New Twist on Light Beams for Quantum
Robert W. Boyd, Jonathan Leach, Barry Jack, Jacqui Romero, Anand K. Jha, Alison M. Yao, Sonja
Franke-Arnold, David G. Ireland, Stephen M. Barnett and Miles J. Padgett
Recent research has opened path- ways for new protocols in quantum
information science based on the orbital
angular momentum states of photons.
Light beams can carry angular momentum via two mechanisms. Spin angular
momentum is associated with the circular polarization of light. A light beam
can also carry angular momentum by
means of any helicity associated with the
phase fronts. 1 For example, a light field
possessing an azimuthal phase structure
of the sort exp(il ϕ), where l is an integer,
carries an angular momentum of l h – per
photon. The Laguerre-Gauss modes
familiar from laser physics provide an
example of a field distribution that carries orbital angular momentum (OAM).
These OAM states have important
implications for quantum information
science because they reside in infinite-dimensional state space. Photons can
be prepared in any one of these modes
or in fact in any linear combination of
them. It is thereby possible to impress
large amounts of information onto a
single photon. An application that has
attracted much attention recently is new
protocols for quantum key distribution,
in which more than one bit of information is carried by each photon. 2 In this
application, the data transfer rate is
increased in proportion to the number
of bits of information carried by each
photon; moreover, the security of the
protocol is increased.
Because these applications rely on the
quantum properties of the OAM states, 3
much effort has been invested in quantifying these properties. We recently performed a quantitative study of the degree
of entanglement between two photons
created by parametric downconversion. 4
Entanglement of the properties of two
separated particles constitutes a fundamental signature of quantum mechanics and is a key resource for quantum
An intense laser beam excites a nonlinear crystal, and two new photons are created by the
nonlinear process. They are strongly correlated in both birthplace and OAM. Specifically,
even though the OAM of either is undetermined, the two OAMs always add up to zero. In
addition, the angular position of the birthplace of one photon is highly correlated to that
of the other. Since the photons are strongly correlated in both angular position and OAM,
they are entangled.
information science. We quantified
entanglement by measuring the degree
of correlation of both the OAM and the
azimuthal position of the birthplaces
of the two photons. These correlations
demonstrate the Einstein-Podolsky-Rosen
effect for angle and angular momentum
and were found to be an order of magnitude stronger than those allowed by the
uncertainty principle for independent
In a separate experiment, 5 we stu-
died angular two-photon interference
in a scheme in which entangled photons
are made to pass through apertures in the
form of double angular slits. Using this
scheme, we demonstrated an entangled
two-qubit state that is based on the an-
gular-position correlations of entangled
photons. A high degree of entanglement,
as quantified by a property known
as the concurrence, was measured for
these states. This technique provides
a means for preparing entangled two-
qubit states for use in quantum infor-
mation protocols. t
Robert W. Boyd ( firstname.lastname@example.org) is with the
department of physics at the University of Ottawa,
in Ontario, Canada, and the Institute of Optics and
department of physics and astronomy at the University of Rochester, N. Y., U.S.A. Miles J. Padgett
is with the department of physics and astronomy,
University of Glasgow, United Kingdom. Stephen
M. Barnett is with the department of physics, University of Strathclyde, Glasgow, United Kingdom.
1. L. Allen et al. Phys. Rev. A 45, 8185 (1992).
2. G. A. Tyler and R. W. Boyd. Opt. Lett. 34, 142 (2009).
3. A. Mair et al. Nature 412, 313 (2001).
4. J. Leach et al. Science 329, 662 (2010).
5. A. K. Jha et al. Phys. Rev. Lett. 104, 010501 (2010).
48 | OPN Optics & Photonics News