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

arXiv:1910.10933 · Physical Review Letters

Direct Measurement of a Nonlocal Entangled Quantum State

Wei-Wei Pan, Xiao‐Ye Xu, Yaron Kedem, Qinqin Wang, Zhe Chen, Munsif Jan, Kai Sun, Jin‐Shi Xu, Yong‐Jian Han, Chuan‐Feng Li, Guang‐Can Guo

Published Oct 9, 2019• 61 citations
arXivHTMLPDF

Abstract

Entanglement and the wave function description are two of the core concepts that make quantum mechanics such a unique theory. A method to directly measure the wave function, using weak values, was demonstrated by Lundeen et al. [Nature 474, 188 (2011)]. However, it is not applicable to a scenario of two disjoint systems, where nonlocal entanglement can be a crucial element, since that requires obtaining weak values of nonlocal observables. Here, for the first time, we propose a method to directly measure a nonlocal wave function of a bipartite system, using modular values. The method is experimentally implemented for a photon pair in a hyperentangled state, i.e., entangled both in polarization and momentum degrees of freedom.

DOI
10.1103/physrevlett.123.150402

Related papers

Experimental extraction of nonlocal weak values for demonstrating the failure of a product rule

Xiao-Ye Xu, Wei-Wei Pan, Yaron Kedem +7 more

We experimentally demonstrate an alternative method for measuring nonlocal weak values in linear optics, avoiding the use of second-order interaction. The method is based on the concept of modular values. The paths of two photons, initialized in hyperentangled states, are adopted as the meter with the polarization acting as the system. The modular values are read out through the reconstructed final states of the meter. The weak value of nonlocal observables is given through its connection to the modular value. Comparing the weak values of local and nonlocal observables, we demonstrate the failure of product rules for an entangled system. Our results significantly simplify the task of measuring nonlocal weak values and will play an important role in the application of weak measurement.

Optics Letters•Feb 13, 2020•2 citations

Nonlocal generalized quantum measurement of product observables with mixed entanglement

Lan Jiang, Zhenhua Li, Tao Li

Nonlocal observables of spacelike separated quantum systems in combination with their measurements contribute greatly to quantum theory and its applications. We present a nonlocal generalized quantum measurement protocol for measuring product observables, assisted by a meter in a mixed entangled state rather than maximally or partially entangled pure states. By tuning the entanglement of the meter, measurement strength of arbitrary values can be achieved for nonlocal product observables, since measurement strength equals the concurrence of the meter. Furthermore, we present a specific scheme to measure the polarization of two nonlocal photons using linear optics. We refer to the polarization and spatial-mode degrees of freedom of the same photon pair as the system and the meter, respectively, which significantly simplifies the interaction between the system and the meter. This protocol can be useful for applications involving nonlocal product observables and nonlocal weak values, and for tests of quantum foundations in nonlocal scenarios.

Optics Express•Mar 21, 2023•8 citations

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 measurement of the two-dimensional spatial quantum wave function via strong measurements

Chen-Rui Zhang, Mengjun Hu, Zhibo Hou +6 more

The wave function is at the foundation of quantum theory, which is assumed to give a complete description of a quantum system. From early inception, the wave function was introduced as an abstract element of the theory and lacked any way to measure it directly. The situation, however, has somewhat changed with the reporting of the direct measurement of the quantum wave function via weak measurements, giving the wave function a clearly operational definition. The weak measurement method requires sequential measurements of conjugate observables position and momentum with the position measurement sufficiently weak. Surprisingly, recent research showed that performing sequential strong measurements realized the same object, in which case no approximation in weak measurements has to be made. Here, we report on experiments of direct measurements of the two-dimensional transverse wave function of photons via strong measurement, implying that an accurate and clear operational definition may be given to the wave function. We have measured the Gaussian and Laguerre--Gaussian of $l=1$ spatial wave functions of photons with fidelity of 0.93. As a potential important application, we show that this direct measurement of the wave function provides an alternative way to realize digital holography of three-dimensional objects. This realization of direct measurement of the wave function has significant consequences in quantum information processing and quantum imaging.

arXiv:1811.01560•Physical Review A•Jan 22, 2020•26 citations

Strong Measurements Give a Better Direct Measurement of the Quantum Wave Function

Giuseppe Vallone, Daniele Dequal

Weak measurements have thus far been considered instrumental in the so-called direct measurement of the quantum wave function [4J. S. Lundeen, Nature (London) 474, 188 (2011).]. Here we show that a direct measurement of the wave function can be obtained by using measurements of arbitrary strength. In particular, in the case of strong measurements, i.e., those in which the coupling between the system and the measuring apparatus is maximum, we compared the precision and the accuracy of the two methods, by showing that strong measurements outperform weak measurements in both for arbitrary quantum states in most cases. We also give the exact expression of the difference between the original and reconstructed wave function obtained by the weak measurement approach; this will allow one to define the range of applicability of such a method.

arXiv:1504.06551•Physical Review Letters•Jan 29, 2016•98 citations

Nonlocal Polarization Interferometry and Entanglement Detection

Brian P. Williams

At present, quantum entanglement is a resource, distributed to enable a variety of quantum information applications such as quantum key distribution, superdense coding, and teleportation. Necessarily, the distribution and characterization of entanglement is fundamental to its application. This dissertation details three research efforts to enable nonlocal entanglement detection, distribution, and characterization. Foremost of these efforts, we present the theory and demonstration of a nonlocal polarization interferometer capable of detecting entanglement and identifying Bell states statistically. This is possible due to the interferometer’s unique correlation dependence on the anti-diagonal elements of the density matrix, which have distinct bounds for separable states and unique values for the four Bell states. Second, we propose a nonlocal method of interferometrically mapping time-entangled photons to polarization entangled states, capitalizing on the strengths of both the robust temporal degree of freedom and the “easy to measure” polarization degree of freedom. Finally, we propose a method of estimating and representing correlation probabilities in nonlocal two-photon experiments using Bayes’ rule. Numerical simulations confirm that a vigorous consideration of the available information offers a correlation characterization superior to the standard approach.

