Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Experimental Device-Independent Certification of a SIC-POVM

Massimiliano Smania, Piotr Mironowicz, Mohamed Nawareg, Marcin Pawłowski, Adán Cabello, Mohamed Bourennane

Published Jun 1, 2019• 0 citations
Publisher

Abstract

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.

DOI
10.1109/cleoe-eqec.2019.8872159

Related papers

Experimental scheme for qubit and qutrit symmetric informationally complete positive operator-valued measurements using multiport devices

Gelo Noel M. Tabia

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.

arXiv:1207.6035•Physical Review A•Dec 14, 2012•49 citations

Experimental realization and self-testing of semisymmetric informationally complete measurements via a one-dimensional photonic quantum walk

Xu Xu, Han-Yu Cheng, Meng-Yun Ma +7 more

Generalized quantum measurements play a crucial role in quantum mechanics, and symmetric informationally complete positive operator-valued measurements (SIC POVMs) provide a powerful and flexible framework for extracting information from quantum systems. However, the existence of SIC-POVMs in every finite dimension remains an open question, which has stimulated extensive research into alternative classes of POVMs. Recently, Geng $et$ $al$. [Phys. Rev. Lett. 126, 100401 (2021)] proposed a broader class of SIC POVM, called semisymmetric informationally complete POVM (semi-SIC POVM), which extends beyond SIC POVM. In this work, we focus on the four-outcome POVMs and experimentally realize the semi-SIC POVMs using a one-dimensional discrete-time quantum walk. Additionally, employing single photons and linear optics, we perform an experimental self-testing of semi-SIC POVMs in the semi-device-independent manner. Our results pave the way for exploring quantum certification with generalized quantum measurements.

quant-pharXiv:2603.01802•Mar 3, 2026•0 citations

Experimental realization of a single qubit SIC POVM on via a one-dimensional photonic quantum walk

Zhihao Bian, Jian Li, Qin, Hao +2 more

Symmetric informationally complete positive operator-valued measurement (SIC-POVM) is one important class of quantum measurement which is crucial for various quantum information processing tasks. SIC-POVMs have the advantage of providing an unbiased estimator for quantum states with the minimal number of outcomes needed for full tomography. We present an experimental approach on a photonic quantum walk which can be used to implement SIC-POVMs on a single-qbubit. The projection measurements of single-photons' positions correspond to elements of SIC-POVM on the polarization of single-photons.

arXiv:1412.2355•Dec 7, 2014•1 citation

Experimental scheme for qubit and qutrit SIC-POVMs using multiport devices

Gelo Noel M. Tabia

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.

•Jul 25, 2012•3 citations

Experimental characterization of qutrits using symmetric, informationally complete positive operator-valued measures

Zachari Medendorp, Fabian A. Torres-Ruiz, Lynden K. Shalm +3 more

Generalized quantum measurements (also known as positive operator-valued measures or POVMs) are of great importance in quantum information and quantum foundations, but often difficult to perform. We present an experimental approach which can in principle be used to perform arbitrary POVMs in a linear-optical context. One of the most interesting POVMs, the symmetric, informationally complete-POVM (or SIC-POVM), is the most compact set of measurements that can be used to fully describe a quantum state. We use our technique to carry out the first experimental characterization of the state of a qutrit using SIC-POVMs. Because of the highly symmetric nature of this measurement, such a representation has the unique property that it permits all other measurement outcomes to be predicted by a simple extension of the classical Bayesian sum rule, making no use of complex amplitudes or Hilbert-space operators. We demonstrate this approach on several qutrit states encoded in single photons.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 21, 2011•1 citation

Necessary condition for existence of conditional SIC-POVM (Mathematics for Uncertainty and Fuzziness)

博通 大野

This paper is an announcement of our result and the detailed version will be submitted to somewhere.(See [2].)POVMs (positive operator valued measure) on quantum systems are considered as a measurement in quantum physics.If POVMs have a good condition, then we can determine a state by results of a measurement.In this case, the POVM is called informationally complete and the process is called quantum state tomography.First, we introduce SIC-POVMs (symmetric informationally complete POVM).SIC-POVMs is generated by vectors in $\mathbb{C}^{n}$ whose the absolute values of inner products of each vectors are same.Zauner conjectured that there exist such $n^{2}$ vectors in $\mathbb{C}^{n}$ for any $n$ .But the existence is only proved when $n\leq 15$ and $n=19$ , 24, 35,48[5, 8].Next, we introduce conditional SIC-POVMs.A state of a quantum system is a density matrix which has several parameters.When a few parameters are known, then SIC-POVM is not the best measurement to determine the state.Hence we need another POVM and it is a conditional SIC-POVM.Conditional SIC-POVMs are also generated by vectors in $\mathbb{C}^{n}$ .But the existence of conditional SIC-POVMs depends on the system.We will discuss the details in Sect. 4. 2 Preliminaries Definition 2.1 $\rho\in M_{n}(\mathbb{C})$ is called a density matrix (or state) if $\rho\geq 0$ and $\prime b(\rho)=1.$For any density matrix $\rho$ , we can define a state $\hat{\rho}$ by $\hat{\rho}(X)=h(\rho X)$ .Conversely, any state is written by the above form.Therefore, there exists a one-t $(\succ$ one correspondence between density matrices and states.Definition 2.2 A set of positive operators $\{P_{i}\}_{i=1}^{k}\subset M_{n}(\mathbb{C})$ is called a positive operator valued measure (POVM) if $P_{i}\geq 0(1\leq i\leq k)$ and $\sum_{i=1}^{k}P=I.$If $P_{1}$ is a projection, then $\{P_{i}\}_{i=1}^{k}$ is called a projection valued measure $(PVM)$ .

