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 A

Detection of nonlocal superpositions

A. J. Gutiérrez-Esparza, Wanderson M. Pimenta, Breno Marques, A. A. Matoso, Jan Sperling, W. Vogel, Sebastião Pádua

Published Sep 26, 2014• 20 citations
Publisher

Abstract

We study in theory and experiment the verification of the Schmidt number of quantum correlated radiation fields. This measure of entanglement counts the number of global superpositions of product states which are needed to describe a compound quantum system. For unraveling a certain value of this measure, a family of entanglement and Schmidt number tests is constructed. The measurement of the whole class of witnesses is realized. By generating a path entangled two-photon state, we demonstrate the feasibility to directly count quantum superpositions.

DOI
10.1103/physreva.90.032328

Related papers

Entanglement witnesses and detection of nonlocal superpositions

A. J. Gutiérrez-Esparza, Wanderson M. Pimenta, Breno Marques +5 more

A complete characterization of entanglement in a two-qutrit state generated using the transverse spatial correlations of two parametric down-converted photons is discussed. We verify entanglement for a particular case via entanglement witness operators which are decomposed into a sum of local observables. Experimentally, these operators are accomplished by using a spatial light modulator and a polarizing beam splitter. The quantification of entanglement is computed by the negativity. We also realize an experiment for the verification of the Schmidt number of quantum correlated photons. This measure of entanglement counts the number of global superpositions of product states which are needed to describe a compound quantum system. For unraveling a certain value of this measure, a family of entanglement and Schmidt number tests is constructed.

Latin America Optics and Photonics Conference•Jan 1, 2014•0 citations

Families of $k$-positive maps and Schmidt number witnesses from generalized equiangular measurements

Katarzyna Siudzińska

Quantum entanglement is an important resource in many modern technologies, like quantum computation or quantum communication and information processing. Therefore, most interest is given to detect and quantify entangled states. Entanglement degree of bipartite mixed quantum states can be measured using the Schmidt number. Witnesses of the Schmidt number are closely related to $k$-positive linear maps, for which there is no general construction. Here, we use the generalized equiangular measurements to define a family of $k$-positive linear maps and the corresponding Schmidt number witnesses. We present examples of witnesses that detect two-parameter entangled states with Schmidt number $k+1$ in any dimension. Our approach allows for a more efficient entanglement quantification than other known Schmidt number witnesses constructed from symmetric measurement operators.

quant-pharXiv:2512.18807•Journal of Physics A Mathematical and Theoretical•Dec 23, 2025•0 citations

Detection of quantum correlations

Aleksandra Dimić

One of the main foci of modern applied quantum information theory\nis the production of large-scale quantum entanglement involving many\nparticles, to achieve the next-generation quantum technologies. Although a full-scale quantum computer is still far away in time, in the next\nfew years we can expect to have quantum devices composed of up to a\nhundred controllable qubits. The primary challenge in moving towards\nsuch devices lies in the development of reliable and resource-efficient\ndetection techniques to prove genuine quantum advantage. The main\nobjective of this thesis is to investigate novel methods to detect the presence of quantum correlations in such systems, in particular, quantum\nentanglement and quantum nonlocality.\nThe first part of this thesis is dedicated to entanglement detection\nin large-scale quantum systems. Our main goal is to develop a novel\nprobabilistic method in which entanglement is seen as an ability of a\nquantum system to accomplish certain information-processing tasks.\nWe show that for certain classes of large (e.g. few tens of qubits) quantum states, even a single copy of a quantum state suffices to detect\nentanglement with a high confidence. Compared to the standard detection methods, this makes our method exceptionally resource-efficient.\nThe developed probabilistic scheme applies to multiple classes of states, vital for quantum computation, such as cluster states or ground\nstates of local Hamiltonians.\nIn the second part of this thesis, we develop a generic framework\nfor translating any entanglement witness into a resource-efficient probabilistic scheme. We show that the confidence level of entanglement\ndetection grows exponentially fast with the number of detection events,\nwhich makes this ansatz very efficient and reliable. Furthermore, we\npresent the first experimental performance of our method by verifying\nthe presence of entanglement in a photonic six-qubit cluster state.\nThe third part of this thesis describes the extension of our entanglement verification method to quantum nonlocality. Concrete examples\nare presented where we convert Bell’s inequalities into the probabilistic\nprocedure and incorporate our method into self-testing schemes. We\nshow that the performance of our method significantly exceeds the ability of the existing methods for detection of quantum nonlocality and\nself-testing.\nThe last part of this thesis is a study of the weak-convergence properties of random variables generated by quantum measurements. Beginning with a sequence of random variables generated by repeated\nunsharp quantum measurements, we study the limit distribution of\nmeasured relative frequency. We provide the de Finetti-type of representation theorem for all separable states, showing that the measured\ndistribution can be well approximated by a mixture of normal distributions. Additionally, we investigate the convergence rates and show\nthat the relative frequency converges to some constant at the rate of\norder 1=pN for all separable inputs. Finally, we provide an example of\na strictly unsharp quantum measurement where we obtain better scaling by using entangled inputs. We find such behaviour of entangled\nstates relevant for quantum information processing.

