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arXiv:2310.08838 · Optica

Higher-dimensional symmetric informationally complete measurement via programmable photonic integrated optics

Lan‐Tian Feng, Xiao‐Min Hu, Ming Zhang, Yujie Cheng, Chao Zhang, Yu Hua Guo, Yuyang Ding, Zhibo Hou, Fang‐Wen Sun, Guang‐Can Guo, Daoxin Dai A, Armin Tavakoli, Xi-Feng Ren, Bi‐Heng Liu

Published Jun 2, 2025• 2 citations
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Abstract

Symmetric informationally complete measurements are both important building blocks in many quantum information protocols and the seminal example of a generalized, non-orthogonal, and quantum measurement. In higher-dimensional systems, these measurements become both increasingly interesting and increasingly complex to implement. Here, we demonstrate an integrated quantum photonic platform, operating at high fidelities, to realize such a measurement on three-level quantum systems. We demonstrate the quality of the measurement device by verifying a genuine many-outcome quantum measurement, performing near-optimal quantum state discrimination, and beating the projective limit in quantum random number generation. Moreover, the device is programmable and can readily implement other quantum measurements at similarly high quality. Our work paves the way for the implementation of sophisticated higher-dimensional quantum measurements that go beyond the traditional orthogonal projections.

DOI
10.1364/optica.551264

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Symmetric informationally complete measurements are both important building blocks in many quantum information protocols and the seminal example of a generalized, non-orthogonal, and quantum measurement. In higher-dimensional systems, these measurements become both increasingly interesting and increasingly complex to implement. Here, we demonstrate an integrated quantum photonic platform, operating at high fidelities, to realize such a measurement on three-level quantum systems. We demonstrate the quality of the measurement device by verifying a genuine many-outcome quantum measurement, performing near-optimal quantum state discrimination, and beating the projective limit in quantum random number generation. Moreover, the device is programmable and can readily implement other quantum measurements at similarly high quality. Our work paves the way for the implementation of sophisticated higher-dimensional quantum measurements that go beyond the traditional orthogonal projections.
Programmable photonic quantum processors face a critical challenge: despite significant advances in quantum state preparation and manipulation, measurements remain limited to projective techniques. Here, we demonstrate a programmable measurement processor that overcomes this limitation by enabling arbitrary quantum measurements within a scalable circuit framework. Our large-scale integrated photonic architecture achieves precise coherent control of ancillary quantum systems, realizing a universal four-dimensional quantum measurement device. We benchmark the processor by performing measurement tomography on 100 randomly selected measurements, achieving an average fidelity of 97.7%. The processor's performance exceeds the theoretical limits of projective measurements in three key quantum information tasks: state discrimination (with 23 times lower error), state estimation (with 10.6% higher fidelity), and randomness generation (with 37% more randomness yield), demonstrating its high operational quality. This work establishes a fully programmable quantum measurement processor, advancing the development of universal quantum operations for photonic quantum information processing by providing the key missing component.
It is crucial for various quantum information processing tasks that the state of a quantum system can be determined reliably and efficiently from general quantum measurements. One important class of measurements for this purpose is symmetric informationally complete positive operator-valued measurements (SIC-POVMs). SIC-POVMs have the advantage of providing an unbiased estimator for the quantum state with the minimal number of outcomes needed for full tomography. By virtue of Naimark's dilation theorem, any POVM can always be realized with a suitable coupling between the system and an auxiliary system and by performing a projective measurement on the joint system. In practice, finding the appropriate coupling is rather nontrivial. Here we propose an experimental design for directly implementing SIC-POVMs using multiport devices and path-encoded qubits and qutrits, the utility of which has recently been demonstrated by several experimental groups around the world. Furthermore, we describe how these multiports can be attained in practice with an integrated photonic system composed of nested linear optical elements.
Quantum measurements play a fundamental role in quantum mechanics. Especially, generalized quantum measurements provide a powerful and versatile tool to extract information from quantum systems. However, how to realize them on an arbitrary higher-dimensional quantum system remains a challenging task. Here we propose a simple recipe for the implementation of a general positive-operator valued measurement (POVM) on a higher-dimensional quantum system via a one-dimensional discrete-time quantum walk with a two-dimensional coin. Furthermore, using single photons and linear optics, we realize experimentally a symmetric, informationally complete (SIC) POVM on a three-dimensional system with high fidelity. As an application, we realize a qutrit state tomography with SIC-POVM and confirm that the infidelity scaling achieved by the qutrit SIC-POVM is as good as that based on mutually unbiased bases. Our study paves the way to explore physics and information in higher-dimensional quantum systems and finds applications in various quantum information processing tasks that rely on generalized quantum measurements.
Integrated optics allow the generation and control of increasingly complex photonic states on chip based architectures. Here, we implement two entangled qutrits - a 9-dimensional quantum system - and demonstrate an exceptionally high degree of experimental control. The approach which is conceptually different to common bulk optical implementations is heavily based on methods of integrated in-fiber and on-chip technologies and further motivated by methods commonly used in today's telecommunication industry. The system is composed of an in-fiber source creating entangled qutrit states of any amplitude and phase and an on-chip integrated general Multiport enabling the realization of any desired local unitary transformation within the two qutrit 9-dimensional Hilbert space. The complete design is readily extendible towards higher-dimensions with moderate increase in complexity. Ultimately, our scheme allows for complete on-chip integration. We demonstrate the flexibility and generality of our system by realizing a complete characterization of the two qutrit space of higher-order Einstein-Podolsky-Rosen correlations.
It is crucial for various quantum information processing tasks that the state of a quantum system can be determined reliably and efficiently from general quantum measurements. One important class of measurements for this purpose are symmetric, informationally complete POVMs. SIC-POVMs have the advantage of providing an unbiased estimator for the quantum state with the minimal number of outcomes needed for full tomography. By virtue of Naimark's dilation theorem, any POVM can always be realized with a suitable coupling between the system and an auxiliary system and performing a projective measurement on the joint system. In practice, finding the appropriate coupling is rather non-trivial. Here we propose an experimental design for directly implementing SIC-POVMs using multiport devices and path-encoded qubits and qutrits, the utility of which has recently been emphasized by the Zeilinger group in Vienna. Furthermore, we describe how these multiports can be attained in practice with an integrated photonic system composed of nested linear optical elements.
Quantum information science has leaped forward with the exploration of high-dimensional quantum systems, offering greater potential than traditional qubits in quantum communication and quantum computing. To advance the field of high-dimensional quantum technology, a significant effort is underway to progressively enhance the entanglement dimension between two particles. An alternative effective strategy involves not only increasing the dimensionality but also expanding the number of particles that are entangled. We present an experimental study demonstrating multi-partite quantum non-locality beyond qubit constraints, thus moving into the realm of strongly entangled high-dimensional multi-particle quantum systems. In the experiment, quantum states were encoded in the path degree of freedom (DoF) and controlled via polarization, enabling efficient operations in a two-dimensional plane to prepare three- and four-particle Greenberger-Horne-Zeilinger (GHZ) states in three-level systems. Our experimental results reveal ways in which high-dimensional systems can surpass qubits in terms of violating local-hidden-variable theories. Our realization of multiple complex and high-quality entanglement technologies is an important primary step for more complex quantum computing and communication protocols. Experimental demonstrations of genuine high-dimensional multipartite quantum nonlocality have been lacking so far. Here, the authors fill this gap using entangled photons, surpassing qubit-based limits and paving the way for device-independent quantum information processing in more complex systems.