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 $N$-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

Exact Spectral Analysis of Single-h and Multi-h CPM Signals through PAM decomposition and Matrix Series Evaluation

In this paper we address the problem of closed-form spectral evaluation of CPM. We show that the multi-h CPM signal can be conveniently generated by a PTI SM. The output is governed by a Markov chain with the unusual peculiarity of being cyclostationary and reducible; this holds also in the single-h context. Judicious reinterpretation of the result leads to a formalization through a stationary and irreducible Markov chain, whose spectral evaluation is known in closed-form from the literature. Two are the major outcomes of this paper. First, unlike the literature, we obtain a PSD in true closed-form. Second, we give novel insights into the CPM format.Comment: 31 pages, 10 figure

Efficient Optimal Minimum Error Discrimination of Symmetric Quantum States

This paper deals with the quantum optimal discrimination among mixed quantum states enjoying geometrical uniform symmetry with respect to a reference density operator $\rho_0$. It is well-known that the minimal error probability is given by the positive operator-valued measure (POVM) obtained as a solution of a convex optimization problem, namely a set of operators satisfying geometrical symmetry, with respect to a reference operator $\Pi_0$, and maximizing $\textrm{Tr}(\rho_0 \Pi_0)$. In this paper, by resolving the dual problem, we show that the same result is obtained by minimizing the trace of a semidefinite positive operator $X$ commuting with the symmetry operator and such that $X >= \rho_0$. The new formulation gives a deeper insight into the optimization problem and allows to obtain closed-form analytical solutions, as shown by a simple but not trivial explanatory example. Besides the theoretical interest, the result leads to semidefinite programming solutions of reduced complexity, allowing to extend the numerical performance evaluation to quantum communication systems modeled in Hilbert spaces of large dimension.Comment: 5 pages, 1 Table, no figure

Segnali e Sistemi

Il testo si propone di fornire una visione organica delle problematiche fondamentali connesse ai segnali e alla loro elaborazione attraverso i sistemi e si rivolge agli studenti di ingegneria dell’informazione, delle telecomunicazioni, dell’automazione, elettronica, informatica e biomedica, corsi di studio in cui è basilare l’insegnamento della Teoria dei segnali e della Teoria dei sistemi. L’utilizzo di frequenti esempi svolti e la presentazione di esercizi di difficoltà variabile rendono il libro un ottimo strumento didattico, rigoroso ma sufficientemente agevole per i corsi delle lauree triennali

Compression of Pure and Mixed States in Quantum Detection

Quantum detection in an N-dimensional Hilbert space H involves quantum states and corresponding measurement operators which span an r-dimensional subspace U of H, with r<=N. Quantum detection could be restricted to this subspace, but the detection operations performed in U are still redundant, since the kets have N components. By applying the singular-value decomposition to the state matrix, it is possible to perform a compression from the subspace U onto a "compressed" space $overline{U}$, where the redundancy is removed and kets are represented by r components. The quantum detection can be perfectly reformulated in the "compressed" space, without loss of information, with a greatly reduced complexity. The compression is particularly attractive when r<<N, as shown with an example of application to quantum optical communications