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arXiv:2005.06783 · Physical Review Applied

Programmable Coherent Linear Quantum Operations with High-Dimensional Optical Spatial Modes

Shikang Li, Shan Zhang, Xue Feng, Stephen M. Barnett, Wei Zhang, Kaiyu Cui, Fang Liu, Yidong Huang

Published Aug 12, 2020• 11 citations
arXivHTMLPDF

Abstract

A simple and flexible scheme for high-dimensional linear quantum operations is demonstrated on optical discrete spatial modes in the transverse plane. Quantum-state tomography via symmetric informationally complete positive-operator-valued measures and quantum Fourier transformation are implemented with dimensionality of 15. The statistical fidelity of symmetric informationally complete positive-operator-valued measures and the fidelity of quantum-state tomography are approximately 0.97 and up to 0.853, respectively, while the matrix fidelity of quantum Fourier transformation is 0.85. We believe that our approach has the potential for further exploration of high-dimensional spatial entanglement provided by spontaneous parametric down-conversion in nonlinear crystals.

DOI
10.1103/physrevapplied.14.024027

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A simple and flexible scheme for high-dimensional linear quantum operations is demonstrated on optical discrete spatial modes in the transverse plane. Quantum-state tomography via symmetric informationally complete positive-operator-valued measures and quantum Fourier transformation are implemented with dimensionality of 15. The statistical fidelity of symmetric informationally complete positive-operator-valued measures and the fidelity of quantum-state tomography are approximately 0.97 and up to 0.853, respectively, while the matrix fidelity of quantum Fourier transformation is 0.85. We believe that our approach has the potential for further exploration of high-dimensional spatial entanglement provided by spontaneous parametric down-conversion in nonlinear crystals.
Symmetric informationally complete positive operator-valued measures provide efficient quantum state tomography in any finite dimension.In this work, we implement state tomography using symmetric informationally complete positive operator-valued measures for both pure and mixed photonic qudit states in Hilbert spaces of orbital angular momentum, including spaces whose dimension is not power of a prime.Fidelities of reconstruction within the range of 0.81-0.96are obtained for both pure and mixed states.These results are relevant to high-dimensional quantum information and computation experiments, especially to those where a complete set of mutually unbiased bases is unknown.
Abstract Linear optical operations are fundamental and significant for both quantum mechanics and classical technologies. We demonstrate a non-cascaded approach to perform arbitrary linear operations for N -dimensional phase-coherent spatial modes using meticulously designed phase gratings. As implemented on spatial light modulators (SLMs), the unitary transformation matrix has been realized with dimensionalities ranging from 7 to 24 and the corresponding fidelities are from 95.1% to 82.1%. For the non-unitary operators, a matrix is presented for the tomography of a 4-level quantum system with a fidelity of 94.9%. Thus, the linear operator has been successfully implemented with much higher dimensionality than that in previous reports. It should be mentioned that our approach is not limited to SLMs and can be easily applied on other devices. Thus, our proposal could provide another option to perform linear operations with a simple, fixed, error-tolerant and scalable scheme.
Unitary transformations are the fundamental building blocks of gates and operations in quantum information processing, allowing the complete manipulation of quantum systems in a coherent manner. In the case of photons, optical elements that can perform unitary transformations are readily available only for some degrees of freedom, e.g., wave plates for polarization. However, for high-dimensional states encoded in the transverse spatial modes of light, performing arbitrary unitary transformations remains a challenging task for both theoretical proposals and actual implementations. Following the idea of multi-plane light conversion, we show that it is possible to perform a broad variety of unitary operations at high quality by using only a few phase modulation planes. More importantly, we experimentally implement several high-dimensional quantum gates for up to five-dimensional states encoded in the full-field mode structure of photons. In particular, we realize cyclic and quantum Fourier transformations, known as Pauli X ^ -gates and Hadamard H ^ -gates, respectively, with an average visibility of more than 90%. In addition, we demonstrate near-perfect “unitarity” by means of quantum process tomography, unveiling a process purity of 99%. Last, we demonstrate the benefit of the two independent spatial degrees of freedom, i.e., azimuthal and radial, and implement a two-qubit controlled-NOT quantum operation on a single photon. Thus, our demonstrations open up new paths to implement high-dimensional quantum operations, which can be applied to various tasks in quantum communication, computation, and sensing schemes.
An experimental demonstration of two-qutrit state tomography via one-qutrit symmetric informationally complete positive operator-valued measure (SIC-POVM) is presented. A two-qutrit state is encoded in the transversal paths of a spontaneous parametric down-converted photon pair. A spatial light modulator allows us to implement the necessary 81 POVM elements to reconstruct the state. The quality of the reconstruction is evaluated by comparing independent measurements with the predicted results calculated with the reconstructed state. Entanglement in the system is calculated via negativity and generalized robustness from the two-qutrit reconstructed density operator.
Positive operator valued measurements (POVMs) play an important role in efficient quantum communication and computation. While optical systems are one of the strongest candidates for long distance quantum communication and information processing, efficient methods to implement POVMs in these systems are scarce. Here we propose an all-optical scheme to implement an arbitrary POVM using linear optical components on m-dimensional Hilbert space of internal degrees of freedom. Linear optical nature of the proposed scheme makes it efficient and robust. We show how the scheme can be applied for state tomography and for preparing arbitrary mixed states.
High-dimensional linear operations are significant for the quantum optics. A non-cascaded approach is demonstrated to achieve arbitrary linear operations for phase-coherent spatial modes. With spatial light modulators (SLMs), unitary transformation matrices are obtained with dimensionalities ranging from 7 to 24 with the fidelities from 95.1% to 82.1%, respectively. Non-unitary matrix transformations are also presented in this work. Much higher dimensionality has been achieved compared to the previous reports with our approach, which is very promising for various applications in quantum domain.