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

A linear optical scheme to implement arbitrary positive operator valued measures

Jaskaran Singh, Arvind Arvind, Sandeep K. Goyal

Published Jun 8, 2021• 0 citations
OpenAlex

Abstract

Positive operator valued measurements (POVMs) play an important role in efficient quantum communication and computation. While optical systems are one of the strongest candidates for long distance quantum communication and information processing, efficient methods to implement POVMs in these systems are scarce. Here we propose an all-optical scheme to implement an arbitrary POVM using linear optical components on m-dimensional Hilbert space of internal degrees of freedom. Linear optical nature of the proposed scheme makes it efficient and robust. We show how the scheme can be applied for state tomography and for preparing arbitrary mixed states.

Related papers

Implementation of discrete positive operator valued measures on linear optical systems using cosine-sine decomposition

Jaskaran Singh, Arvind, Sandeep K. Goyal

Positive operator valued measurements (POVMs) play an important role in efficient quantum communication and computation. While optical systems are one of the strongest candidates for long distance quantum communication and information processing, efficient methods to implement POVMs in these systems are scarce. Here we propose an all-optical scheme to implement an arbitrary POVM using linear optical components on $m$-dimensional Hilbert space of internal degrees of freedom. Linear optical nature of the proposed scheme makes it efficient and robust. We show how the scheme can be applied for state tomography and for preparing arbitrary mixed states.

arXiv:2106.04160•Physical Review Research•Jan 3, 2022•8 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

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

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

Generalized quantum measurements [also known as positive operator-valued measures (POVMs)] are of great importance in quantum information and quantum foundations but are 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 (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.

arXiv:1006.4905•Physical Review A•May 11, 2011•89 citations

Generalized Quantum Measurements on a Higher-Dimensional System via Quantum Walks

Xiaowei Wang, Xiang Zhan, Yulin Li +6 more

Quantum measurements play a fundamental role in quantum mechanics. Especially, generalized quantum measurements provide a powerful and versatile tool to extract information from quantum systems. However, how to realize them on an arbitrary higher-dimensional quantum system remains a challenging task. Here we propose a simple recipe for the implementation of a general positive-operator valued measurement (POVM) on a higher-dimensional quantum system via a one-dimensional discrete-time quantum walk with a two-dimensional coin. Furthermore, using single photons and linear optics, we realize experimentally a symmetric, informationally complete (SIC) POVM on a three-dimensional system with high fidelity. As an application, we realize a qutrit state tomography with SIC-POVM and confirm that the infidelity scaling achieved by the qutrit SIC-POVM is as good as that based on mutually unbiased bases. Our study paves the way to explore physics and information in higher-dimensional quantum systems and finds applications in various quantum information processing tasks that rely on generalized quantum measurements.

Physical Review Letters•Oct 10, 2023•32 citations

General implementation of all possible positive-operator-value measurements of single-photon polarization states

Sebastian E. Ahnert, Mike C. Payne

Positive-operator-value measures (POVM's) are the most general class of quantum measurements. We propose a setup in which all possible POVM's of a single-photon polarization state (corresponding to all possible sets of two-dimensional Kraus operators) can be implemented easily using linear optics elements. This method makes it possible to experimentally realize any projective orthogonal, projective nonorthogonal or nonprojective sets of any number of POVM operators. Furthermore, our implementation only requires vacuum ancillas and is deterministic rather than probabilistic. Thus it realizes every POVM with the correct set of output states. We give the settings required to implement two different well-known nonorthogonal projective POVM's.

arXiv:quant-ph/0408011•Physical Review A•Jan 20, 2005•51 citations

All possible bipartite positive-operator-value measurements of two-photon polarization states

Sebastian E. Ahnert, Mike C. Payne

Here we propose an implementation of all possible positive-operator-value measures (POVMs) of two-photon polarization states. POVMs are the most general class of quantum measurements. Our setup requires linear optics, Bell state measurements, and an entangled three-photon ancilla state, which can be prepared separately and in advance (or ``off-line''). As an example we give the detailed settings for a simultaneous measurement of all four Bell states for an arbitrary two-photon polarization state, which is impossible with linear optics alone.

arXiv:quant-ph/0512227•Physical Review A•Feb 21, 2006•20 citations
Positive operator valued measurements (POVMs) play an important role in efficient quantum communication and computation. While optical systems are one of the strongest candidates for long distance quantum communication and information processing, efficient methods to implement POVMs in these systems are scarce. Here we propose an all-optical scheme to implement an arbitrary POVM using linear optical components on m-dimensional Hilbert space of internal degrees of freedom. Linear optical nature of the proposed scheme makes it efficient and robust. We show how the scheme can be applied for state tomography and for preparing arbitrary mixed states.
Positive operator valued measurements (POVMs) play an important role in efficient quantum communication and computation. While optical systems are one of the strongest candidates for long distance quantum communication and information processing, efficient methods to implement POVMs in these systems are scarce. Here we propose an all-optical scheme to implement an arbitrary POVM using linear optical components on mmm-dimensional Hilbert space of internal degrees of freedom. Linear optical nature of the proposed scheme makes it efficient and robust. We show how the scheme can be applied for state tomography and for preparing arbitrary mixed states.
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.
Generalized quantum measurements [also known as positive operator-valued measures (POVMs)] are of great importance in quantum information and quantum foundations but are 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 (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.
Quantum measurements play a fundamental role in quantum mechanics. Especially, generalized quantum measurements provide a powerful and versatile tool to extract information from quantum systems. However, how to realize them on an arbitrary higher-dimensional quantum system remains a challenging task. Here we propose a simple recipe for the implementation of a general positive-operator valued measurement (POVM) on a higher-dimensional quantum system via a one-dimensional discrete-time quantum walk with a two-dimensional coin. Furthermore, using single photons and linear optics, we realize experimentally a symmetric, informationally complete (SIC) POVM on a three-dimensional system with high fidelity. As an application, we realize a qutrit state tomography with SIC-POVM and confirm that the infidelity scaling achieved by the qutrit SIC-POVM is as good as that based on mutually unbiased bases. Our study paves the way to explore physics and information in higher-dimensional quantum systems and finds applications in various quantum information processing tasks that rely on generalized quantum measurements.
Positive-operator-value measures (POVM's) are the most general class of quantum measurements. We propose a setup in which all possible POVM's of a single-photon polarization state (corresponding to all possible sets of two-dimensional Kraus operators) can be implemented easily using linear optics elements. This method makes it possible to experimentally realize any projective orthogonal, projective nonorthogonal or nonprojective sets of any number of POVM operators. Furthermore, our implementation only requires vacuum ancillas and is deterministic rather than probabilistic. Thus it realizes every POVM with the correct set of output states. We give the settings required to implement two different well-known nonorthogonal projective POVM's.
Here we propose an implementation of all possible positive-operator-value measures (POVMs) of two-photon polarization states. POVMs are the most general class of quantum measurements. Our setup requires linear optics, Bell state measurements, and an entangled three-photon ancilla state, which can be prepared separately and in advance (or ``off-line''). As an example we give the detailed settings for a simultaneous measurement of all four Bell states for an arbitrary two-photon polarization state, which is impossible with linear optics alone.