•Jan 1, 2014•0 citations
Entanglement and the wave function description are two of the core concepts that make quantum mechanics such a unique theory. A method to directly measure the wave function, using weak values, was demonstrated by Lundeen et al. [Nature 474, 188 (2011)]. However, it is not applicable to a scenario of two disjoint systems, where nonlocal entanglement can be a crucial element, since that requires obtaining weak values of nonlocal observables. Here, for the first time, we propose a method to directly measure a nonlocal wave function of a bipartite system, using modular values. The method is experimentally implemented for a photon pair in a hyperentangled state, i.e., entangled both in polarization and momentum degrees of freedom.
We experimentally demonstrate an alternative method for measuring nonlocal weak values in linear optics, avoiding the use of second-order interaction. The method is based on the concept of modular values. The paths of two photons, initialized in hyperentangled states, are adopted as the meter with the polarization acting as the system. The modular values are read out through the reconstructed final states of the meter. The weak value of nonlocal observables is given through its connection to the modular value. Comparing the weak values of local and nonlocal observables, we demonstrate the failure of product rules for an entangled system. Our results significantly simplify the task of measuring nonlocal weak values and will play an important role in the application of weak measurement.
Nonlocal observables of spacelike separated quantum systems in combination with their measurements contribute greatly to quantum theory and its applications. We present a nonlocal generalized quantum measurement protocol for measuring product observables, assisted by a meter in a mixed entangled state rather than maximally or partially entangled pure states. By tuning the entanglement of the meter, measurement strength of arbitrary values can be achieved for nonlocal product observables, since measurement strength equals the concurrence of the meter. Furthermore, we present a specific scheme to measure the polarization of two nonlocal photons using linear optics. We refer to the polarization and spatial-mode degrees of freedom of the same photon pair as the system and the meter, respectively, which significantly simplifies the interaction between the system and the meter. This protocol can be useful for applications involving nonlocal product observables and nonlocal weak values, and for tests of quantum foundations in nonlocal scenarios.
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.
The wave function is at the foundation of quantum theory, which is assumed to give a complete description of a quantum system. From early inception, the wave function was introduced as an abstract element of the theory and lacked any way to measure it directly. The situation, however, has somewhat changed with the reporting of the direct measurement of the quantum wave function via weak measurements, giving the wave function a clearly operational definition. The weak measurement method requires sequential measurements of conjugate observables position and momentum with the position measurement sufficiently weak. Surprisingly, recent research showed that performing sequential strong measurements realized the same object, in which case no approximation in weak measurements has to be made. Here, we report on experiments of direct measurements of the two-dimensional transverse wave function of photons via strong measurement, implying that an accurate and clear operational definition may be given to the wave function. We have measured the Gaussian and Laguerre--Gaussian of l=1l=1l=1 spatial wave functions of photons with fidelity of 0.93. As a potential important application, we show that this direct measurement of the wave function provides an alternative way to realize digital holography of three-dimensional objects. This realization of direct measurement of the wave function has significant consequences in quantum information processing and quantum imaging.
Weak measurements have thus far been considered instrumental in the so-called direct measurement of the quantum wave function [4J. S. Lundeen, Nature (London) 474, 188 (2011).]. Here we show that a direct measurement of the wave function can be obtained by using measurements of arbitrary strength. In particular, in the case of strong measurements, i.e., those in which the coupling between the system and the measuring apparatus is maximum, we compared the precision and the accuracy of the two methods, by showing that strong measurements outperform weak measurements in both for arbitrary quantum states in most cases. We also give the exact expression of the difference between the original and reconstructed wave function obtained by the weak measurement approach; this will allow one to define the range of applicability of such a method.
At present, quantum entanglement is a resource, distributed to enable a variety of quantum information applications such as quantum key distribution, superdense coding, and teleportation. Necessarily, the distribution and characterization of entanglement is fundamental to its application. This dissertation details three research efforts to enable nonlocal entanglement detection, distribution, and characterization. Foremost of these efforts, we present the theory and demonstration of a nonlocal polarization interferometer capable of detecting entanglement and identifying Bell states statistically. This is possible due to the interferometer’s unique correlation dependence on the anti-diagonal elements of the density matrix, which have distinct bounds for separable states and unique values for the four Bell states. Second, we propose a nonlocal method of interferometrically mapping time-entangled photons to polarization entangled states, capitalizing on the strengths of both the robust temporal degree of freedom and the “easy to measure” polarization degree of freedom. Finally, we propose a method of estimating and representing correlation probabilities in nonlocal two-photon experiments using Bayes’ rule. Numerical simulations confirm that a vigorous consideration of the available information offers a correlation characterization superior to the standard approach.