数理解析研究所講究録•Jul 1, 2014•0 citations
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.
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.
Generalized quantum measurements play a crucial role in quantum mechanics, and symmetric informationally complete positive operator-valued measurements (SIC POVMs) provide a powerful and flexible framework for extracting information from quantum systems. However, the existence of SIC-POVMs in every finite dimension remains an open question, which has stimulated extensive research into alternative classes of POVMs. Recently, Geng etetet alalal. [Phys. Rev. Lett. 126, 100401 (2021)] proposed a broader class of SIC POVM, called semisymmetric informationally complete POVM (semi-SIC POVM), which extends beyond SIC POVM. In this work, we focus on the four-outcome POVMs and experimentally realize the semi-SIC POVMs using a one-dimensional discrete-time quantum walk. Additionally, employing single photons and linear optics, we perform an experimental self-testing of semi-SIC POVMs in the semi-device-independent manner. Our results pave the way for exploring quantum certification with generalized quantum measurements.
Symmetric informationally complete positive operator-valued measurement (SIC-POVM) is one important class of quantum measurement which is crucial for various quantum information processing tasks. SIC-POVMs have the advantage of providing an unbiased estimator for quantum states with the minimal number of outcomes needed for full tomography. We present an experimental approach on a photonic quantum walk which can be used to implement SIC-POVMs on a single-qbubit. The projection measurements of single-photons' positions correspond to elements of SIC-POVM on the polarization of single-photons.
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.
Generalized quantum measurements (also known as positive operator-valued measures or POVMs) are of great importance in quantum information and quantum foundations, but often difficult to perform. We present an experimental approach which can in principle be used to perform arbitrary POVMs in a linear-optical context. One of the most interesting POVMs, the symmetric, informationally complete-POVM (or SIC-POVM), is the most compact set of measurements that can be used to fully describe a quantum state. We use our technique to carry out the first experimental characterization of the state of a qutrit using SIC-POVMs. Because of the highly symmetric nature of this measurement, such a representation has the unique property that it permits all other measurement outcomes to be predicted by a simple extension of the classical Bayesian sum rule, making no use of complex amplitudes or Hilbert-space operators. We demonstrate this approach on several qutrit states encoded in single photons.
This paper is an announcement of our result and the detailed version will be submitted to somewhere.(See [2].)POVMs (positive operator valued measure) on quantum systems are considered as a measurement in quantum physics.If POVMs have a good condition, then we can determine a state by results of a measurement.In this case, the POVM is called informationally complete and the process is called quantum state tomography.First, we introduce SIC-POVMs (symmetric informationally complete POVM).SIC-POVMs is generated by vectors in Cn\mathbb{C}^{n}Cn whose the absolute values of inner products of each vectors are same.Zauner conjectured that there exist such n2n^{2}n2 vectors in Cn\mathbb{C}^{n}Cn for any nnn .But the existence is only proved when n≤15n\leq 15n≤15 and n=19n=19n=19 , 24, 35,48[5, 8].Next, we introduce conditional SIC-POVMs.A state of a quantum system is a density matrix which has several parameters.When a few parameters are known, then SIC-POVM is not the best measurement to determine the state.Hence we need another POVM and it is a conditional SIC-POVM.Conditional SIC-POVMs are also generated by vectors in Cn\mathbb{C}^{n}Cn .But the existence of conditional SIC-POVMs depends on the system.We will discuss the details in Sect. 4. 2 Preliminaries Definition 2.1 ρ∈Mn(C)\rho\in M_{n}(\mathbb{C})ρ∈Mn​(C) is called a density matrix (or state) if ρ≥0\rho\geq 0ρ≥0 and ′b(ρ)=1.\prime b(\rho)=1.′b(ρ)=1.For any density matrix ρ\rhoρ , we can define a state ρ^\hat{\rho}ρ^​ by ρ^(X)=h(ρX)\hat{\rho}(X)=h(\rho X)ρ^​(X)=h(ρX) .Conversely, any state is written by the above form.Therefore, there exists a one-t (≻(\succ(≻ one correspondence between density matrices and states.Definition 2.2 A set of positive operators {Pi}i=1k⊂Mn(C)\{P_{i}\}_{i=1}^{k}\subset M_{n}(\mathbb{C}){Pi​}i=1k​⊂Mn​(C) is called a positive operator valued measure (POVM) if Pi≥0(1≤i≤k)P_{i}\geq 0(1\leq i\leq k)Pi​≥0(1≤i≤k) and ∑i=1kP=I.\sum_{i=1}^{k}P=I.∑i=1k​P=I.If P1P_{1}P1​ is a projection, then {Pi}i=1k\{P_{i}\}_{i=1}^{k}{Pi​}i=1k​ is called a projection valued measure (PVM)(PVM)(PVM) .