100 research outputs found
Finite-key security analysis for multilevel quantum key distribution
We present a detailed security analysis of a d-dimensional quantum key
distribution protocol based on two and three mutually unbiased bases (MUBs)
both in an asymptotic and finite key length scenario. The finite secret key
rates are calculated as a function of the length of the sifted key by (i)
generalizing the uncertainly relation-based insight from BB84 to any d-level
2-MUB QKD protocol and (ii) by adopting recent advances in the second-order
asymptotics for finite block length quantum coding (for both d-level 2- and
3-MUB QKD protocols). Since the finite and asymptotic secret key rates increase
with d and the number of MUBs (together with the tolerable threshold) such QKD
schemes could in principle offer an important advantage over BB84. We discuss
the possibility of an experimental realization of the 3-MUB QKD protocol with
the orbital angular momentum degrees of freedom of photons.Comment: v4: close to the published versio
Twisted Photons: New Quantum Perspectives in High Dimensions
Quantum information science and quantum information technology have seen a
virtual explosion world-wide. It is all based on the observation that
fundamental quantum phenomena on the individual particle or system-level lead
to completely novel ways of encoding, processing and transmitting information.
Quantum mechanics, a child of the first third of the 20th century, has found
numerous realizations and technical applications, much more than was thought at
the beginning. Decades later, it became possible to do experiments with
individual quantum particles and quantum systems. This was due to technological
progress, and for light in particular, the development of the laser. Hitherto,
nearly all experiments and also nearly all realizations in the fields have been
performed with qubits, which are two-level quantum systems. We suggest that
this limitation is again mainly a technological one, because it is very
difficult to create, manipulate and measure more complex quantum systems. Here,
we provide a specific overview of some recent developments with
higher-dimensional quantum systems. We mainly focus on Orbital Angular Momentum
(OAM) states of photons and possible applications in quantum information
protocols. Such states form discrete higher-dimensional quantum systems, also
called qudits. Specifically, we will first address the question what kind of
new fundamental properties exist and the quantum information applications which
are opened up by such novel systems. Then we give an overview of recent
developments in the field by discussing several notable experiments over the
past 2-3 years. Finally, we conclude with several important open questions
which will be interesting for investigations in the future.Comment: 15 pages, 7 figure
Generation of Caustics and Spatial Rogue Waves from Nonlinear Instability
Caustics are natural phenomena in which nature concentrates the energy of
waves. Although, they are known mostly in optics, caustics are intrinsic to all
wave phenomena. For example, studies show that fluctuations in the profile of
an ocean floor can generate random caustics and focus the energy of tsunami
waves. Caustics share many similarities to rogue waves, as they both exhibit
heavy-tailed distribution, i.e. an overpopulation of large events. Linear
Schr\"odinger-type equations are usually used to explain the wave dynamics of
caustics. However, in that the wave amplitude increases dramatically in
caustics, nonlinearity is inevitable in many systems. In this Letter, we
investigate the effect of nonlinearity on the formation of optical caustics. We
show experimentally that, in contrast to linear systems, even small phase
fluctuations can generate strong caustics upon nonlinear propagation. We
simulated our experiment based on the nonlinear Schr\"odinger equation (NLSE)
with Kerr-type nonlinearity, which describes the wave dynamics not only in
optics, but also in some other physical systems such as oceans. Therefore, our
results may also aid our understanding of ocean phenomena.Comment: 5 pages, 4 figure
High-dimensional two-photon interference effects in spatial modes
Two-photon interference is a fundamental quantum optics effect with numerous
applications in quantum information science. Here, we study two-photon
interference in multiple transverse-spatial modes along a single beam-path.
Besides implementing the analogue of the Hong-Ou-Mandel interference using a
two-dimensional spatial-mode splitter, we extend the scheme to observe
coalescence and anti-coalescence in different three and four-dimensional
spatial-mode multiports. The operation within spatial modes, along a single
beam-path, lifts the requirement for interferometric stability and opens up new
pathways of implementing linear optical networks for complex quantum
information tasks.Comment: 14 pages, 12 figure
Controlling induced coherence for quantum imaging
Induced coherence in parametric down-conversion between two coherently pumped
nonlinear crystals that share a common idler mode can be used as an imaging
technique. Based on the interference between the two signal modes of the
crystals, an image can be reconstructed. By obtaining an expression for the
interference pattern that is valid in both the low- and the high-gain regimes
of parametric down-conversion, we show how the coherence of the light emitted
by the two crystals can be controlled. With our comprehensive analysis we
provide deeper insight into recent discussions about the application of induced
coherence to imaging in different regimes. Moreover, we propose a scheme for
optimizing the visibility of the interference pattern so that it directly
corresponds to the degree of coherence of the light generated in the two
crystals. We find that this scheme leads in the high-gain regime to a
visibility arbitrarily close to unity.Comment: 9 pages, 4 figure
Automated Search for new Quantum Experiments
Quantum mechanics predicts a number of at first sight counterintuitive
phenomena. It is therefore a question whether our intuition is the best way to
find new experiments. Here we report the development of the computer algorithm
Melvin which is able to find new experimental implementations for the creation
and manipulation of complex quantum states. And indeed, the discovered
experiments extensively use unfamiliar and asymmetric techniques which are
challenging to understand intuitively. The results range from the first
implementation of a high-dimensional Greenberger-Horne-Zeilinger (GHZ) state,
to a vast variety of experiments for asymmetrically entangled quantum states --
a feature that can only exist when both the number of involved parties and
dimensions is larger than 2. Additionally, new types of high-dimensional
transformations are found that perform cyclic operations. Melvin autonomously
learns from solutions for simpler systems, which significantly speeds up the
discovery rate of more complex experiments. The ability to automate the design
of a quantum experiment can be applied to many quantum systems and allows the
physical realization of quantum states previously thought of only on paper.Comment: 5+8 pages, 4+1 figures (main text + supplementary
Cyclic transformation of orbital angular momentum modes
The spatial modes of photons are one realization of a QuDit, a quantum system
that is described in a D-dimensional Hilbert space. In order to perform quantum
information tasks with QuDits, a general class of D-dimensional unitary
transformations is needed. Among these, cyclic transformations are an important
special case required in many high-dimensional quantum communication protocols.
In this paper, we experimentally demonstrate a cyclic transformation in the
high-dimensional space of photonic orbital angular momentum (OAM). Using simple
linear optical components, we show a successful four-fold cyclic transformation
of OAM modes. Interestingly, our experimental setup was found by a computer
algorithm. In addition to the four-cyclic transformation, the algorithm also
found extensions to higher-dimensional cycles in a hybrid space of OAM and
polarization. Besides being useful for quantum cryptography with QuDits, cyclic
transformations are key for the experimental production of high-dimensional
maximally entangled Bell-states.Comment: 18 pages, 6 figure
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