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arXiv:1204.3544 · Physical Review Letters

Weak Measurements with Orbital-Angular-Momentum Pointer States

Graciana Puentes, Nathaniel Hermosa, Juan P. Torres

Published Jul 24, 2012• 63 citations
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Abstract

Weak measurements are a unique tool for accessing information about weakly interacting quantum systems with minimal back action. Joint weak measurements of single-particle operators with pointer states characterized by a two-dimensional Gaussian distribution can provide, in turn, key information about quantum correlations that can be relevant for quantum information applications. Here we demonstrate that by employing two-dimensional pointer states endowed with orbital angular momentum (OAM), it is possible to extract weak values of the higher order moments of single-particle operators, an inaccessible quantity with Gaussian pointer states only. We provide a specific example that illustrates the advantages of our method both in terms of signal enhancement and information retrieval.

DOI
10.1103/physrevlett.109.040401

Related papers

Puentes, Hermosa, and Torres Reply:

Graciana Puentes, Nathaniel Hermosa, Juan P. Torres

In a preceding Comment [1] to our Letter [2] concerning weak measurements with orbital-angular-momentum (OAM) pointer states [2], Pan and Panigrahi show that the real and imaginary parts of higher-order weak values can be made accessible using Gaussian pointer states.In [2], our goal is to show that by using pointer states embedded with OAM it is possible to extract higher-order weak values where pointer states with a Gaussian shape cannot.As a consequence, our work put forward a new tool for weak amplification schemes, i.e., the use of pointer states with more general spatial forms that could be advantageous in some scenarios.We did not intend to claim that a pointer state with orbital angular momentum was needed to extract higherorder weak values in general.We clarify our point with this Reply.In our Letter we consider a specific Hamiltonian of interaction of the form H ¼ g A AP x þ g B BP y , where A, B are operators, (P x , P y ) are the pointer momentum operators, conjugate to the pointer position operators (X, Y), and g A;B are coupling constants.Moreover, we calculate the two-dimensional pointer displacement hXYi, corresponding to a specific measurement.We emphasize that we consider a particular interaction and a specific measurement, which are generally dictated by the physical system under investigation.The result, Eq. ( 4) of our Letter, shows that pointer states with OAM (l ¼ Æ1) can be used to retrieve the imaginary part of the higher-order weak values hA 2 i w and hB 2 i w , whereas this is not possible with pointer states with no OAM (l ¼ 0).In addition, Eq. ( 9) of our Letter shows, by means of a specific example with B ¼ 0, that hXYi ¼ 0 for Gaussian pointer states.On the contrary, a pointer state with l ¼ Æ1 allows us to extract the imaginary part of the weak value hA 2 i w .Pan and Panigrahi show that by measuring hX 2 i one can obtain the real part of the weak value hA 2 i w using a Gaussian pointer [see Eq. ( 4) of [1]].However, in order to access its imaginary part, they are forced to use a different interaction Hamiltonian, and a measurement observable involving noncommuting operators.The work of Pan and Panigrahi proves the strength of our proposal: One

Physical Review Letters•Jul 10, 2013•1 citation

Comment on “Weak Measurements with Orbital-Angular-Momentum Pointer States”

A. K. Pan, Prasanta Kumar Panigrahi

In a recent Letter (Phys. Rev. Lett. 109, 040401 (2012)), G. Puentes, N. Hermosa and J. P. Torres report a scheme for extracting higher-order weak values by using orbital-angular momentum states as pointer states. They claim that such weak values are inaccessible with a Gaussian pointer state only. In this Comment, we show that the Gaussian pointer state by itself can provide access to the higher-order weak value, if suitable pointer displacement is observed.

arXiv:1308.4523•Physical Review Letters•Jul 10, 2013•5 citations

Extraction of Product and Higher Moment Weak Values: Applications in Quantum State Reconstruction

Sahil, S Sohail, Subhrajit Modak +2 more

Weak measurements introduced by Aharonov, Albert and Vaidman (AAV) can provide informations about the system with minimal back action. Weak values of product observables (commuting) or higher moments of an observable are informationally important in the sense that they are useful to resolve some paradoxes,realize strange quantum effects, construct density matrices, etc. In this work, we show that it is possible to access the higher moment weak values of an observable using weak values of that observable with pairwise orthogonal post-selections. Although the higher moment weak values of an observable are inaccessible with Gaussian pointer states, our method allows any pointer state. We have calculated product weak values in a bipartite system for any given pure and mixed pre selected states. Such product weak values can be obtained using only the measurements of local weak values (which are defined as single system weak values in a multi-partite system). As an application, we use higher moment weak values and product weak values to reconstruct unknown quantum states of single and bipartite systems, respectively. Robustness of our method which occurs due to inappropriate choices of quantum observables and noisy post-selections is also discussed here. Our method can easily be generalized to the multi-partite systems.

