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Romanian Reports in Physics

SIC-POVM tomography in integrated photonics chips

Andrei-Emanuel Dragomir, Radu Ionicioiu

Published Nov 14, 2023• 1 citation
Publisher

Abstract

Reconstructing the state of a quantum system, called quantum state tomography, is an essential task in quantum technologies.Standard methods are inefficient, as they scale exponentially with the number of qubits.Better scaling methods, such as SIC-POVM tomography, are not yet widespread due to their measurement complexity.As such, there is an urgent need to find efficient and compact devices for performing tomography of photonic states.Here we present simulations of photonic devices implementing SIC-POVM tomography in photonic chips.We obtain fidelities F = 0.8452 (for qubits) and F = 0.7609 (for qutrits).Our results show that we can design efficient and compact SIC-POVM tomography modules for integrated-photonics quantum chips.Since integrated photonics is a major quantum technology platform, we expect our results to be instrumental in the future development of compact, costeffective quantum devices.Applications include quantum communications, quantum computing, quantum sensing and quantum imaging.

DOI
10.59277/romrepphys.2023.75.409

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Reconstructing the state of a quantum system, called quantum state tomography, is an essential task in quantum technologies.Standard methods are inefficient, as they scale exponentially with the number of qubits.Better scaling methods, such as SIC-POVM tomography, are not yet widespread due to their measurement complexity.As such, there is an urgent need to find efficient and compact devices for performing tomography of photonic states.Here we present simulations of photonic devices implementing SIC-POVM tomography in photonic chips.We obtain fidelities F = 0.8452 (for qubits) and F = 0.7609 (for qutrits).Our results show that we can design efficient and compact SIC-POVM tomography modules for integrated-photonics quantum chips.Since integrated photonics is a major quantum technology platform, we expect our results to be instrumental in the future development of compact, costeffective quantum devices.Applications include quantum communications, quantum computing, quantum sensing and quantum imaging.
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.
Abstract Quantum information systems are on a path to vastly exceed the complexity of any classical device. The number of entangled qubits in quantum devices is rapidly increasing, and the information required to fully describe these systems scales exponentially with qubit number. This scaling is the key benefit of quantum systems, however it also presents a severe challenge. To characterize such systems typically requires an exponentially long sequence of different measurements, becoming highly resource demanding for large numbers of qubits. Here we propose and demonstrate a novel and scalable method for characterizing quantum systems based on expanding a multi-photon state to larger dimensionality. We establish that the complexity of this new measurement technique only scales linearly with the number of qubits, while providing a tomographically complete set of data without a need for reconfigurability. We experimentally demonstrate an integrated photonic chip capable of measuring two- and three-photon quantum states with statistical reconstruction fidelity of 99.71%.
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.
Summary form only given. Full characterization of quantum states is increasingly important as ever more complex quantum systems are realized. Quantum state tomography of these systems is a difficult task because individual measurements only give partial information about the underlying density matrix of the system. Thus, conventionally the measurement apparatus must be reconfigured to take multiple measurements in order to fully determine the density matrix. It is accepted that for an W-qubit system an exponentially increasing number of measurements are needed [1]. As a consequence, the complexity of typical quantum state tomography grows exponentially with increasing photon number, which makes characterizing large quantum systems highly challenging. We formulate a concept of on-chip quantum tomography where the complexity scales linearly with the number of photons. This is achieved by using a single specially designed non-reconfigurable linear optical circuit as in Fig. 1(a). Crucially, the number of waveguides in this circuit scales linearly with the number of photons in the state to be measured. Furthermore, our approach is simple and robust, and we demonstrate it experimentally with a specially designed photonic chip.
Symmetric, informationally complete, positive operator-valued measurements (SIC-POVM) are fundamental in quantum information and foundations of quantum theory[1]. For example, SIC-POVMs are crucial for optimal quantum state tomography, quantum key distribution with optimal trade-off between security and key rate, device-independent certification of optimal randomness from one bit of entanglement, and information-based interpretations and operational reconstructions of quantum theory. Experimentally, photonic experiments of qubit and qutrit tomography, and quantum key distribution[2] have aimed for SIC-POVMs. However, these experiments rely on specific models for parts of the experimental setups and do not allow us to test whether the target measurements are truly SIC-POVMs in a "device independent" (DI) way that is, without relying on any modelling of the devices.
Integrated photonic quantum chips have emerged as a promising platform for realizing fault-tolerant photonic quantum computers. Compared with bulk-optics systems, integrated photonics offer compact device footprints, enhanced programmability, and exceptional stability, attributes that are essential for executing large-scale and computationally demanding quantum tasks. In this review, we provide a comprehensive overview of recent advances in both discrete-variable and continuous-variable universal photonic quantum computation. We survey progress in fault-tolerant architectures and state-of-the-art integrated platforms and highlight the key challenges that must be addressed to scale photonic systems toward full fault tolerance. Finally, we outline future opportunities and research directions aimed at bridging the gap between current proof-of-principle demonstrations and fully scalable quantum microprocessors.