•Sep 13, 2019•0 citations

Certification of high-dimensional entanglement in continuous-variable systems

Ida Mishra, Simon Morelli, Klára Baksová +2 more

The dimensionality of entanglement in high-dimensional quantum systems is quantified by the Schmidt number, whose large value signals potential advantages for quantum communication and quantum computation. A commonly used approach to practical Schmidt-number detection in finite-dimensional systems is based on the estimation of fidelities to pure states with large entanglement dimensionality or lower bounds to these fidelities. However, for mode-entangled continuous-variable systems, the corresponding measurements are typically difficult to realize. Here, we introduce and assess fidelity bounds for Schmidt-number detection based on practically more accessible measurements of the first and second statistical moments of arbitrary continuous-variable quantum states. We provide analytical formulas that allow evaluating these bounds and test them for families of Gaussian and non-Gaussian states, including two-mode squeezed thermal states and photon-added displaced two-mode squeezed vacuum states. We compare our bounds to other methods for the certification of high-dimensional entanglement based on the same measurements.

quant-pharXiv:2610.03113•Oct 5, 2026•0 citations

Constructingk-Schmidt witnesses for infinite-dimensional systems

Xin Li, Xiaochun Fang

We study the structure of k-Schmidt witnesses in infinite dimensions. We show that for any states with Schmidt number greater than , there exists a -Schmidt witnesses of the form to detect it, where and is a finite rank self-adjoint operator. We provide a method to construct -Schmidt witnesses with these forms. An elementary operator criterion to determine the lower bound of the Schmidt number of a state is obtained. We also construct a class of 2-Schmidt witnesses, from which we can detect the entanglement of states by entries of their matrix representations.

Linear and Multilinear Algebra•Apr 17, 2014•0 citations

Absolute Schmidt number: characterization, detection and resource-theoretic quantification

Bivas Mallick, Saheli Mukherjee, Nirman Ganguly +1 more

The dimensionality of entanglement, quantified by the Schmidt number, is a valuable resource for a wide range of quantum information processing tasks. In this work, we introduce the notion of the absolute Schmidt number, referring to states whose Schmidt number cannot be increased by any global unitary transformation. We provide a characterization of the set of arbitrary-dimensional states whose Schmidt number is invariant under all global unitaries. Our approach enables us to develop both witness-based and moment-based techniques to detect nonabsolute Schmidt number states which could provide significant operational advantages through Schmidt number enhancement by global unitaries. We next formulate two resource-theoretic measures of nonabsolute Schmidt number states, based respectively on Schmidt number witness and robustness, and demonstrate an operational utility of the latter in a channel discrimination task. Finally, we extend our analysis to quantum channels by introducing a new class of channels that possess the absolute Schmidt number property. We derive a necessary and sufficient condition for identifying when a channel has the absolute Schmidt number property, confining our analysis to the class of covariant channels.

