Entanglement-enhanced testing of multiple quantum hypotheses

Quantum hypothesis testing has been greatly advanced for the binary discrimination of two states, or two channels. In this setting, we already know that quantum entanglement can be used to enhance the discrimination of two bosonic channels. Here, we remove the restriction of binary hypotheses and show that entangled photons can remarkably boost the discrimination of multiple bosonic channels. More precisely, we formulate a general problem of channel-position finding where the goal is to determine the position of a target channel among many background channels. We prove that, using entangled photons at the input and a generalized form of conditional nulling receiver at the output, we may outperform any classical strategy. Our results can be applied to enhance a range of technological tasks, including the optical readout of sparse classical data, the spectroscopic analysis of a frequency spectrum, and the determination of the direction of a target at fixed range

Excessive factorizations of bipartite multigraphs.

An excessive factorization of a multigraph G is a set F = {F(1), F(2), ... F(r)) of 1-factors of G whose union is E(G) and, subject to this condition, r is minimum. The integer r is called the excessive index of G and denoted by chi'(e)(G). We set chi'(e)(G) = infinity if an excessive factorization does not exist. Analogously, let m be a fixed positive integer. An excessive vertical bar m vertical bar-factorization is a set M = {M(1), M(2) ... M(k)} of matchings of G, all of size m, whose union is E(G) and, subject to this condition, k is minimum. The integer k is denoted by chi'([m])(G) and called the excessive [m]-index of G. Again, we set chi'(vertical bar m vertical bar) (G) = infinity if an excessive [m]-factorization does not exist. In this paper we shall prove that, for bipartite multigraphs, both the parameters chi'(e) and chi'([m]) are computable in polynomial time, and we shall obtain an efficient algorithm for finding an excessive factorization and excessive [m]-factorization, respectively, of any bipartite multigraph

On the Complexity of Computing the Excessive [B]-Index of a Graph

Let B be a positive integer and let G be a simple graph. An excessive [B]-factorization of G is a minimum set of matchings, each of size B, whose union is E(G). The number of matchings in an excessive [B]-factorization of G (or ∞ if an excessive [B]-factorization does not exist) is a graph parameter called the excessive [B]-index of G and denoted by χ[B]′(G). In this article we prove that, for any fixed value of B, the parameter χ[B]′(G) can be computed in polynomial time in the size of the graph G. This solves a problem posed by one of the authors at the 21st British Combinatorial Conference. © 2015 Wiley Periodicals, Inc

A quantum vocal theory of sound

Concepts and formalism from acoustics are often used to exemplify quantum mechanics. Conversely, quantum mechanics could be used to achieve a new perspective on acoustics, as shown by Gabor studies. Here, we focus in particular on the study of human voice, considered as a probe to investigate the world of sounds. We present a theoretical framework that is based on observables of vocal production, and on some measurement apparati that can be used both for analysis and synthesis. In analogy to the description of spin states of a particle, the quantum-mechanical formalism is used to describe the relations between the fundamental states associated with phonetic labels such as phonation, turbulence, and supraglottal myoelastic vibrations. The intermingling of these states, and their temporal evolution, can still be interpreted in the Fourier/Gabor plane, and effective extractors can be implemented. The bases for a quantum vocal theory of sound, with implications in sound analysis and design, are presented