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

Encoding arbitrary four-qubit states in the spatial parity of a photon pair

Ayman F. Abouraddy, Timothy M. Yarnall, Giovanni Di Giuseppe, Malvin Carl Teich, Bahaa E. A. Saleh

Published Jun 21, 2012• 11 citations
Publisher

Abstract

Advancing quantum information processing is predicated on the preparation of ever-larger multiqubit states. Photonic realizations of such states may be achieved by increasing the number of photons populating the state or the number of qubits encoded per photon. Typical approaches to the latter strategy utilize distinct degrees of freedom of the photon field. We present here an approach that encodes two qubits per photon in the spatial parity of its transverse spatial profile. Simple linear optical devices transform each parity qubit separately or the two qubits jointly. Furthermore, we demonstrate that entangled photon pairs produced by spontaneous parametric down-conversion may be used to prepare arbitrary four-qubit states through sculpting the spatial profile of the classical optical pump. Two examples are highlighted---the preparation of two-photon four-qubit Greenberger-Horne-Zeilinger and $W$ states, whose encoding in a photon pair has thus far eluded other approaches.

DOI
10.1103/physreva.85.062317

Related papers

Implementing one-photon three-qubit quantum gates using spatial light modulators

Ayman F. Abouraddy, Giovanni Di Giuseppe, Timothy M. Yarnall +2 more

Increasing the information-carrying capacity of a single photon may be achieved by utilizing multiple degrees of freedom. We describe here an approach that utilizes two degrees of freedom to encode three qubits per photon: one in polarization and two in the spatial-parity symmetry of the transverse field. In this conception, a polarization-sensitive spatial light modulator corresponds to a three-qubit controlled-unitary gate with one control qubit (polarization) and two target (spatial-parity-symmetry) qubits. We describe the construction of controlled-not (cnot), $\sqrt[n]{cnot}$, controlled-phase, and Fredkin gates, and the preparation of one-photon, three-qubit Greenberger-Horne-Zeilinger (GHZ) and $W$ states. This approach enables simple optical implementations of few-qubit tasks in quantum information processing.

Physical Review A•Nov 8, 2012•31 citations

Engineering quantum correlations for m×n spatially encoded two-photons states

Paula Machado, A. A. Matoso, Mariana R. Barros +2 more

Discretizing transverse linear momentum of photon pairs, generated by spontaneous parametric down conversion (SPDC), is one of the simplest methods for producing bipartite entangled states in high dimensions. So far, it has been employed only to prepare states in dimensions $m\ifmmode\times\else\texttimes\fi{}m$. In this work, we study the generalization for engineering entangled states in dimensions $m\ifmmode\times\else\texttimes\fi{}n$. Our approach relies on the manipulation of the pump beam transverse profile and the phase-matching function of the SPDC process to prepare, behind an $m$- and $n$-slit aperture, different $m\ifmmode\times\else\texttimes\fi{}n$ spatial entangled states. We demonstrate the technique experimentally for some $2\ifmmode\times\else\texttimes\fi{}3$ states. Compared to previous approaches in producing $2\ifmmode\times\else\texttimes\fi{}n$ photonic entanglement, which require either more than two photons or hybrid entanglement, our scheme is less demanding and simpler since we employ only two photons and a single degree of freedom to encode the states.

Physical Review A•Jun 28, 2019•6 citations

Proposed optical realisation of a two photon, four-qubit entangled χ state

Atirach Ritboon, Sarah Croke, Stephen M Barnett

Abstract The four-qubit states ∣ χ ij 〉 , exhibiting genuine multi-partite entanglement have been shown to have many interesting properties and have been suggested for novel applications in quantum information processing. In this work we propose a simple quantum circuit and its corresponding optical embodiment with which to prepare photon pairs in the ∣ χ ij 〉 states. Our approach uses hyper-entangled photon pairs, produced by the type-I spontaneous parametric down-conversion process in two contiguous nonlinear crystals, together with a set of simple linear-optical transformations. Our photon pairs are maximally hyper-entangled in both their polarisation and orbital angular momentum. After one of these daughter photons passes through our optical setup, we obtain photon pairs in the hyper-entangled state ∣ χ 00 〉 , and the ∣ χ ij 〉 states can be achieved by further simple transformations.