•Jul 1, 2021•0 citations

Extracting joint weak values from two-dimensional spatial displacements

H. Kobayashi, Graciana Puentes, Yutaka Shikano

The joint weak value is a counterfactual quantity related to quantum correlations and quantum dynamics, which can be retrieved via weak measurements, as initiated by Aharonov and colleagues. In this paper, we provide a full analytical extension of the method described by Puentes et al. [Phys. Rev. Lett. 109, 040401 (2012)], to extract the joint weak values of single-particle operators from two-dimensional spatial displacements of Laguerre-Gauss probe states, for the case of the azimuthal index $|l|>1$. This method has a statistical advantage over previous ones since information about the conjugate observable, i.e., the momentum displacement of the probe, is not required. Moreover, we demonstrate that, under certain conditions, the joint weak value can be extracted directly from spatial displacements without any additional data processing.

arXiv:1209.3110•Physical Review A•Nov 5, 2012•30 citations

Postselected von Neumann measurement with superpositions of orbital angular momentum pointer states

Janarbek Yuanbek, Yi-Fang Ren, Yusuf Turek

We investigated an orbital angular momentum (OAM) pointer within the framework of von Neumann measurements and discovered its significant impact on optimizing superpositions of Gaussian and Laguerre-Gaussian (LG) states. Calculations of the quadrature squeezing, the second-order cross-correlation function, the Wigner function, and the signal-to-noise ratio (SNR) support our findings. Specifically, by carefully selecting the anomalous weak value and the coupling strength between the measured system and the pointer, we demonstrated that the initial Gaussian state transforms into a non-Gaussian state after postselection. This transition highlights the potential of OAM pointers in enhancing the performance of quantum systems by tailoring state properties for specific applications.

arXiv:2411.14210•Physical Review A•Jun 9, 2025•1 citation

Amplification of Angular Rotations Using Weak Measurements

Omar S. Magaña‐Loaiza, Mohammad Mirhosseini, Brandon Rodenburg +1 more

We present a weak measurement protocol that permits a sensitive estimation of angular rotations based on the concept of weak-value amplification. The shift in the state of a pointer, in both angular position and the conjugate orbital angular momentum bases, is used to estimate angular rotations. This is done by an amplification of both the real and imaginary parts of the weak-value of a polarization operator that has been coupled to the pointer, which is a spatial mode, via a spin-orbit coupling. Our experiment demonstrates the first realization of weak-value amplification in the azimuthal degree of freedom. We have achieved effective amplification factors as large as 100, providing a sensitivity that is on par with more complicated methods that employ quantum states of light or extremely large values of orbital angular momentum.

