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

Optics Express

Generation of two pairs of qudits using four photons and a single degree of freedom

Pierre-Louis de Assis, M. A. D. Carvalho, L. P. Berruezo, José Ferraz, Sebastião Pádua

Published Dec 21, 2016• 2 citations
Publisher

Abstract

Qudits, d-level quantum systems, have been shown to provide a better resource for quantum key distribution and other Quantum Information protocols. It is customary to generate photonic qudits using more than one degree of freedom of the same photon. In much the same way, multi-qubit states are generated using only a pair of photons and ingenious ways to manipulate more than one degree of freedom independently. In contrast to such costly implementations in terms of quantum resources, we present the controlled generation of two copies of two-qudit states using four photons and a single degree of freedom, transverse momentum. The degree of entanglement within each pair was inferred by exploiting the availability of two copies of the same state, without the need of a full tomographic reconstruction of the states, and both highly-entangled and separable states were generated. We show theoretically that the set of states obtainable using our setup is very diverse, ranging from maximally entangled states of qudits to separable states.

DOI
10.1364/oe.24.030149

Related papers

Generation of Qudits Using Four Photons and a Single Degree of Freedom

Pierre-Louis de Assis, M. A. D. Carvalho, L. P. Berruezo +2 more

We present the controlled generation of two copies of two-qudit states using four photons and a single degree of freedom, transverse momentum. It is experimentally and theoretically shown that both highly-entangled and separable states were generated.

Frontiers in Optics•Jan 1, 2017•0 citations

Estados emaranhados de Qubits e Qudits criados com pares de fótons produzidos na conversão paramétrica descendente

Leonardo Teixeira-Neves

In this thesis, we explore the properties of photons generated by parametric down-conversion (PDC) and entangled in continuous variables of transverse momentum, with the aim of using this degree of freedom for developing a new method for generating en-tangled states in discrete and multidimensional spaces. Such states have a great potential for applications in fundamental problems of quantum mechanics as well as in quantum information protocols. Our study is based on the theory of angular spectrum transfer from the laser beam tothe two-photon state, proposed and demonstrated by Monken, Souto Ribeiro and P Ladua [Phys. Rev. A 57, 3123 (1998)]. Using it, we investigate theoretically the evolution of the quantum state of photon pairs when they propagate from the crystal and are transmitted through linear optical systems like lenses and apertures. The two-photon state is calculated when there is only one optical system in the path of each photon and we also discuss the generalization of the method employed in the calculation, for more complex experiments. With the two-photon state obtained, we propose a method for generating entangledstates of qubits (two-dimensional quantum systems) and qudits (D-dimensional quantum systems), using the transverse momentum of photons from PDC. The method is based on the selection of specific transverse spatial modes of each photon, by using an array of D-slits (D . 2) in the path of these photons. In this method we have the control of the dimension, D, of each qudit and also the degree of entanglement between them, by manipulating the transverse laser beam profile, which is due to the transfer of angular spectrum. In order to test the theory, we make an experiment for a specific case, which has a great interest in practical applications of entanglement: we demonstrate the generation of maximally entangled states of qudits with D = 4 and D = 8. The quantum character of the correlations is assured qualitatively by measuring two-photon interference patterns with conditional fringes. We also investigate the propagation of these entangled states of qudits through free space and with a simple experiment we show that they can be distributed for distant and spatially separated parts, keeping the correlations. Finally, we perform an experiment for quantifying entanglement in this type of state that we are producing. In this work, we restrict ourselves to the simplest case of two qubits. We prepare different states by manipulating the transverse laser beam profile and their degree of entanglement is measured in two ways: (i) through the degree ofconditionality of the two-photon interference patterns and (ii) through the measurement of marginal probability. We discuss the extension of the method (i) for two-qudit states.

