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

Laser Physics

Entanglement of biphoton-based qutrits and ququarts

S. P. Kulik, Stanislav S. Straupe

Published Aug 15, 2014• 2 citations
Publisher

Abstract

In this paper we discuss physical aspects of entanglement in biphoton-based qutrits and ququarts, taking into account the bosonic correlations due to the indistinguishability of photons. We show that two apparently different types of entanglement in these systems, 'entanglement of modes' and 'entanglement of photons', are in fact closely related to each other. The latter is to a remarkable extent connected with the degree of polarization of two-photon light. Specifically, we demonstrate that a beamsplitter and subsequent post-selection using a coincidence circuit converts 'entanglement of photons' of a qutrit into 'entanglement of modes' of a ququart.

DOI
10.1088/1054-660x/24/9/094007

Related papers

Entanglement of qutrits and ququarts

Mikhail Vladimirovich Fedorov, P. A. Volkov, J. M. Mikhailova +2 more

We investigate in a general form entanglement of biphoton qutrits and ququarts, i.e. states formed in the processes of collinear and, correspondingly, degenerate and non-degenerate Spontaneous Parametric Down-Conversion. Indistinguishability of photons and, for ququarts, joint presence of the frequency and and polarization entanglement are fully taken into account. In the case of qutrits the most general 3-parametric families of maximally entangled and non-entangled states are found, and anti-correlation of the degree of entanglement and polarization is shown to occur and to be characterized by a rather simple formula. Biphoton ququarts are shown to be two-qudits with the single-photon Hilbert space dimensionality $d=4$, which differs them significantly from the often used two-qubit model ($d=2$). New expressions for entanglement quantifiers of biphoton ququarts are derived and discussed. Rather simple procedures for a direct measurement of the degree of entanglement are described for both qutrits and ququarts.

arXiv:1009.2744•Sep 14, 2010•4 citations

Entanglement of biphoton states: qutrits and ququarts

Mikhail Vladimirovich Fedorov, P. A. Volkov, J. M. Mikhailova +2 more

We investigate, in a general form, entanglement of biphoton qutrits and ququarts, i.e. states formed in the processes of, correspondingly, degenerate and non-degenerate spontaneous parametric down-conversion. Indistinguishability of photons and, for ququarts, joint presence of the frequency and polarization entanglement are fully taken into account. In the case of qutrits, the most general three-parametric families of maximally entangled and non-entangled states are found, and anticorrelation of the degree of entanglement and polarization is shown to occur and to be characterized by a rather simple formula. Biphoton ququarts are shown to be two-qudits with the single-photon Hilbert space dimensionality d =4, which differentiates them significantly from the often used two-qubit model ( d =2). New expressions for entanglement quantifiers of biphoton ququarts are derived and discussed. Rather simple procedures for a direct measurement of the degree of entanglement are described for both qutrits and ququarts.

New Journal of Physics•Aug 8, 2011•37 citations

Qutrits and ququarts in spontaneous parametric down-conversion, correlations and entanglement

Mikhail Vladimirovich Fedorov, P. A. Volkov, J. M. Mikhailova

We investigate features of biphoton qutrits and ququarts with the symmetry of biphoton wavefunctions fully taken into account. Entanglement quantifiers of such states are found as functions of qutrit and ququart parameters. For biphoton qutrits, a general relation between degrees of entanglement and polarization is established. In the case of biphoton ququarts, photon frequencies are considered as variables independent of polarization variables, with both polarization and frequency degrees of freedom equally contributing to the total ququart entanglement. Averaging over one of these two degrees of freedom is shown to reduce pure ququart states to mixed two-qubit states. The degree of polarization and degrees of correlations in mixed polarization states are investigated.

Journal of Experimental and Theoretical Physics•Jul 1, 2012•9 citations

State entanglement of biphoton qutrits and ququarts

Mikhail Vladimirovich Fedorov

Properties of biphoton qutrits and ququarts are characterized with allowance for the demands of the symmetry of wave functions of two-boson states and, in the case of ququarts, for the presence of two independent degrees of freedom (e.g., polarization and frequency) of the photons.

Bulletin of the Russian Academy of Sciences Physics•Mar 1, 2012•1 citation

Biphoton ququarts and their entanglement

Yoon-Ho Kim

A four-dimensional quantum system (ququart) can be constructed by using the biphoton polarization states of frequency-nondegenerate spontaneous parametric down-conversion. We first discuss how to generate and characterize general single-ququart states with varying degrees of mixedness. We then discuss schemes to entangle multiple biphoton ququarts using linear optics and coincidence post-selection.

Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR)•Aug 1, 2007•0 citations

Manipulating Biphotonic Qutrits

B. P. Lanyon, Till J. Weinhold, Nathan K. Langford +4 more

Quantum information carriers with higher dimension than the canonical qubit offer significant advantages. However, manipulating such systems is extremely difficult. We show how measurement-induced nonlinearities can dramatically extend the range of possible transforms on biphotonic qutrits-three-level quantum systems formed by the polarization of two photons in the same spatiotemporal mode. We fully characterize the biphoton-photon entanglement that underpins our technique, thereby realizing the first instance of qubit-qutrit entanglement. We discuss an extension of our technique to generate qutrit-qutrit entanglement and to manipulate any bosonic encoding of quantum information.

arXiv:0707.2880•Physical Review Letters•Feb 14, 2008•182 citations
In this paper we discuss physical aspects of entanglement in biphoton-based qutrits and ququarts, taking into account the bosonic correlations due to the indistinguishability of photons. We show that two apparently different types of entanglement in these systems, 'entanglement of modes' and 'entanglement of photons', are in fact closely related to each other. The latter is to a remarkable extent connected with the degree of polarization of two-photon light. Specifically, we demonstrate that a beamsplitter and subsequent post-selection using a coincidence circuit converts 'entanglement of photons' of a qutrit into 'entanglement of modes' of a ququart.
We investigate in a general form entanglement of biphoton qutrits and ququarts, i.e. states formed in the processes of collinear and, correspondingly, degenerate and non-degenerate Spontaneous Parametric Down-Conversion. Indistinguishability of photons and, for ququarts, joint presence of the frequency and and polarization entanglement are fully taken into account. In the case of qutrits the most general 3-parametric families of maximally entangled and non-entangled states are found, and anti-correlation of the degree of entanglement and polarization is shown to occur and to be characterized by a rather simple formula. Biphoton ququarts are shown to be two-qudits with the single-photon Hilbert space dimensionality d=4d=4d=4, which differs them significantly from the often used two-qubit model (d=2d=2d=2). New expressions for entanglement quantifiers of biphoton ququarts are derived and discussed. Rather simple procedures for a direct measurement of the degree of entanglement are described for both qutrits and ququarts.
We investigate, in a general form, entanglement of biphoton qutrits and ququarts, i.e. states formed in the processes of, correspondingly, degenerate and non-degenerate spontaneous parametric down-conversion. Indistinguishability of photons and, for ququarts, joint presence of the frequency and polarization entanglement are fully taken into account. In the case of qutrits, the most general three-parametric families of maximally entangled and non-entangled states are found, and anticorrelation of the degree of entanglement and polarization is shown to occur and to be characterized by a rather simple formula. Biphoton ququarts are shown to be two-qudits with the single-photon Hilbert space dimensionality d =4, which differentiates them significantly from the often used two-qubit model ( d =2). New expressions for entanglement quantifiers of biphoton ququarts are derived and discussed. Rather simple procedures for a direct measurement of the degree of entanglement are described for both qutrits and ququarts.
We investigate features of biphoton qutrits and ququarts with the symmetry of biphoton wavefunctions fully taken into account. Entanglement quantifiers of such states are found as functions of qutrit and ququart parameters. For biphoton qutrits, a general relation between degrees of entanglement and polarization is established. In the case of biphoton ququarts, photon frequencies are considered as variables independent of polarization variables, with both polarization and frequency degrees of freedom equally contributing to the total ququart entanglement. Averaging over one of these two degrees of freedom is shown to reduce pure ququart states to mixed two-qubit states. The degree of polarization and degrees of correlations in mixed polarization states are investigated.
Quantum information carriers with higher dimension than the canonical qubit offer significant advantages. However, manipulating such systems is extremely difficult. We show how measurement-induced nonlinearities can dramatically extend the range of possible transforms on biphotonic qutrits-three-level quantum systems formed by the polarization of two photons in the same spatiotemporal mode. We fully characterize the biphoton-photon entanglement that underpins our technique, thereby realizing the first instance of qubit-qutrit entanglement. We discuss an extension of our technique to generate qutrit-qutrit entanglement and to manipulate any bosonic encoding of quantum information.