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Physical Review A

Automated quantum operations in photonic qutrits

G. F. Borges, Roberto D. Baldijão, J. G. L. Condé, Jader Cabral, Breno Marques, Marcelo Terra Cunha, Adán Cabello, Sebastião Pádua

Published Feb 2, 2018• 8 citations
Publisher

Abstract

We report an experimental implementation of automated state transformations on spatial photonic qutrits following the theoretical proposal made by Baldij\~ao et al. [Phys. Rev. A 96, 032329 (2017)]. A qutrit state is simulated by using three Gaussian beams, and after some state operations, the transformed state is available in the end in terms of the basis state. The state transformation setup uses a spatial light modulator and a calcite-based interferometer. The results reveal the usefulness of the operation method. The experimental data show a good agreement with theoretical predictions, opening possibilities for explorations in higher dimensions and in a wide range of applications. This is a necessary step in qualifying spatial photonic qudits as a competitive setup for experimental research in the implementation of quantum algorithms which demand a large number of steps.

DOI
10.1103/physreva.97.022301

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We report an experimental implementation of automated state transformations on spatial photonic qutrits following the theoretical proposal made by Baldij~ao et al. [Phys. Rev. A 96, 032329 (2017)]. A qutrit state is simulated by using three Gaussian beams, and after some state operations, the transformed state is available in the end in terms of the basis state. The state transformation setup uses a spatial light modulator and a calcite-based interferometer. The results reveal the usefulness of the operation method. The experimental data show a good agreement with theoretical predictions, opening possibilities for explorations in higher dimensions and in a wide range of applications. This is a necessary step in qualifying spatial photonic qudits as a competitive setup for experimental research in the implementation of quantum algorithms which demand a large number of steps.
We propose a method for implementing automated state transformations on single-photon multipath qudits encoded in a one-dimensional transverse spatial domain. It relies on transferring the encoding from this domain to the orthogonal one by applying a spatial phase modulation with diffraction gratings, merging all the initial propagation paths by using a stable interferometric network, and filtering out the unwanted diffraction orders. The automation feature is attained by utilizing a programmable phase-only spatial light modulator (SLM) where properly designed diffraction gratings displayed on its screen will implement the desired transformations, including, among others, projections, permutations, and random operations. We discuss the losses in the process which is, in general, inherently nonunitary. Some examples of transformations are presented and, considering a realistic scenario, we analyze how they will be affected by the pixelated structure of the SLM screen. The method proposed here enables one to implement much more general transformations on multipath qudits than is possible with a SLM alone operating in the diagonal basis of which-path states. Therefore, it will extend the range of applicability for this encoding in high-dimensional quantum information and computing protocols as well as fundamental studies in quantum theory.
Higher dimensional quantum systems have a very important role to play in quantum information, computation as well as communication. In photonic systems, it is common to use the photon's polarization degree of freedom for various investigations. However, this restricts us to only two orthogonal states, hence qubits for manipulation. In this paper, we have theoretically analysed and experimentally demonstrated a system of two photonic qutrits which are correlated in the spatial degree of freedom. The qutrits have been generated by modulating the pump beam in a spontaneous parametric down conversion process using an aperture based system. In principle, this system can be scaled up to generation of even higher dimensional correlated qudits with possible application for quantum communication and computation implementations.
Higher dimensional quantum systems have a very important role to play in quantum information, computation as well as communication. While the polarization degree of freedom of the photon is a common choice for many studies, it is restricted to only two orthogonal states, hence qubits for manipulation. In this paper, we theoretically model as well as experimentally verify a novel scheme of approximating photonic qutrits by modulating the pump beam in a spontaneous parametric down conversion process using a three-slit aperture. The emerging bi-photon fields behave like qutrits and are found to be highly correlated in the spatial degree of freedom and effectively represent spatially correlated qutrits with a Pearson coefficient as high as 0.9. In principle, this system provides us a scalable architecture for generating and experimenting with higher dimensional correlated qudits.
Abstract Discussions about quantum interference, indistinguishability, and superposition between quantum states go back to the beginning of quantum mechanics. However, the theoretical problem, concerning quantitative measures for quantum coherence, was only recently solved by Baumgratz et al (2014 Phys. Rev. Lett. 113 140401). Since then, many works have explored one of the possible coherence measures: the l 1 norm, which has not yet been obtained experimentally for spatial photonic states in high dimensions. In this article, we study the measurement of spatial qudits quantum coherence. We treat the optical measure-operators as path-markers and show in which condition an interference pattern can be used for measure l 1 norm. We analyze the validity of a l 1 norm measurement method, proposed by Paul and Qureshi (2017 Phys. Rev. A 95 042110), implementing it experimentally in qutrit states, and propose an alternative method for qudits states in which one of their assumptions does not apply.
This work proposes to carry out a study on integrated photonic circuits. Our goal is to develop a methodology for obtaining the parameters of a photonic circuit that allows us to perform a set of quantum operations necessary for the realization of a given task or quantum processing. More specifically, the quantum tasks involve the implementation of a POVM (Positive Operator Value Measure) through integrated photonic circuits. Thus, we seek to obtain optimized configurations for these devices so that the reduction of their structural complexity simplifies their manufacturing process. In addition, it is also our goal that such objects are robust against errors and losses and that the experimental applications that involve them present a minimization of the time necessary for their realization. We studied the symmetries of the proposed POVMs to, from them, configure the circuit in an optimized way. Initially, we studied the case of quantum state tomography for qubits and qutrits. We obtained planar circuits that had a smaller number of optical elements and an optical depth than those obtained by methods already known in the literature. In addition, these circuits implement all POVM elements at once, making it possible to obtain all their associated probabilities at once, minimizing the time spent on the experiment compared to experiments on an optical table or with reconfigurable circuits, where it is necessary to make changes to the configuration of the experimental apparatus from one POVM element to another. Looking for a way to generalize our protocol to larger systems, we developed a method to obtain three-dimensional photonic circuits that can be used in the experimental realization of quantum state tomography in qudits of any finite dimension. Our protocol generates circuits whose number of beam splitters and optical depth scale with functions less than in other protocols already known, showing a drastic reduction in their complexity. In addition, these circuits were highly robust in relation to the occurrence of losses. The same protocol used to obtain three-dimensional circuits for performing quantum tomography can be used to obtain circuits to implement quantum coherence measurements. The circuits obtained here also have the same advantages as the tomographic case.