arXiv:1703.01965•Journal of Optics•May 12, 2017•2 citations

Single-photon three-qubit quantum logic using spatial light modulators

Kumel H. Kagalwala, Giovanni Di Giuseppe, Ayman F. Abouraddy +1 more

The information-carrying capacity of a single photon can be vastly expanded by exploiting its multiple degrees of freedom: spatial, temporal, and polarization. Although multiple qubits can be encoded per photon, to date only two-qubit single-photon quantum operations have been realized. Here, we report an experimental demonstration of three-qubit single-photon, linear, deterministic quantum gates that exploit photon polarization and the two-dimensional spatial-parity-symmetry of the transverse single-photon field. These gates are implemented using a polarization-sensitive spatial light modulator that provides a robust, non-interferometric, versatile platform for implementing controlled unitary gates. Polarization here represents the control qubit for either separable or entangling unitary operations on the two spatial-parity target qubits. Such gates help generate maximally entangled three-qubit Greenberger-Horne-Zeilinger and W states, which is confirmed by tomographical reconstruction of single-photon density matrices. This strategy provides access to a wide range of three-qubit states and operations for use in few-qubit quantum information processing protocols.Photons are essential for quantum information processing, but to date only two-qubit single-photon operations have been realized. Here the authors demonstrate experimentally a three-qubit single-photon linear deterministic quantum gate by exploiting polarization along with spatial-parity symmetry.

Nature Communications•Sep 25, 2017•70 citations

Demonstration of a programmable source of two-photon multiqubit entangled states

S. Cialdi, Davide Brivio, Matteo G. A. Paris

We suggest and demonstrate a novel source of two-photon multipartite entangled states which exploits the transverse spatial structure of spontaneous parametric down-conversion together with a programmable spatial light modulator (SLM). The one-dimensional SLM is used to perform polarization entanglement purification and to realize arbitrary phase gates between polarization and momentum degrees of freedom of photons. We experimentally demonstrate our scheme by generating two-photon three-qubit linear cluster states with high fidelity using a diode laser pump with a limited coherence time and power on the crystal as low as $~2.5$ mW.

arXiv:0912.2975•Physical Review A•Apr 26, 2010•19 citations

Encoding qubits into the spatial distribution of single photons and entangled photon pairs

