We present an experimental scheme to calculate the inner product of two arbitrary scalar optical fields. The scheme is based on using an interferometer to generate superpositions of the optical fields with a relative phase difference between the two fields. The intensity observed permits the calculation of the inner product using numerical integration. The experimental results obtained for the inner product of a few common optical fields are presented along with comparison with simulations.
Combining the multiple degrees of freedom of photons has become topical in quantum communication and information
processes. This provides advantages such as increasing the amount of information that is be packed into
a photon or probing the wave-particle nature of light through path-polarisation entanglement. Here we present
two experiments that show the advantages of using hybrid entanglement between orbital angular moment (OAM)
and polarisation. Firstly, we present results where high dimensional quantum key distribution is demonstrated
with spatial modes that have non-separable polarisation-OAM DOF called vector modes. Secondly, we show
that through OAM-polarisation entanglement, the traditional which-way experiment can be performed without
using the traditional physical path interference approach.
High-dimensional encoding using higher degrees of freedom has become topical in quantum communication protocols. When taking advantage of entanglement correlations, the state space can be made even larger. Here, we exploit the entanglement between two dimensional space and polarization qubits, to realize a four-dimensional quantum key distribution protocol. This is achieved by using entangled states as a basis, analogous to the Bell basis, rather than typically encoding information on individual qubits. The encoding and decoding in the required complementary bases is achieved by manipulating the Pancharatnam-Berry phase with a single optical element: a q-plate. Our scheme shows a transmission fidelity of 0.98 and secret key rate of 0.9 bits per photon. While the use of only static elements is preferable, we show that the low secret key rate is a consequence of the filter based detection of the modes, rather than our choice of encoding modes.
We study the realization of quantum algorithms using classical optical elements and a coherent laser source. The encoded qubits are present in form of path qubits, polarization and orbital angular momentum. In particular, we propose an implementation for the Deutsch Algorithm in a Sagnac interferometer and the Deutsch-Jozsa Algorithm in a ring cavity.
Vector beams are defined by spatially inhomogeneous states of polarization, that is, the spatial distribution and polarization state of the beam are non-separable. These beams have found interest in a variety of optical fields such as microscopy, interferometry and optical tweezing. It is therefore important to determine the degree to which these beams are non-separable or to determine the vectorness of such beams. We show that the nonseparability of vector beams is analogous to that of entangled quantum states and as such, we use traditionally quantum techniques such as a Bell inequality, to determine the vectorness of our generated vector vortex beams.
Quantum ghost imaging using entangled photon pairs has become an interesting field of investigation as it illustrates the quantum correlation between the photon pairs. We introduce a new technique using spatial light modulators encoded with appropriate digital holograms to recover not only the amplitude, but also the phase of the digital object. Down-converted photon pairs are entangled in the orbital angular momentum basis, which are typically measured using a spiral phase hologram. Thus by encoding a spiral annular slit hologram into the idler arm, and varying it radially we can simultaneously recover the phase and amplitude of the field in question. We show that there is a good correlation between the encoded field function and the reconstructed images.
A quantum walk is the quantum analog of the classical random walks. Despite their simple structure they form a universal platform to implement any algorithm of quantum computation. However, it is very hard to realize quantum walks with a sufficient number of iterations in quantum systems due to their sensitivity to environmental influences and subsequent loss of coherence. Here we present a scalable implementation scheme for one-dimensional quantum walks for arbitrary number of steps using the orbital angular momentum modes of classical light beams. Furthermore, we show that using the same setup with a minor adjustment we can also realize electric quantum walks.
The use of Higher-dimensional entangled systems have been proved to signi cantly improve many quantum in- formation tasks. For instance, it has been shown that the use of higher-dimensional entangled systems provides a higher information capacity and an increased security in quantum cryptography. The orbital angular momentum (OAM) state of light is a potential candidate for the implementation of higher-dimensional entangled systems and has thus been considered for free-space quantum communication. However, atmospheric turbulence severely affects the OAM state of photons. In this work, we study the evolution of the OAM entanglement between two qutrits (three-dimensional quantum systems) in atmospheric turbulence both numerically and experimentally. The qutrits are photons entangled in their orbital angular momentum (OAM) states generated by spontaneous parametric down conversion. We propagate one of the photons through turbulence while leaving the other undis- turbed. To compare our results with previous work, we simulate the turbulent atmosphere with a single phase screen based on the Kolmogorov theory of turbulence and we use the tangle to quantify the amount of entangle- ment between the two qutrits. We compare our results with the evolution of OAM entanglement between two qubits.
We encode mutually unbiased bases (MUBs) using the higher-dimensional orbital angular momentum (OAM) degree of freedom and illustrate how these states are encoded on a phase-only spatial light modulator (SLM). We perform (d - 1)- mutual unbiased measurements in both a classical prepare and measure scheme and on entangled photon pairs for dimensions ranging from d = 2 to 5. The calculated average error rate, mutual information and secret key rate show an increase in information capacity as well as higher generation rates as the dimension increases.
The OAM or spiral bandwidth indicates the dimensionality of an entangled state that is produced by the spontaneous parametric down-conversion process. Normally this bandwidth is determined by modulating the signal and idler beams with helical phase functions with opposite azimuthal indices on the spatial light modulators in the signal and idler beams, respectively. We added an additional binary Bessel function to the helical phase, thereby specifying the radial dependence of the mode to be Bessel-Gaussian (BG) modes. This comes down to a post selection process, which is known to have the ability to increase entanglement. The result is a modification to the shape of the OAM spectrum, which leads to a higher dimensionality for the quantum states. We perform analytical calculations to show that the bandwidths obtained by measuring in the BG modal basis are larger than those for the LG modes. These theoretical predictions are confirmed by experimental measurements of the bandwidths for LG modes and for BG modes with different transverse scales.
The orbital angular momentum (OAM) state of light can potentially be used to implement higher dimensional
entangled systems for quantum communication. Unfortunately, optical fibers in use today support only modes
with zero OAM values. Free-space quantum communication is an alternative to traditional way of communicating
through optical fibers. However the refractive index fluctuation of the atmosphere gives rise to random phase
aberrations on a propagating optical beam. To transmit quantum information successfully through a free-space
optical channel, one needs to understand how atmospheric turbulence influences quantum entanglement. Here,
we present a numerical study of the evolution of quantum entanglement between a pair of qubits. The qubits
consist of photons entangled in the OAM basis. The photons propagate in a turbulent atmosphere modeled by a
series of consecutive phase screens based on the Kolmogorov theory of turbulence. Maximally entangled initial
states are considered, and the concurrence is used as a measure of entanglement. We show how the evolution
of entanglement is influenced by various parameters such as the beam waist, the strength of the turbulence and
the wavelength of the beam. We restricted our analysis to the OAM values l = ±1 and we compared our results
to previous work.