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arXiv:1906.09148 · Quantum Science and Technology

Generation of hybrid maximally entangled states in a one-dimensional quantum walk

Aikaterini Gratsea, Maciej Lewenstein, Alexandre Dauphin

Published Jan 16, 2020• 31 citations
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Abstract

Abstract We study the generation of hybrid entanglement in a one-dimensional quantum walk. In particular, we explore the preparation of maximally entangled states between position and spin degrees of freedom. We address it as an optimization problem, where the cost function is the Schmidt norm. We then benchmark the algorithm and compare the generation of entanglement between the Hadamard quantum walk, the random quantum walk and the optimal quantum walk. Finally, we discuss an experimental scheme with a photonic quantum walk in the orbital angular momentum of light. The experimental measurement of entanglement can be achieved with quantum state tomography.

DOI
10.1088/2058-9565/ab6ce6

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Abstract We study the generation of hybrid entanglement in a one-dimensional quantum walk. In particular, we explore the preparation of maximally entangled states between position and spin degrees of freedom. We address it as an optimization problem, where the cost function is the Schmidt norm. We then benchmark the algorithm and compare the generation of entanglement between the Hadamard quantum walk, the random quantum walk and the optimal quantum walk. Finally, we discuss an experimental scheme with a photonic quantum walk in the orbital angular momentum of light. The experimental measurement of entanglement can be achieved with quantum state tomography.
We study maximal coin-position entanglement generation via a discrete-time quantum walk, in which the coin operation is randomly selected from one of two coin operators set at each step. We solve maximal entanglement generation as an optimization problem with quantum process fidelity as the cost function. Then we determine the maximal entanglement that can be rigorously generated for any step beyond the second regardless of initial conditions with appropriate coin sequences. The simplest coin sequence comprising Hadamard and identity operations is equivalent to the generalized elephant quantum walk, which exhibits an increasingly faster spreading in terms of probability distribution. Experimentally, we demonstrate a ten-step quantum walk driven by such coin sequences with linear optics and thereby show the desired high-dimensional bipartite entanglement as well as the transport behavior of faster spreading.
Hybrid entangled states exhibit entanglement between different degrees of freedom of a particle pair and thus could be useful for asymmetric optical quantum network where the communication channels are characterized by different properties. We report the first experimental realization of hybrid polarization-orbital angular momentum (OAM) entangled states by adopting a spontaneous parametric down conversion source of polarization entangled states and a polarization-OAM transferrer. The generated quantum states have been characterized through quantum state tomography. Finally, the violation of Bell's inequalities with the hybrid two photon system has been observed.
High-dimensional entangled states in an orbital-angular-momentum (OAM) basis offer several unique advantages for quantum information applications. However, for the optimal performance of a given application, one requires a generation technique for OAM entangled states that is completely postselection-free and fully controllable. Nonetheless, despite several efforts in the past, no such technique currently exists. In this paper, we propose just such a technique and experimentally demonstrate postselection-free generation of up to about 150-dimensional OAM entangled states. We report the generation accuracy, which is a measure of the control, to be more than $98\mathrm{%}$ for states with Gaussian and triangular OAM Schmidt spectra, and up to $90\mathrm{%}$ for the maximally entangled OAM states, which have rectangular spectra.
Bell state measurement (BSM) plays an important role in quantum information processing. However, a complete BSM cannot be achieved with linear optics with current technology. In this paper, we present a scheme for realizing single-photon BSM via a one-dimensional photonic quantum random walk. In our scheme, the maximally entangled states with polarization and path degrees of freedom are used as Bell states; then a complete BSM based on quantum random walk can be implemented in single-photon Hilbert space. Detecting single-photon count at different positions can provide unambiguous discrimination of all four Bell states to verify our scheme. Furthermore, we also discuss how to apply our BSM scheme to the proposed single-photon cryptography system.
Quantum walks can be used either as tools for quantum algorithm development or as entanglement generators, potentially useful to test quantum hardware. We present a novel algorithm based on a discrete Hadamard quantum walk on a line with one coin and two walkers whose purpose is to generate entanglement between walkers. We provide several classical computer simulations of our quantum algorithm in which we show that, although the asymptotical amount of entanglement generated between walkers does not reach the highest degree of entanglement possible at each step for either coin measurement outcome, the entanglement ratio (entanglement generated/highest value of entanglement possible, for each step) tends to converge, and the actual convergence value depends on the coin initial state and on the coin measurement outcome. Furthermore, our numerical simulations show that, for the quantum walks used in our algorithm, the value towards which entanglement ratio converges also depends on the position probability distribution symmetry of a quantum walk computed with one single walker and the same coin initial state employed in the corresponding quantum walk with two walkers.
While the existence of disorders is commonly believed to weaken the unique properties of quantum systems, recent progress has predicted that it can exhibit a counterintuitive enhanced effect on the behavior of entanglement generation, which is even independent of the chosen initial conditions and physical platforms. However, to achieve a maximally entangled state in such disordered quantum systems, the key limitation of this is the scarcity of an infinite coherence time, which makes its experimental realization challenging. Here, we experimentally investigate the entanglement entropy dynamics in a photonic quantum walk with disorders in time. Through the incorporation of a classic optimization algorithm, we experimentally demonstrate that such disordered systems can relax to a high-entanglement hybrid state at any given time step. Moreover, this prominent entangling ability is universal for a wide variety of initial conditions. Our results may inspire achieving a well-controlled entanglement generator for quantum computation and information tasks.