Ayman F. Abouraddy, Bahaa E. A. Saleh

We discuss an approach to encoding qubits in the spatial distribution of single photons and entangled-photon pairs based on utilizing the spatial parity of the photon wave fronts. Using simple optical components, that do not require nonlinearities or moving parts, we discuss implementing rotations in the Hilbert space of spatial parity and measurement of the state of parity. Using entangled photon pairs, we use spatial parity to demonstrate quantum nonlocality by violating a Bell inequality using an EPR state. We also discuss generalizations of this scheme that may allow for a larger number of qubits to be encoded per photon.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 13, 2011•0 citations
Advancing quantum information processing is predicated on the preparation of ever-larger multiqubit states. Photonic realizations of such states may be achieved by increasing the number of photons populating the state or the number of qubits encoded per photon. Typical approaches to the latter strategy utilize distinct degrees of freedom of the photon field. We present here an approach that encodes two qubits per photon in the spatial parity of its transverse spatial profile. Simple linear optical devices transform each parity qubit separately or the two qubits jointly. Furthermore, we demonstrate that entangled photon pairs produced by spontaneous parametric down-conversion may be used to prepare arbitrary four-qubit states through sculpting the spatial profile of the classical optical pump. Two examples are highlighted---the preparation of two-photon four-qubit Greenberger-Horne-Zeilinger and WWW states, whose encoding in a photon pair has thus far eluded other approaches.
Increasing the information-carrying capacity of a single photon may be achieved by utilizing multiple degrees of freedom. We describe here an approach that utilizes two degrees of freedom to encode three qubits per photon: one in polarization and two in the spatial-parity symmetry of the transverse field. In this conception, a polarization-sensitive spatial light modulator corresponds to a three-qubit controlled-unitary gate with one control qubit (polarization) and two target (spatial-parity-symmetry) qubits. We describe the construction of controlled-not (cnot), cnotn\sqrt[n]{cnot}ncnot​, controlled-phase, and Fredkin gates, and the preparation of one-photon, three-qubit Greenberger-Horne-Zeilinger (GHZ) and WWW states. This approach enables simple optical implementations of few-qubit tasks in quantum information processing.
Discretizing transverse linear momentum of photon pairs, generated by spontaneous parametric down conversion (SPDC), is one of the simplest methods for producing bipartite entangled states in high dimensions. So far, it has been employed only to prepare states in dimensions $m\ifmmode\times\else\texttimes\fi{}m$. In this work, we study the generalization for engineering entangled states in dimensions $m\ifmmode\times\else\texttimes\fi{}n$. Our approach relies on the manipulation of the pump beam transverse profile and the phase-matching function of the SPDC process to prepare, behind an mmm- and nnn-slit aperture, different $m\ifmmode\times\else\texttimes\fi{}n$ spatial entangled states. We demonstrate the technique experimentally for some $2\ifmmode\times\else\texttimes\fi{}3$ states. Compared to previous approaches in producing $2\ifmmode\times\else\texttimes\fi{}n$ photonic entanglement, which require either more than two photons or hybrid entanglement, our scheme is less demanding and simpler since we employ only two photons and a single degree of freedom to encode the states.
Abstract The four-qubit states ∣ χ ij 〉 , exhibiting genuine multi-partite entanglement have been shown to have many interesting properties and have been suggested for novel applications in quantum information processing. In this work we propose a simple quantum circuit and its corresponding optical embodiment with which to prepare photon pairs in the ∣ χ ij 〉 states. Our approach uses hyper-entangled photon pairs, produced by the type-I spontaneous parametric down-conversion process in two contiguous nonlinear crystals, together with a set of simple linear-optical transformations. Our photon pairs are maximally hyper-entangled in both their polarisation and orbital angular momentum. After one of these daughter photons passes through our optical setup, we obtain photon pairs in the hyper-entangled state ∣ χ 00 〉 , and the ∣ χ ij 〉 states can be achieved by further simple transformations.
The information-carrying capacity of a single photon can be vastly expanded by exploiting its multiple degrees of freedom: spatial, temporal, and polarization. Although multiple qubits can be encoded per photon, to date only two-qubit single-photon quantum operations have been realized. Here, we report an experimental demonstration of three-qubit single-photon, linear, deterministic quantum gates that exploit photon polarization and the two-dimensional spatial-parity-symmetry of the transverse single-photon field. These gates are implemented using a polarization-sensitive spatial light modulator that provides a robust, non-interferometric, versatile platform for implementing controlled unitary gates. Polarization here represents the control qubit for either separable or entangling unitary operations on the two spatial-parity target qubits. Such gates help generate maximally entangled three-qubit Greenberger-Horne-Zeilinger and W states, which is confirmed by tomographical reconstruction of single-photon density matrices. This strategy provides access to a wide range of three-qubit states and operations for use in few-qubit quantum information processing protocols.Photons are essential for quantum information processing, but to date only two-qubit single-photon operations have been realized. Here the authors demonstrate experimentally a three-qubit single-photon linear deterministic quantum gate by exploiting polarization along with spatial-parity symmetry.
We suggest and demonstrate a novel source of two-photon multipartite entangled states which exploits the transverse spatial structure of spontaneous parametric down-conversion together with a programmable spatial light modulator (SLM). The one-dimensional SLM is used to perform polarization entanglement purification and to realize arbitrary phase gates between polarization and momentum degrees of freedom of photons. We experimentally demonstrate our scheme by generating two-photon three-qubit linear cluster states with high fidelity using a diode laser pump with a limited coherence time and power on the crystal as low as  2.5~2.5 2.5 mW.
We discuss an approach to encoding qubits in the spatial distribution of single photons and entangled-photon pairs based on utilizing the spatial parity of the photon wave fronts. Using simple optical components, that do not require nonlinearities or moving parts, we discuss implementing rotations in the Hilbert space of spatial parity and measurement of the state of parity. Using entangled photon pairs, we use spatial parity to demonstrate quantum nonlocality by violating a Bell inequality using an EPR state. We also discuss generalizations of this scheme that may allow for a larger number of qubits to be encoded per photon.