Experimental realization of a quantum quincunx by use of linear optical elements

We discuss quantum random walk of two photons using linear optical elements. We analyze the quantum random walk using photons in a variety of quantum states including entangled states. We find that for photons initially in separable Fock states, the final state is entangled. For polarization entangled photons produced by type II downconverter, we calculate the joint probability of detecting two photons at a given site. We show the remarkable dependence of the two photon detection probability on the quantum nature of the state. In order to understand the quantum random walk, we present exact analytical results for small number of steps like five. We present in details numerical results for a number of cases and supplement the numerical results with asymptotic analytical results.

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“…Here unitary coin operator C and the conditioned shift operator S for QRW are given by the Eqs. (8) and (9) of the previous section.…”

Section: Qrw Of Two Photons With Separable Initial Statementioning

confidence: 92%

“…As a result various classical sources like low intensity lasers [8,13] and coherent state of radiation fields [4,14] are used to realize QRW. In order to explore further the quantum nature of random walk, we consider the case when two photons start QRW from a separable initial state…”

Section: Qrw Of Two Photons With Separable Initial Statementioning

confidence: 99%

Quantum Random Walk of two Entangled Qubits

Pathak

Agarwal

2006

Frontiers in Optics

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“…Single photon detector posed linear-optical version of the Galton board based on beamsplitters and phaseshifters [12,27]. A similar, polarization-encoded setup has been proposed for cube polarizing beamsplitters [28].…”

Section: Pbsmentioning

confidence: 99%

Discrete Single-Photon Quantum Walks With Tunable Decoherence

Broome

Fedrizzi

Lanyon

et al. 2010

Frontiers in Optics 2010/Laser Science XXVI

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Quantum walks have a host of applications, ranging from quantum computing to the simulation of biological systems. We present an intrinsically stable, deterministic implementation of discrete quantum walks with single photons in space. The number of optical elements required scales linearly with the number of steps. We measure walks with up to 6 steps and explore the quantum-to-classical transition by introducing tunable decoherence. Finally, we also investigate the effect of absorbing boundaries and show that decoherence significantly affects the probability of absorption.

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“…3 These properties generated broad interest in applying QWs to quantum information processing tasks. 4 Experimentally, QWs have been implemented using a wide array of platforms, including photonics, [5][6][7][8][9][10][11][12] trapped ions, 13,14 and ultra-cold atoms. [15][16][17] The current degree of experimental control of these systems is remarkable: it is possible to prepare an initial state with single-site and single-particle resolution, to control almost every aspect of the lattice potential, and to directly monitor the evolving wave function.…”

Section: Introductionmentioning

confidence: 99%

“…[15][16][17] The current degree of experimental control of these systems is remarkable: it is possible to prepare an initial state with single-site and single-particle resolution, to control almost every aspect of the lattice potential, and to directly monitor the evolving wave function. Early experiments demonstrated the behavior of single-particle QWs; however, these dynamics can be desribed by classical wave equations (indeed, some of these experiments were performed with coherent light) [5][6][7]9 ), and thus cannot display non-classical features. Non-classical behavior can be observed when several indistinguishable particles participate in the QW simultaneously, as was shown both theoretically 7,12,[18][19][20] and experimentally.…”

Section: Introductionmentioning

confidence: 99%

Quantum logic using correlated one-dimensional quantum walks

Lahini¹,

Steinbrecher²,

Bookatz³

et al. 2018

npj Quantum Inf

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Quantum Walks are unitary processes describing the evolution of an initially localized wavefunction on a lattice potential. The complexity of the dynamics increases significantly when several indistinguishable quantum walkers propagate on the same lattice simultaneously, as these develop non-trivial spatial correlations that depend on the particle's quantum statistics, mutual interactions, initial positions, and the lattice potential. We show that even in the simplest case of a quantum walk on a one dimensional graph, these correlations can be shaped to yield a complete set of compact quantum logic operations. We provide detailed recipes for implementing quantum logic on one-dimensional quantum walks in two general cases. For non-interacting bosons-such as photons in waveguide lattices-we find high-fidelity probabilistic quantum gates that could be integrated into linear optics quantum computation schemes. For interacting quantum-walkers on a one-dimensional lattice-a situation that has recently been demonstrated using ultra-cold atoms-we find deterministic logic operations that are universal for quantum information processing. The suggested implementation requires minimal resources and a level of control that is within reach using recently demonstrated techniques. Further work is required to address error-correction.npj Quantum Information (2018) 4:2 ;

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Experimental realization of a quantum quincunx by use of linear optical elements

Cited by 126 publications

References 26 publications

Quantum Random Walk of two Entangled Qubits

Quantum Random Walk of two Entangled Qubits

Discrete Single-Photon Quantum Walks With Tunable Decoherence

Quantum logic using correlated one-dimensional quantum walks

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