arXiv:1312.2981•Physical Review Letters•May 21, 2014•223 citations
Weak measurements are a unique tool for accessing information about weakly interacting quantum systems with minimal back action. Joint weak measurements of single-particle operators with pointer states characterized by a two-dimensional Gaussian distribution can provide, in turn, key information about quantum correlations that can be relevant for quantum information applications. Here we demonstrate that by employing two-dimensional pointer states endowed with orbital angular momentum (OAM), it is possible to extract weak values of the higher order moments of single-particle operators, an inaccessible quantity with Gaussian pointer states only. We provide a specific example that illustrates the advantages of our method both in terms of signal enhancement and information retrieval.
In a preceding Comment [1] to our Letter [2] concerning weak measurements with orbital-angular-momentum (OAM) pointer states [2], Pan and Panigrahi show that the real and imaginary parts of higher-order weak values can be made accessible using Gaussian pointer states.In [2], our goal is to show that by using pointer states embedded with OAM it is possible to extract higher-order weak values where pointer states with a Gaussian shape cannot.As a consequence, our work put forward a new tool for weak amplification schemes, i.e., the use of pointer states with more general spatial forms that could be advantageous in some scenarios.We did not intend to claim that a pointer state with orbital angular momentum was needed to extract higherorder weak values in general.We clarify our point with this Reply.In our Letter we consider a specific Hamiltonian of interaction of the form H ¼ g A AP x þ g B BP y , where A, B are operators, (P x , P y ) are the pointer momentum operators, conjugate to the pointer position operators (X, Y), and g A;B are coupling constants.Moreover, we calculate the two-dimensional pointer displacement hXYi, corresponding to a specific measurement.We emphasize that we consider a particular interaction and a specific measurement, which are generally dictated by the physical system under investigation.The result, Eq. ( 4) of our Letter, shows that pointer states with OAM (l ¼ Æ1) can be used to retrieve the imaginary part of the higher-order weak values hA 2 i w and hB 2 i w , whereas this is not possible with pointer states with no OAM (l ¼ 0).In addition, Eq. ( 9) of our Letter shows, by means of a specific example with B ¼ 0, that hXYi ¼ 0 for Gaussian pointer states.On the contrary, a pointer state with l ¼ Æ1 allows us to extract the imaginary part of the weak value hA 2 i w .Pan and Panigrahi show that by measuring hX 2 i one can obtain the real part of the weak value hA 2 i w using a Gaussian pointer [see Eq. ( 4) of [1]].However, in order to access its imaginary part, they are forced to use a different interaction Hamiltonian, and a measurement observable involving noncommuting operators.The work of Pan and Panigrahi proves the strength of our proposal: One
Weak measurements introduced by Aharonov, Albert and Vaidman (AAV) can provide informations about the system with minimal back action. Weak values of product observables (commuting) or higher moments of an observable are informationally important in the sense that they are useful to resolve some paradoxes,realize strange quantum effects, construct density matrices, etc. In this work, we show that it is possible to access the higher moment weak values of an observable using weak values of that observable with pairwise orthogonal post-selections. Although the higher moment weak values of an observable are inaccessible with Gaussian pointer states, our method allows any pointer state. We have calculated product weak values in a bipartite system for any given pure and mixed pre selected states. Such product weak values can be obtained using only the measurements of local weak values (which are defined as single system weak values in a multi-partite system). As an application, we use higher moment weak values and product weak values to reconstruct unknown quantum states of single and bipartite systems, respectively. Robustness of our method which occurs due to inappropriate choices of quantum observables and noisy post-selections is also discussed here. Our method can easily be generalized to the multi-partite systems.
The joint weak value is a counterfactual quantity related to quantum correlations and quantum dynamics, which can be retrieved via weak measurements, as initiated by Aharonov and colleagues. In this paper, we provide a full analytical extension of the method described by Puentes et al. [Phys. Rev. Lett. 109, 040401 (2012)], to extract the joint weak values of single-particle operators from two-dimensional spatial displacements of Laguerre-Gauss probe states, for the case of the azimuthal index ∣l∣>1|l|>1∣l∣>1. This method has a statistical advantage over previous ones since information about the conjugate observable, i.e., the momentum displacement of the probe, is not required. Moreover, we demonstrate that, under certain conditions, the joint weak value can be extracted directly from spatial displacements without any additional data processing.
We investigated an orbital angular momentum (OAM) pointer within the framework of von Neumann measurements and discovered its significant impact on optimizing superpositions of Gaussian and Laguerre-Gaussian (LG) states. Calculations of the quadrature squeezing, the second-order cross-correlation function, the Wigner function, and the signal-to-noise ratio (SNR) support our findings. Specifically, by carefully selecting the anomalous weak value and the coupling strength between the measured system and the pointer, we demonstrated that the initial Gaussian state transforms into a non-Gaussian state after postselection. This transition highlights the potential of OAM pointers in enhancing the performance of quantum systems by tailoring state properties for specific applications.
We present a weak measurement protocol that permits a sensitive estimation of angular rotations based on the concept of weak-value amplification. The shift in the state of a pointer, in both angular position and the conjugate orbital angular momentum bases, is used to estimate angular rotations. This is done by an amplification of both the real and imaginary parts of the weak-value of a polarization operator that has been coupled to the pointer, which is a spatial mode, via a spin-orbit coupling. Our experiment demonstrates the first realization of weak-value amplification in the azimuthal degree of freedom. We have achieved effective amplification factors as large as 100, providing a sensitivity that is on par with more complicated methods that employ quantum states of light or extremely large values of orbital angular momentum.