed for generic spin states, thus indicating the broad adequacy of our model. In possession of solution (18), we are ready to conduct a thorough study of several quantumness that develop over time in the two-body quantum walk under scrutiny. Basically, we divide the presentation in two parts.…”

Section: B Two Walkersmentioning

confidence: 99%

“…Using the state (18) we computed all possible reduced states 1 ρ γ i . For instance, for the two-spin state we found…”

Section: Genuine Fourpartite Entanglementmentioning

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%

“…Using the state (18) we computed all possible reduced states 1 ρ γ i . For instance, for the two-spin state we found…”

Section: Genuine Fourpartite Entanglementmentioning

confidence: 99%

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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“…Details differ for specific implementations of * e-mail: simond@bu.edu † e-mail: sosawa@bu.edu ‡ e-mail: alexserg@bu.edu quantum walks, but discussion of quadratic speedups can be found in [7] for Hadamard walks and in [8,9] for Grover walk-based searches. A variety of two-particle quantum walks have been studied [10][11][12][13][14][15][16][17][18][19]. Here we look at a novel arrangement in which two indistinguishable bosons undergo a discretetime quantum walk along a dual rail or ladder type system ( Fig.…”

Section: Introductionmentioning

confidence: 99%

Quantum-clustered two-photon walks

Simon

Osawa

2020

Phys. Rev. A

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We demonstrate a previously unknown two-photon effect in a discrete-time quantum walk. Two identical bosons with no mutual interactions nonetheless can remain clustered together as they walk on a lattice of directionally-reversible optical four-ports acting as Grover coins; both photons move in the same direction at each step due to a two-photon quantum interference phenomenon reminiscent of the Hong-Ou-Mandel effect. The clustered two-photon amplitude splits into two localized parts, one oscillating near the initial point, and the other moving ballistically without spatial spread, in soliton-like fashion. But the two photons are always clustered in the same part of the superposition, leading to potential applications for transport of entanglement and opportunities for novel two-photon interferometry experiments.

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“…Extension of single-particle DQW with entangled coin operation has been previously studied [34][35][36]. Two-particle quantum walk under position dependent or independent coin operations which are separable in their coin degrees of freedom, has been investigated [37][38][39][40][41][42]. Here we study a two-particle coined SS-DQW whose coin operations are both position and time dependent and entangled in coin degrees of freedom of the individual particlethe interaction comes solely from the coin operations, while no interaction among the particles is present via their spatial shift operations.…”

Section: Introductionmentioning

confidence: 99%

Simulating Dirac Hamiltonian in curved space-time by split-step quantum walk

et al. 2019

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Dirac particle represents a fundamental constituent of our nature. Simulation of Dirac particle dynamics by a controllable quantum system using quantum walks will allow us to investigate the nonclassical nature of dynamics in its discrete form. In this work, starting from a modified version of onespatial dimensional general inhomogeneous split-step discrete quantum walk we derive an effective Hamiltonian which mimics a single massive Dirac particle dynamics in curved (1+1) space-time dimension coupled to U(1) gauge potential-which is a forward step towards the simulation of the unification of electromagnetic and gravitational forces in lower dimension and at the single particle level. Implementation of this simulation scheme in simple qubit-system has been demonstrated. We show that the same Hamiltonian can represent (2+1) space-time dimensional Dirac particle dynamics when one of the spatial momenta remains fixed. We also discuss how we can include U(N) gauge potential in our scheme, in order to capture other fundamental force effects on the Dirac particle. The emergence of curvature in the two-particle split-step quantum walk has also been investigated while the particles are interacting through their entangled coin operation.operations-mimics the Dirac evolution under influence of gravitational waves in (2+1) dimension-was also recently reported in [24]. In [25], it is shown that the SS-DQW, where the coin parameters are space and timestep independent, can capture properties of the discretized Dirac particle dynamics in flat (1+1) dimension, while conventional DQW is unable to capture all properties of it. This motivates us to generalize the SS-DQW operation and study the consequences of it.In this paper starting from a slightly modified version of the single-step split-step DQW (SS-DQW) [26] whose coin operators are time and position-step dependent (inhomogeneous both in time and space), we derive a SS-DQW version of the (1+1) dimensional massive Dirac particle Hamiltonian under the influence of the U(1) gauge potential in curved space-time. This scheme is realizable in various physical table-top system as the SS-DQW has been proposed and successfully implemented in various systems like cold atoms [27], superconducting qubits [28,29], photonic systems [30,31]. Our scheme can also describe the (2+1) dimensional Dirac Hamiltonian in curved space-time when one component of momentum of the particle remains fixed. We provide realization of our simulation scheme using qubit systems. This scheme doesn't require any prior encoding or decoding, nor it demands extra conditions on the coin parameters in order to satisfy the boundedness (well-defined eigenvalues) of the generator which is the effective Hamiltonian in our case, i.e.the unitary operator should start evolution from identity while the parameter of the corresponding lie group evolves from zero to a nonzero real value. Our coin operations are general U(2) group elements in coinspace. After considering all the terms up to first order in time-step s...

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Entanglement dynamics of two-particle quantum walks

Cited by 18 publications

References 25 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

Quantum-clustered two-photon walks

Simulating Dirac Hamiltonian in curved space-time by split-step quantum walk

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