•Sep 25, 2006•0 citations

Hybrid photonic entanglement: Realization, characterization, and applications

Leonardo Neves, G. Lima, A. Delgado +1 more

We show that the quantum disentanglement eraser implemented on a two-photon system from parametric downconversion is a general method to create hybrid photonic entanglement, namely the entanglement between different degrees of freedom of the photon pair. To demonstrate this, we generate and characterize a source with tunable degree of hybrid entanglement between two qubits, one encoded in the transverse momentum and position of a photon, and the other in the polarization of its partner. In addition, we show that a simple extension of our setup enables the generation of two-photon qubit-qudit hybrid entangled states. Finally, we discuss the advantages that this type of entanglement can bring for an optical quantum network.

arXiv:0906.4528•Physical Review A•Oct 22, 2009•61 citations

Shaping frequency-entangled qudits

Christof Bernhard, Bänz Bessire, Thomas Feurer +1 more

We demonstrate the creation, characterization, and manipulation of frequency-entangled qudits by shaping the energy spectrum of entangled photons. The generation of maximally entangled qudit states is verified up to dimension $d=4$ through tomographic quantum-state reconstruction. Subsequently, we measure Bell parameters for qubits and qutrits as a function of their degree of entanglement. In agreement with theoretical predictions, we observe that for qutrits the Bell parameter is less sensitive to a varying degree of entanglement than for qubits. For frequency-entangled photons, the dimensionality of a qudit is ultimately limited by the bandwidth of the pump laser and can be on the order of a few millions.

arXiv:1303.6202•Physical Review A•Sep 23, 2013•104 citations

Experimental implementations of multidimensional multi-photon states

Andrea Tabacchini

Multi-particle entangled states are becoming more and more interesting for different applications in quantum information, such as quantum multi-particle teleportation, entangled based cryptography and quantum communication schemes based on multi-particle states, but also for fundamental reasons such as testing local realism by means of the Greenberger-Horne-Zeilinger states (GHZ) arguments . The advantage of multiparticle entanglement versus the most common two particle one lies in the fact that the greater the number of particles involved in the entangled state, the more clearly the quantum effects are exhibited. Our final goal is to exploit the multi-photon entangled states for quantum metrology. By the interaction of those states with nanostructures (mostly nanoholes, but in a future also nanospheres), we expect to reach sub-wavelength sensitivity phase measurements beating the Standard Quantum Limit as well as to detect plasmonic effects. In this thesis we present our work consisting on designing and building an experimental setup for the generation of states of 4-photon entangled in the transverse linear momentum. In the first part we explain some basics in the form of a technical introduction. We then adapt a general theoretical model to our particular case, explaining the physics of the process of generation of entangled states of photons. We proceed explaining the details of our setup, as well as the procedure of measurement. We then present the results of our tests in a "standard" 2-photon regime to show the correct functioning of the setup itself. Some more sophisticated measurements using structured light in the form of a first-order Hermite-Gaussian mode has been performed to generate entanglement in higher spatial modes are also presented. We conclude with theoretical and experimental details regarding the 4-photon experiments feasible with our setup. Our source is based on Spontaneous Parametric Down-Conversion (SPDC). In the last two decades it has been extensively studied for the generation of two-photon entangled states, since Kwiat et al. published in 1995 the new scheme based on polarization entangled photons. Most of the studies regarding entangled states involving more than two photons are indeed based on quantum correlations in the polarization or in the path of the down converted beams. The great advantage of entangling a spatial degree of freedom (as we do) is related to the dimensionality of the Hilbert space in which the state is defined. In the particular case of linear momentum, which is a continuous variable, we are dealing with infinite dimensions. Since in each dimension of the state one quanta of information can be encoded, the advantage of having multidimension entanglement for the field of quantum communication and computing is clear. The specs of our setup include a periodically-poled KTP crystals offering high conversion efficiency and cut for type-0 SPDC. The photons generated are well known to be inherently entangled in different degrees of freedom such as polarization, energy-time, linear momentum, and orbital angular momentum. Since each single SPDC event generates one photon pair, in order to reach four photon we entangle two consecutive SPDC events per each state. Furthermore, it is possible to manipulate (to enhance) the dimensionality of the entanglement by properly tailoring the pump spatial profile. The key point for the generation of four-photon entangled states is that, under some conditions, two consecutive pairs generated via SPDC cannot be described as two independent pairs but necessarily as a four-photon state showing genuine entanglement. This can happen when using a pulsed laser to generate the entangled photons; in particular, in the regime in which the coherence time of the down-converted photons τc is (much) longer than the temporal length of the pumping pulse Δt. In this condition the emission of a second pair is stimulated by the presence of the first one. That effect can be ultimately seen as a constructive multi-particle interference effect, the deep origin of which has to be sought in the boson statistic of photons.

