15 research outputs found
Accessing the purity of a single photon by the width of the Hong-Ou-Mandel interference
We demonstrate a method to determine the spectral purity of single photons.
The technique is based on the Hong-Ou-Mandel (HOM) interference between a
single photon state and a suitably prepared coherent field. We show that the
temporal width of the HOM dip is not only related to reciprocal of the spectral
width but also to the underlying quantum coherence. Therefore, by measuring the
width of both the HOM dip and the spectrum one can directly quantify the degree
of spectral purity. The distinct advantage of our proposal is that it obviates
the need for perfect mode matching, since it does not rely on the visibility of
the interference. Our method is particularly useful for characterizing the
purity of heralded single photon states.Comment: Extended version, 16 pages, 9 figure
Noise reduction in 3D noncollinear parametric amplifier
We analytically find an approximate Bloch-Messiah reduction of a noncollinear
parametric amplifier pumped with a focused monochromatic beam. We consider type
I phase matching. The results are obtained using a perturbative expansion and
scaled to a high gain regime. They allow a straightforward maximization of the
signal gain and minimization of the parametric fluorescence noise. We find the
fundamental mode of the amplifier, which is an elliptic Gaussian defining the
optimal seed beam shape. We conclude that the output of the amplifier should be
stripped of higher order modes, which are approximately Hermite-Gaussian beams.
Alternatively, the pump waist can be adjusted such that the amount of noise
produced in the higher order modes is minimized.Comment: 18 pages, 9 figures, accepted to Applied Physics
Geometric Entanglement of Symmetric States and the Majorana Representation
Permutation-symmetric quantum states appear in a variety of physical
situations, and they have been proposed for quantum information tasks. This
article builds upon the results of [New J. Phys. 12, 073025 (2010)], where the
maximally entangled symmetric states of up to twelve qubits were explored, and
their amount of geometric entanglement determined by numeric and analytic
means. For this the Majorana representation, a generalization of the Bloch
sphere representation, can be employed to represent symmetric n qubit states by
n points on the surface of a unit sphere. Symmetries of this point distribution
simplify the determination of the entanglement, and enable the study of quantum
states in novel ways. Here it is shown that the duality relationship of
Platonic solids has a counterpart in the Majorana representation, and that in
general maximally entangled symmetric states neither correspond to anticoherent
spin states nor to spherical designs. The usability of symmetric states as
resources for measurement-based quantum computing is also discussed.Comment: 10 pages, 8 figures; submitted to Lecture Notes in Computer Science
(LNCS
The maximally entangled symmetric state in terms of the geometric measure
The geometric measure of entanglement is investigated for permutation
symmetric pure states of multipartite qubit systems, in particular the question
of maximum entanglement. This is done with the help of the Majorana
representation, which maps an n qubit symmetric state to n points on the unit
sphere. It is shown how symmetries of the point distribution can be exploited
to simplify the calculation of entanglement and also help find the maximally
entangled symmetric state. Using a combination of analytical and numerical
results, the most entangled symmetric states for up to 12 qubits are explored
and discussed. The optimization problem on the sphere presented here is then
compared with two classical optimization problems on the S^2 sphere, namely
Toth's problem and Thomson's problem, and it is observed that, in general, they
are different problems.Comment: 18 pages, 15 figures, small corrections and additions to contents and
reference
Effects of imperfect noise correlations on decoherence-free subsystems: SU(2) diffusion model
We present a model of an N-qubit channel where consecutive qubits experience
correlated random rotations. Our model is an extension to the standard
decoherence-free subsystems approach (DFS) which assumes that all the qubits
experience the same disturbance. The variation of rotations acting on
consecutive qubits is modeled as diffusion on the SU(2) group. The model may be
applied to spins traveling in a varying magnetic field, or to photons passing
through a fiber whose birefringence fluctuates over the time separation between
photons. We derive an explicit formula describing the action of the channel on
an arbitrary N-qubit state. For N=3 we investigate the effects of diffusion on
both classical and quantum capacity of the channel. We observe that
nonorthogonal states are necessary to achieve the optimal classical capacity.
Furthermore we find the threshold for the diffusion parameter above which
coherent information of the channel vanishes.Comment: 11 pages, 6 figures, improved clarity, more discussion, many new
references and the title change