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

Physical Review Applied

Efficient Direct Measurement of Arbitrary Quantum Systems via Weak Measurement

Changliang Ren, Ya Wang, Jiangfeng Du

Published Jul 24, 2019• 14 citations
Publisher

Abstract

Efficient, reliable determination of a system's state is at the heart of quantum science. Directly measuring any desired density-matrix elements is a unique challenge for both theorists and experimentalists, as standard methods have always suffered from the rapid increase in complexity of measurements and reconstruction algorithms. This study presents an efficient scheme for directly measuring arbitrary density matrices with only one strong measurement, or a weak measurement, of each qudit. This method is important for characterizing large-scale quantum systems, and the technology that will be derived from it will be easy to expand and integrate, for example, on a quantum chip.

DOI
10.1103/physrevapplied.12.014045

Related papers

Direct measurement of nonlocal quantum states without approximation

Gang 冈 Yang 杨, Ran 然 Yang 杨, Yan-Xiao Gong +1 more

Efficient acquiring information from a quantum state is important for research in fundamental quantum physics and quantum information applications. Instead of using standard quantum state tomography method with reconstruction algorithm, weak values were proposed to directly measure density matrix elements of quantum state. Recently, similar to the concept of weak value, modular values were introduced to extend the direct measurement scheme to nonlocal quantum wavefunction. However, this method still involves approximations, which leads to inherent low precision. Here, we propose a new scheme which enables direct measurement for ideal value of the nonlocal density matrix element without taking approximations. Our scheme allows more accurate characterization of nonlocal quantum states, and therefore has greater advantages in practical measurement scenarios.

Chinese Physics B•Sep 1, 2023•3 citations

Direct Reconstruction of the Quantum Density Matrix by Strong Measurements

Luca Calderaro, Giulio Foletto, Daniele Dequal +2 more

New techniques based on weak measurements have recently been introduced to the field of quantum state reconstruction. Some of them allow the direct measurement of each matrix element of an unknown density operator and need only O(d) different operations, compared to d^{2} linearly independent projectors in the case of standard quantum state tomography, for the reconstruction of an arbitrary mixed state. However, due to the weakness of these couplings, these protocols are approximated and prone to large statistical errors. We propose a method which is similar to the weak measurement protocols but works regardless of the coupling strength: our protocol is not approximated and thus improves the accuracy and precision of the results with respect to weak measurement schemes. We experimentally apply it to the polarization state of single photons and compare the results to those of preexisting methods for different values of the coupling strength. Our results show that our method outperforms previous proposals in terms of accuracy and statistical errors.

arXiv:1803.10703•Physical Review Letters•Dec 7, 2018•56 citations

Resource-Efficient Direct Characterization of General Density Matrix

Liang Xu, Ming-Ti Zhou, Runxia Tao +12 more

Sequential weak measurements allow for the direct extraction of individual density-matrix elements, rather than relying on global reconstruction of the entire density matrix, which opens a new avenue for the characterization of quantum systems. Nevertheless, extending the sequential scheme to multiqudit quantum systems is challenging due to the requirement of multiple coupling processes for each qudit and the lack of appropriate precision evaluation. To address these issues, we propose a resource-efficient scheme (RES) that directly characterizes the density matrix of general multiqudit systems while optimizing measurements and establishing a feasible estimation analysis. In the RES, an efficient observable of the quantum system is constructed such that a single meter state coupled to each qudit is sufficient to extract the corresponding density-matrix element. An appropriate model based on the statistical distribution of errors is utilized to evaluate the precision and feasibility of the scheme. We have experimentally applied the RES to the direct characterization of general single-photon qutrit states and two-photon entangled states. The results show that the RES outperforms sequential schemes in terms of efficiency and precision in both weak- and strong-coupling scenarios. This Letter sheds new light on the practical characterization of large-scale quantum systems and the investigation of their nonclassical properties.

