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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

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

Ayman F. Abouraddy, Bahaa E. A. Saleh

Published May 13, 2011• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.883983

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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.
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.
The Einstein-Podolsky-Rosen (EPR) argument revealed the paradoxical properties of a two-particle system entangled continuously in the spatial parameter. Yet a direct test of quantum nonlocality exhibited by this state, via a violation of Bell's inequality, has not been forthcoming. In this paper, we identify and construct experimental arrangements comprising simple optical components, without nonlinearities or moving parts, that implement operators in the spatial-parity space of single-photon fields that correspond to the familiar Pauli spin operators. We achieve this by first establishing an isomorphism between the single-mode multiphoton electromagnetic-field space spanned by a Fock-state basis and the single-photon multimode electromagnetic-field space spanned by a spatial-eigenmode basis. We then proceed to construct a Hilbert space with a two-dimensional basis of spatial even-odd parity modes. In particular, we describe an arrangement that implements a rotation in the parity space of each photon of an entangled-photon pair, allowing for a straightforward experimental test of Bell's inequality using the EPR state. Finally, the violation of a Bell inequality is quantified in terms of the physical parameters of the two-photon source.
We present the novel embodiment of a photonic qubit that makes use of one continuous spatial degree of freedom of a single photon and relies on the parity of the photon's transverse spatial distribution. Using optical spontaneous parametric down-conversion to produce photon pairs, we demonstrate the controlled generation of entangled-photon states in this new space. Specifically, two Bell states, and a continuum of their superpositions, are generated by simple manipulation of a classical parameter, the optical-pump spatial parity, and not by manipulation of the entangled photons themselves. An interferometric device, isomorphic in action to a polarizing beam splitter, projects the spatial-parity states onto an even-odd basis. This new physical realization of photonic qubits could be used as a foundation for future experiments in quantum information processing.