6 research outputs found
Gaussian states and geometrically uniform symmetry
Quantum Gaussian states can be considered as the majority of the practical
quantum states used in quantum communications and more generally in quantum
information. Here we consider their properties in relation with the
geometrically uniform symmetry, a property of quantum states that greatly
simplifies the derivation of the optimal decision by means of the square root
measurements. In a general framework of the -mode Gaussian states we show
the general properties of this symmetry and the application of the optimal
quantum measurements. An application example is presented, to quantum
communication systems employing pulse position modulation. We prove that the
geometrically uniform symmetry can be applied to the general class of multimode
Gaussian states
Theory of Quantum Pulse Position Modulation and Related Numerical Problems
The paper deals with quantum pulse position modulation (PPM), both in the
absence (pure states) and in the presence (mixed states) of thermal noise,
using the Glauber representation of coherent laser radiation. The objective is
to find optimal (or suboptimal) measurement operators and to evaluate the
corresponding error probability. For PPM, the correct formulation of quantum
states is given by the tensorial product of m identical Hilbert spaces, where m
is the PPM order. The presence of mixed states, due to thermal noise, generates
an optimization problem involving matrices of huge dimensions, which already
for 4-PPM, are of the order of ten thousand. To overcome this computational
complexity, the currently available methods of quantum detection, which are
based on explicit results, convex linear programming and square root
measurement, are compared to find the computationally less expensive one. In
this paper a fundamental role is played by the geometrically uniform symmetry
of the quantum PPM format. The evaluation of error probability confirms the
vast superiority of the quantum detection over its classical counterpart.Comment: 10 pages, 7 figures, accepted for publication in IEEE Trans. on
Communication