arXiv:2303.06903•Physical Review Letters•Jan 16, 2024•6 citations

Direct Reconstruction of the Quantum Density Operator via Measurements of Arbitrary Strength

Giulio Foletto

One of the fundamental problems of experimental quantum physics is the determination of the state of a system, which provides its accurate description and contains all the available information about it. The standard solution is quantum state tomography, a technique that employs a large number of measurements of complementary observables to reconstruct a general density operator. Recently, new protocols have been proposed which allow to obtain the matrix elements one by one with fewer and less complicated observations by exploiting so-called weak measurements, that perturb the system less than ideal projections at the cost of being less precise. This thesis presents an evolution of these schemes that eschews the weakness of the measurement, thus gaining in the accuracy of the results and in practical feasibility. We realized an experiment that uses these methods to reconstruct the density operator of the polarization state of light in single photons regime.

•Sep 1, 2017•0 citations

Direct Measurement of the Density Matrix of a Quantum System

Guillaume Thekkadath, Lambert Giner, Yamn Chalich +3 more

One drawback of conventional quantum state tomography is that it does not readily provide access to single density matrix elements since it requires a global reconstruction. Here, we experimentally demonstrate a scheme that can be used to directly measure individual density matrix elements of general quantum states. The scheme relies on measuring a sequence of three observables, each complementary to the last. The first two measurements are made weak to minimize the disturbance they cause to the state, while the final measurement is strong. We perform this joint measurement on polarized photons in pure and mixed states to directly measure their density matrix. The weak measurements are achieved using two walk-off crystals, each inducing a polarization-dependent spatial shift that couples the spatial and polarization degrees of freedom of the photons. This direct measurement method provides an operational meaning to the density matrix and promises to be especially useful for large dimensional states.

arXiv:1604.07917•Physical Review Letters•Sep 12, 2016•153 citations

Scheme of directly measuring quantum density matrix by δ-quench method

Yong-Li Wen, Shanchao Zhang, Hui Yan +1 more

Density matrix, which characterizes a quantum state, plays an important role in quantum mechanics. Recently, a method which can directly measure the elements of a density matrix was proposed. Compared with the conventional quantum state tomography which is widely used to reconstruct the density matrix, this measurement method has the advantages of directness and simplicity. However, this direct measurement method relies on an extra pointer space. The addition of this extra pointer can increase the complexity of an experiment. In this paper, we first review previous work on direct measurement, then we propose a scheme to directly measure the density matrix based on δ-quench, which is also a direct measurement method but needs no additional pointer. This proposal reduces the complexity of the measuring system and further simplifies the measurement. We propose two schemes to realize this δ-quench measurement, then analyse their superiorities in different situations of measurement. An experiment to measure photon's density matrix is also designed.