•Dec 6, 2017•0 citations

TWO-PHOTON HIGH-DIMENSIONAL SPATIAL ENTANGLEMENT: THEORY AND EXPERIMENT

Leonardo Neves, G. Lima, J. G. Aguirre Gómez +3 more

We review recent theoretical and experimental works where are proposed and demonstrated how to use photon pairs created by spontaneous parametric down-conversion to generate entangled states of D-dimensional quantum systems, or qudits. This is the first demonstration of high-dimensional entanglement based on the intrinsic transverse momentum entanglement of the type-II down-converted photons. The qudit space is defined by an aperture made up of an opaque screen with D slits (paths), placed in the arms of the twin photons. By manipulating the pump beam profile we can prepare different entangled states of these possible paths. We focus our attention on an important case for applications in quantum information: the maximally entangled states. Experimental results for qudits with D=4 and D=8 are shown and measuring a two-photon conditional interference, we also demonstrate the nonclassical character of the correlations.

Modern Physics Letters B•Jan 10, 2006•15 citations
Qudits, d-level quantum systems, have been shown to provide a better resource for quantum key distribution and other Quantum Information protocols. It is customary to generate photonic qudits using more than one degree of freedom of the same photon. In much the same way, multi-qubit states are generated using only a pair of photons and ingenious ways to manipulate more than one degree of freedom independently. In contrast to such costly implementations in terms of quantum resources, we present the controlled generation of two copies of two-qudit states using four photons and a single degree of freedom, transverse momentum. The degree of entanglement within each pair was inferred by exploiting the availability of two copies of the same state, without the need of a full tomographic reconstruction of the states, and both highly-entangled and separable states were generated. We show theoretically that the set of states obtainable using our setup is very diverse, ranging from maximally entangled states of qudits to separable states.
In this thesis, we explore the properties of photons generated by parametric down-conversion (PDC) and entangled in continuous variables of transverse momentum, with the aim of using this degree of freedom for developing a new method for generating en-tangled states in discrete and multidimensional spaces. Such states have a great potential for applications in fundamental problems of quantum mechanics as well as in quantum information protocols. Our study is based on the theory of angular spectrum transfer from the laser beam tothe two-photon state, proposed and demonstrated by Monken, Souto Ribeiro and P Ladua [Phys. Rev. A 57, 3123 (1998)]. Using it, we investigate theoretically the evolution of the quantum state of photon pairs when they propagate from the crystal and are transmitted through linear optical systems like lenses and apertures. The two-photon state is calculated when there is only one optical system in the path of each photon and we also discuss the generalization of the method employed in the calculation, for more complex experiments. With the two-photon state obtained, we propose a method for generating entangledstates of qubits (two-dimensional quantum systems) and qudits (D-dimensional quantum systems), using the transverse momentum of photons from PDC. The method is based on the selection of specific transverse spatial modes of each photon, by using an array of D-slits (D . 2) in the path of these photons. In this method we have the control of the dimension, D, of each qudit and also the degree of entanglement between them, by manipulating the transverse laser beam profile, which is due to the transfer of angular spectrum. In order to test the theory, we make an experiment for a specific case, which has a great interest in practical applications of entanglement: we demonstrate the generation of maximally entangled states of qudits with D = 4 and D = 8. The quantum character of the correlations is assured qualitatively by measuring two-photon interference patterns with conditional fringes. We also investigate the propagation of these entangled states of qudits through free space and with a simple experiment we show that they can be distributed for distant and spatially separated parts, keeping the correlations. Finally, we perform an experiment for quantifying entanglement in this type of state that we are producing. In this work, we restrict ourselves to the simplest case of two qubits. We prepare different states by manipulating the transverse laser beam profile and their degree of entanglement is measured in two ways: (i) through the degree ofconditionality of the two-photon interference patterns and (ii) through the measurement of marginal probability. We discuss the extension of the method (i) for two-qudit states.
We show that the quantum disentanglement eraser implemented on a two-photon system from parametric downconversion is a general method to create hybrid photonic entanglement, namely the entanglement between different degrees of freedom of the photon pair. To demonstrate this, we generate and characterize a source with tunable degree of hybrid entanglement between two qubits, one encoded in the transverse momentum and position of a photon, and the other in the polarization of its partner. In addition, we show that a simple extension of our setup enables the generation of two-photon qubit-qudit hybrid entangled states. Finally, we discuss the advantages that this type of entanglement can bring for an optical quantum network.
