arXiv subjects

Julio-José Moyano-Fernández

Publications and source records attributed to Julio-José Moyano-Fernández.

2 recordsLinked to original sources

arXiv2023

No-go theorems for photon state transformations in quantum linear optics

We give a necessary condition for photon state transformations in linear optical setups preserving the total number of photons. From an analysis of the algebra describing the quantum evolution, we find a conserved quantity that appears in all allowed optical transformations. We comment some examples and numerical applications, with example code, and give three general no-go results. These include (i) the impossibility of deterministic transformations which redistribute the photons from one to two different modes, (ii) a proof that it is impossible to generate a perfect Bell state in heralded schemes with a separable input for any number of ancillary photons and modes and a fixed herald and (iii) a restriction for the conversion between different types of entanglement (converting GHZ to W states).

quant-ph↗

arXiv2023

The intrinsic topological nature of the Poincaré series of a plane curve singularity

In this paper we provide some factorization theorems of the Poincaré series $P_C$ of a plane curve singularity $C$ depending on some key values of the semigroup of values of $C$. These results yield an iterative computation of $P_C$ in purely algebraic terms from the dual resolution graph of $C$. On the other hand, Campillo, Delgado and Gusein-Zade showed in 2003 the equality between $P_C$ and the Alexander polynomial $Δ_L$ of the corresponding link $L$. Our procedure supplies a new proof of this coincidence. More concretely, we show that our algebraic construction can be translated to the iterated toric structure of the link $L$. Additionally we show that the semigroup algebra can be defined from the fundamental group of the link exterior in the irreducible case. This gives in particular a conceptual reason for the coincidence of $P_C$ and $Δ_L$.

math.AG↗