Trapping photons on the line: controllable dynamics of a quantum walk

Xue, Peng; Qi, Hao; Tang, Bao Quoc

doi:10.1038/srep04825

Cited by 36 publications

(37 citation statements)

References 41 publications

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“…Compared to the previous work by using position-dependent phase shifters [8,17], the sandwiched waveplates are an important technical advance for QW interferometry because the sandwiched waveplates do not require optical compensators whereas position-dependent phase shifters cause photons to experience phase differences due to optical path differences and must be compensated. The walker's evolution time t thus corresponds to longitudinally sequential QW steps.…”

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confidence: 99%

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Experimental Quantum-Walk Revival with a Time-Dependent Coin

et al. 2015

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We demonstrate a quantum walk with time-dependent coin bias. With this technique we realize an experimental single-photon one-dimensional quantum walk with a linearly-ramped time-dependent coin flip operation and thereby demonstrate two periodic revivals of the walker distribution. In our beam-displacer interferometer, the walk corresponds to movement between discretely separated transverse modes of the field serving as lattice sites, and the time-dependent coin flip is effected by implementing a different angle between the optical axis of half-wave plate and the light propagation at each step. Each of the quantum-walk steps required to realize a revival comprises two sequential orthogonal coin-flip operators, with one coin having constant bias and the other coin having a time-dependent ramped coin bias, followed by a conditional translation of the walker. [4][5][6] plus the fundamental interest of being a natural quantized version of the ubiquitous random walk that appears in statistics, computer science, finance, physics, and chemistry. QW research has focused on evolution due to repeated applications of a time-independent unitary step operator U , but a QW with time-dependent unitary steps U (t), with discrete time t ∈ N := {0, 1, 2, . . . }, opens a much richer array of phenomena including localization and quasiperiodicity [7,8]. Here we demonstrate a time-dependent QW and use this technique to demonstrate a revival of the walker's position distribution.Rather than employing direct time-dependent control, we simulate time-dependent coin control by setting different coin parameters for different steps, which are effected in different locations along the longitudinal axis within our photonic beam-displacer interferometer (BDI) [9]. The quantum walker within the BDI is a single heralded photon produced by spontaneous parametric down conversion, and its walking degree of freedom is the set of discretely spaced transverse beam modes. The coin flip is effected by employing quarter-and half-wave plates.Our method for realizing the first time-dependent QW demonstrates the phenomenon of revivals and also opens the door to realizing a multitude of time-dependent QWs experimentally. Compared to prior work employing position-dependent control [10][11][12], our new technique decreases experimental complexity by relaxing the requirement of optical compensation. Our QW revival displays a different characteristic than typical QW properties such as ballistic spreading and localization of the walker distribution.The QW with a coin proceeds as a sequence of coin flips and then walker-coin entangling operations whereby the walker's position is displaced according to the coin state. We explain the QW now in full generality so the coin operator admits both spatial and temporal dependence. Spatially-dependent coin operations have dramatically demonstrated the realization of topological phases by QWs [4][5][6], but the time-dependent QW is, until now, only a theoretical construct and not yet explored experimentally.We employ a two...

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“…The probability for more than one photon pair is less than 10 −4 hence neglected. The walker photon goes through a BDI [8,9,17], which is a robust interferometer that enables more steps than is the case for other interferometers.…”

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confidence: 99%

Experimental Quantum-Walk Revival with a Time-Dependent Coin

et al. 2015

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“…The quantum walk describes quantum dynamics of particles by a time-evolution operator, instead of a Hamiltonian. The quantum walks have been realized in various experimental setups, such as cold atoms [33], trapped ions [34,35], and optical systems [36][37][38][39][40]. Since quantum walks enable high tunability of the system setup, various phenomena which require delicate setups have been observed, such as Anderson localization [41,42], scattering with positive-and negative-mass pulses [43], emergence of edge states which stem from topological phases [44], and so on.…”

Section: Introductionmentioning

confidence: 99%

Explicit definition ofPTsymmetry for nonunitary quantum walks with gain and loss

Mochizuki¹,

Kim²,

Obuse³

2016

Phys. Rev. A

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PT symmetry, that is, a combined parity and time-reversal symmetry, is a key milestone for non-Hermitian systems exhibiting entirely real eigenenergy. In the present work, motivated by a recent experiment, we study PT symmetry of the time-evolution operator of nonunitary quantum walks. We present the explicit definition of PT symmetry by employing a concept of symmetry time frames. We provide a necessary and sufficient condition so that the time-evolution operator of the nonunitary quantum walk retains PT symmetry even when parameters of the model depend on position. It is also shown that there exist extra symmetries embedded in the time-evolution operator. Applying these results, we clarify that the nonunitary quantum walk in the experiment does have PT symmetry.

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“…This property makes QWs a promising resource in the development of new quantum algorithms [10]. The QW also shows potential for quantum simulation [11][12][13][14][15][16][17][18][19] and for universal quantum computation [20][21][22]. Various studies for implementing QWs in different physical systems have been made [23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Perfect state transfer and efficient quantum routing: A discrete-time quantum-walk approach

Zhan

Bian

et al. 2014

Phys. Rev. A

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We show that a perfect state transfer of an arbitrary unknown two-qubit state can be achieved via a discrete-time quantum walk with various settings of coin flips and extend this method to the distribution of an arbitrary unknown multiqubit entangled state between every pair of sites in the multidimensional network. Furthermore, we study the routing of quantum information on this network in a quantum-walk architecture, which can be used as quantum information processors to communicate between separated qubits.

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Trapping photons on the line: controllable dynamics of a quantum walk

Cited by 36 publications

References 41 publications

Experimental Quantum-Walk Revival with a Time-Dependent Coin

Experimental Quantum-Walk Revival with a Time-Dependent Coin

Explicit definition ofPTsymmetry for nonunitary quantum walks with gain and loss

Perfect state transfer and efficient quantum routing: A discrete-time quantum-walk approach

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