We demonstrate the creation, characterization, and manipulation of frequency-entangled qudits by shaping the energy spectrum of entangled photons. The generation of maximally entangled qudit states is verified up to dimension d=4d=4d=4 through tomographic quantum-state reconstruction. Subsequently, we measure Bell parameters for qubits and qutrits as a function of their degree of entanglement. In agreement with theoretical predictions, we observe that for qutrits the Bell parameter is less sensitive to a varying degree of entanglement than for qubits. For frequency-entangled photons, the dimensionality of a qudit is ultimately limited by the bandwidth of the pump laser and can be on the order of a few millions.
Multi-particle entangled states are becoming more and more interesting for different applications in quantum information, such as quantum multi-particle teleportation, entangled based cryptography and quantum communication schemes based on multi-particle states, but also for fundamental reasons such as testing local realism by means of the Greenberger-Horne-Zeilinger states (GHZ) arguments . The advantage of multiparticle entanglement versus the most common two particle one lies in the fact that the greater the number of particles involved in the entangled state, the more clearly the quantum effects are exhibited. Our final goal is to exploit the multi-photon entangled states for quantum metrology. By the interaction of those states with nanostructures (mostly nanoholes, but in a future also nanospheres), we expect to reach sub-wavelength sensitivity phase measurements beating the Standard Quantum Limit as well as to detect plasmonic effects. In this thesis we present our work consisting on designing and building an experimental setup for the generation of states of 4-photon entangled in the transverse linear momentum. In the first part we explain some basics in the form of a technical introduction. We then adapt a general theoretical model to our particular case, explaining the physics of the process of generation of entangled states of photons. We proceed explaining the details of our setup, as well as the procedure of measurement. We then present the results of our tests in a "standard" 2-photon regime to show the correct functioning of the setup itself. Some more sophisticated measurements using structured light in the form of a first-order Hermite-Gaussian mode has been performed to generate entanglement in higher spatial modes are also presented. We conclude with theoretical and experimental details regarding the 4-photon experiments feasible with our setup. Our source is based on Spontaneous Parametric Down-Conversion (SPDC). In the last two decades it has been extensively studied for the generation of two-photon entangled states, since Kwiat et al. published in 1995 the new scheme based on polarization entangled photons. Most of the studies regarding entangled states involving more than two photons are indeed based on quantum correlations in the polarization or in the path of the down converted beams. The great advantage of entangling a spatial degree of freedom (as we do) is related to the dimensionality of the Hilbert space in which the state is defined. In the particular case of linear momentum, which is a continuous variable, we are dealing with infinite dimensions. Since in each dimension of the state one quanta of information can be encoded, the advantage of having multidimension entanglement for the field of quantum communication and computing is clear. The specs of our setup include a periodically-poled KTP crystals offering high conversion efficiency and cut for type-0 SPDC. The photons generated are well known to be inherently entangled in different degrees of freedom such as polarization, energy-time, linear momentum, and orbital angular momentum. Since each single SPDC event generates one photon pair, in order to reach four photon we entangle two consecutive SPDC events per each state. Furthermore, it is possible to manipulate (to enhance) the dimensionality of the entanglement by properly tailoring the pump spatial profile. The key point for the generation of four-photon entangled states is that, under some conditions, two consecutive pairs generated via SPDC cannot be described as two independent pairs but necessarily as a four-photon state showing genuine entanglement. This can happen when using a pulsed laser to generate the entangled photons; in particular, in the regime in which the coherence time of the down-converted photons τc is (much) longer than the temporal length of the pumping pulse Δt. In this condition the emission of a second pair is stimulated by the presence of the first one. That effect can be ultimately seen as a constructive multi-particle interference effect, the deep origin of which has to be sought in the boson statistic of photons.
We review recent theoretical and experimental works where are proposed and demonstrated how to use photon pairs created by spontaneous parametric down-conversion to generate entangled states of D-dimensional quantum systems, or qudits. This is the first demonstration of high-dimensional entanglement based on the intrinsic transverse momentum entanglement of the type-II down-converted photons. The qudit space is defined by an aperture made up of an opaque screen with D slits (paths), placed in the arms of the twin photons. By manipulating the pump beam profile we can prepare different entangled states of these possible paths. We focus our attention on an important case for applications in quantum information: the maximally entangled states. Experimental results for qudits with D=4 and D=8 are shown and measuring a two-photon conditional interference, we also demonstrate the nonclassical character of the correlations.