quant-pharXiv:2604.02439•Physical Review A•Apr 6, 2026•0 citations
We study in theory and experiment the verification of the Schmidt number of quantum correlated radiation fields. This measure of entanglement counts the number of global superpositions of product states which are needed to describe a compound quantum system. For unraveling a certain value of this measure, a family of entanglement and Schmidt number tests is constructed. The measurement of the whole class of witnesses is realized. By generating a path entangled two-photon state, we demonstrate the feasibility to directly count quantum superpositions.
A complete characterization of entanglement in a two-qutrit state generated using the transverse spatial correlations of two parametric down-converted photons is discussed. We verify entanglement for a particular case via entanglement witness operators which are decomposed into a sum of local observables. Experimentally, these operators are accomplished by using a spatial light modulator and a polarizing beam splitter. The quantification of entanglement is computed by the negativity. We also realize an experiment for the verification of the Schmidt number of quantum correlated photons. This measure of entanglement counts the number of global superpositions of product states which are needed to describe a compound quantum system. For unraveling a certain value of this measure, a family of entanglement and Schmidt number tests is constructed.
Families of kkk-positive maps and Schmidt number witnesses from generalized equiangular measurements
Quantum entanglement is an important resource in many modern technologies, like quantum computation or quantum communication and information processing. Therefore, most interest is given to detect and quantify entangled states. Entanglement degree of bipartite mixed quantum states can be measured using the Schmidt number. Witnesses of the Schmidt number are closely related to kkk-positive linear maps, for which there is no general construction. Here, we use the generalized equiangular measurements to define a family of kkk-positive linear maps and the corresponding Schmidt number witnesses. We present examples of witnesses that detect two-parameter entangled states with Schmidt number k+1k+1k+1 in any dimension. Our approach allows for a more efficient entanglement quantification than other known Schmidt number witnesses constructed from symmetric measurement operators.
One of the main foci of modern applied quantum information theory\nis the production of large-scale quantum entanglement involving many\nparticles, to achieve the next-generation quantum technologies. Although a full-scale quantum computer is still far away in time, in the next\nfew years we can expect to have quantum devices composed of up to a\nhundred controllable qubits. The primary challenge in moving towards\nsuch devices lies in the development of reliable and resource-efficient\ndetection techniques to prove genuine quantum advantage. The main\nobjective of this thesis is to investigate novel methods to detect the presence of quantum correlations in such systems, in particular, quantum\nentanglement and quantum nonlocality.\nThe first part of this thesis is dedicated to entanglement detection\nin large-scale quantum systems. Our main goal is to develop a novel\nprobabilistic method in which entanglement is seen as an ability of a\nquantum system to accomplish certain information-processing tasks.\nWe show that for certain classes of large (e.g. few tens of qubits) quantum states, even a single copy of a quantum state suffices to detect\nentanglement with a high confidence. Compared to the standard detection methods, this makes our method exceptionally resource-efficient.\nThe developed probabilistic scheme applies to multiple classes of states, vital for quantum computation, such as cluster states or ground\nstates of local Hamiltonians.\nIn the second part of this thesis, we develop a generic framework\nfor translating any entanglement witness into a resource-efficient probabilistic scheme. We show that the confidence level of entanglement\ndetection grows exponentially fast with the number of detection events,\nwhich makes this ansatz very efficient and reliable. Furthermore, we\npresent the first experimental performance of our method by verifying\nthe presence of entanglement in a photonic six-qubit cluster state.\nThe third part of this thesis describes the extension of our entanglement verification method to quantum nonlocality. Concrete examples\nare presented where we convert Bell’s inequalities into the probabilistic\nprocedure and incorporate our method into self-testing schemes. We\nshow that the performance of our method significantly exceeds the ability of the existing methods for detection of quantum nonlocality and\nself-testing.\nThe last part of this thesis is a study of the weak-convergence properties of random variables generated by quantum measurements. Beginning with a sequence of random variables generated by repeated\nunsharp quantum measurements, we study the limit distribution of\nmeasured relative frequency. We provide the de Finetti-type of representation theorem for all separable states, showing that the measured\ndistribution can be well approximated by a mixture of normal distributions. Additionally, we investigate the convergence rates and show\nthat the relative frequency converges to some constant at the rate of\norder 1=pN for all separable inputs. Finally, we provide an example of\na strictly unsharp quantum measurement where we obtain better scaling by using entangled inputs. We find such behaviour of entangled\nstates relevant for quantum information processing.
The dimensionality of entanglement in high-dimensional quantum systems is quantified by the Schmidt number, whose large value signals potential advantages for quantum communication and quantum computation. A commonly used approach to practical Schmidt-number detection in finite-dimensional systems is based on the estimation of fidelities to pure states with large entanglement dimensionality or lower bounds to these fidelities. However, for mode-entangled continuous-variable systems, the corresponding measurements are typically difficult to realize. Here, we introduce and assess fidelity bounds for Schmidt-number detection based on practically more accessible measurements of the first and second statistical moments of arbitrary continuous-variable quantum states. We provide analytical formulas that allow evaluating these bounds and test them for families of Gaussian and non-Gaussian states, including two-mode squeezed thermal states and photon-added displaced two-mode squeezed vacuum states. We compare our bounds to other methods for the certification of high-dimensional entanglement based on the same measurements.
We study the structure of k-Schmidt witnesses in infinite dimensions. We show that for any states with Schmidt number greater than , there exists a -Schmidt witnesses of the form to detect it, where and is a finite rank self-adjoint operator. We provide a method to construct -Schmidt witnesses with these forms. An elementary operator criterion to determine the lower bound of the Schmidt number of a state is obtained. We also construct a class of 2-Schmidt witnesses, from which we can detect the entanglement of states by entries of their matrix representations.
The dimensionality of entanglement, quantified by the Schmidt number, is a valuable resource for a wide range of quantum information processing tasks. In this work, we introduce the notion of the absolute Schmidt number, referring to states whose Schmidt number cannot be increased by any global unitary transformation. We provide a characterization of the set of arbitrary-dimensional states whose Schmidt number is invariant under all global unitaries. Our approach enables us to develop both witness-based and moment-based techniques to detect nonabsolute Schmidt number states which could provide significant operational advantages through Schmidt number enhancement by global unitaries. We next formulate two resource-theoretic measures of nonabsolute Schmidt number states, based respectively on Schmidt number witness and robustness, and demonstrate an operational utility of the latter in a channel discrimination task. Finally, we extend our analysis to quantum channels by introducing a new class of channels that possess the absolute Schmidt number property. We derive a necessary and sufficient condition for identifying when a channel has the absolute Schmidt number property, confining our analysis to the class of covariant channels.