Acta Physica Sinica•Jan 1, 2021•0 citations
Efficient, reliable determination of a system's state is at the heart of quantum science. Directly measuring any desired density-matrix elements is a unique challenge for both theorists and experimentalists, as standard methods have always suffered from the rapid increase in complexity of measurements and reconstruction algorithms. This study presents an efficient scheme for directly measuring arbitrary density matrices with only one strong measurement, or a weak measurement, of each qudit. This method is important for characterizing large-scale quantum systems, and the technology that will be derived from it will be easy to expand and integrate, for example, on a quantum chip.
Efficient acquiring information from a quantum state is important for research in fundamental quantum physics and quantum information applications. Instead of using standard quantum state tomography method with reconstruction algorithm, weak values were proposed to directly measure density matrix elements of quantum state. Recently, similar to the concept of weak value, modular values were introduced to extend the direct measurement scheme to nonlocal quantum wavefunction. However, this method still involves approximations, which leads to inherent low precision. Here, we propose a new scheme which enables direct measurement for ideal value of the nonlocal density matrix element without taking approximations. Our scheme allows more accurate characterization of nonlocal quantum states, and therefore has greater advantages in practical measurement scenarios.
New techniques based on weak measurements have recently been introduced to the field of quantum state reconstruction. Some of them allow the direct measurement of each matrix element of an unknown density operator and need only O(d) different operations, compared to d^{2} linearly independent projectors in the case of standard quantum state tomography, for the reconstruction of an arbitrary mixed state. However, due to the weakness of these couplings, these protocols are approximated and prone to large statistical errors. We propose a method which is similar to the weak measurement protocols but works regardless of the coupling strength: our protocol is not approximated and thus improves the accuracy and precision of the results with respect to weak measurement schemes. We experimentally apply it to the polarization state of single photons and compare the results to those of preexisting methods for different values of the coupling strength. Our results show that our method outperforms previous proposals in terms of accuracy and statistical errors.
Sequential weak measurements allow for the direct extraction of individual density-matrix elements, rather than relying on global reconstruction of the entire density matrix, which opens a new avenue for the characterization of quantum systems. Nevertheless, extending the sequential scheme to multiqudit quantum systems is challenging due to the requirement of multiple coupling processes for each qudit and the lack of appropriate precision evaluation. To address these issues, we propose a resource-efficient scheme (RES) that directly characterizes the density matrix of general multiqudit systems while optimizing measurements and establishing a feasible estimation analysis. In the RES, an efficient observable of the quantum system is constructed such that a single meter state coupled to each qudit is sufficient to extract the corresponding density-matrix element. An appropriate model based on the statistical distribution of errors is utilized to evaluate the precision and feasibility of the scheme. We have experimentally applied the RES to the direct characterization of general single-photon qutrit states and two-photon entangled states. The results show that the RES outperforms sequential schemes in terms of efficiency and precision in both weak- and strong-coupling scenarios. This Letter sheds new light on the practical characterization of large-scale quantum systems and the investigation of their nonclassical properties.
One of the fundamental problems of experimental quantum physics is the determination of the state of a system, which provides its accurate description and contains all the available information about it. The standard solution is quantum state tomography, a technique that employs a large number of measurements of complementary observables to reconstruct a general density operator. Recently, new protocols have been proposed which allow to obtain the matrix elements one by one with fewer and less complicated observations by exploiting so-called weak measurements, that perturb the system less than ideal projections at the cost of being less precise. This thesis presents an evolution of these schemes that eschews the weakness of the measurement, thus gaining in the accuracy of the results and in practical feasibility. We realized an experiment that uses these methods to reconstruct the density operator of the polarization state of light in single photons regime.
One drawback of conventional quantum state tomography is that it does not readily provide access to single density matrix elements since it requires a global reconstruction. Here, we experimentally demonstrate a scheme that can be used to directly measure individual density matrix elements of general quantum states. The scheme relies on measuring a sequence of three observables, each complementary to the last. The first two measurements are made weak to minimize the disturbance they cause to the state, while the final measurement is strong. We perform this joint measurement on polarized photons in pure and mixed states to directly measure their density matrix. The weak measurements are achieved using two walk-off crystals, each inducing a polarization-dependent spatial shift that couples the spatial and polarization degrees of freedom of the photons. This direct measurement method provides an operational meaning to the density matrix and promises to be especially useful for large dimensional states.
Density matrix, which characterizes a quantum state, plays an important role in quantum mechanics. Recently, a method which can directly measure the elements of a density matrix was proposed. Compared with the conventional quantum state tomography which is widely used to reconstruct the density matrix, this measurement method has the advantages of directness and simplicity. However, this direct measurement method relies on an extra pointer space. The addition of this extra pointer can increase the complexity of an experiment. In this paper, we first review previous work on direct measurement, then we propose a scheme to directly measure the density matrix based on δ-quench, which is also a direct measurement method but needs no additional pointer. This proposal reduces the complexity of the measuring system and further simplifies the measurement. We propose two schemes to realize this δ-quench measurement, then analyse their superiorities in different situations of measurement. An experiment to measure photon's density matrix is also designed.