Institut Universitari de Matemàtiques i Aplicacions de Castelló (IMAC)http://hdl.handle.net/10234/1733642024-03-29T13:00:35Z2024-03-29T13:00:35ZMDS, Hermitian almost MDS, and Gilbert–Varshamov quantum codes from generalized monomial-Cartesian codesBarbero Lucas, BeatrizHernando, FernandoMartín-Cruz, HelenaMcGuire, Garyhttp://hdl.handle.net/10234/2061992024-03-16T02:07:02Z2024-03-01T00:00:00ZMDS, Hermitian almost MDS, and Gilbert–Varshamov quantum codes from generalized monomial-Cartesian codes
Barbero Lucas, Beatriz; Hernando, Fernando; Martín-Cruz, Helena; McGuire, Gary
We construct new stabilizer quantum error-correcting codes from generalized monomial-Cartesian codes. Our construction uses an explicitly defined twist vector, and we present formulas for the minimum distance and dimension. Generalized monomial-Cartesian codes arise from polynomials in m variables. When
our codes are MDS, and when and our lower bound for the minimum distance is 3, the codes are at least Hermitian almost MDS. For an infinite family of parameters, when we prove that our codes beat the Gilbert–Varshamov bound. We also present many examples of our codes that are better than any known code in the literature.
2024-03-01T00:00:00ZA Geometrical Study about the Biparametric Family of Anomalies in the Elliptic Two-Body Problem with Extensions to Other FamiliesLópez Ortí, José AntonioMarco Castillo, Francisco JoséMartínez Usó, María Joséhttp://hdl.handle.net/10234/2060932024-03-02T02:04:43Z2024-02-01T00:00:00ZA Geometrical Study about the Biparametric Family of Anomalies in the Elliptic Two-Body Problem with Extensions to Other Families
López Ortí, José Antonio; Marco Castillo, Francisco José; Martínez Usó, María José
In the present paper, we efficiently solve the two-body problem for extreme cases such as those with high eccentricities. The use of numerical methods, with the usual variables, cannot maintain the perihelion passage accurately. In previous articles, we have verified that this problem is treated more adequately through temporal reparametrizations related to the mean anomaly through the partition function. The biparametric family of anomalies, with an appropriate partition function, allows a systematic study of these transformations. In the present work, we consider the elliptical orbit as a meridian section of the ellipsoid of revolution, and the partition function depends on two variables raised to specific parameters. One of the variables is the mean radius of the ellipsoid at the secondary, and the other is the distance to the primary. One parameter regulates the concentration of points in the apoapsis region, and the other produces a symmetrical displacement between the polar and equatorial regions. The three most used geodesy latitude variables are also studied, resulting in one not belonging to the biparametric family. However, it is in the one introduced now, which implies an extension of the biparametric method. The results obtained using the method presented here now allow a causal interpretation of the operation of numerous reparametrizations used in the study of orbital motion.
2024-02-01T00:00:00ZArens regularity of ideals of the group algebra of a compact Abelian groupEsmailvandi, RezaFilali, MahmoudGalindo, Jorgehttp://hdl.handle.net/10234/2058802024-02-16T02:05:04Z2023-10-27T00:00:00ZArens regularity of ideals of the group algebra of a compact Abelian group
Esmailvandi, Reza; Filali, Mahmoud; Galindo, Jorge
Let G be a compact Abelian group and E a subset of the group Gˆ of continuous characters of G . We study Arens regularity-related properties of the ideals L1E(G) of L1(G) that are made of functions whose Fourier transform is supported on E⊆Gˆ . Arens regularity of L1E(G) , the centre of L1E(G)∗∗ and the size of L1E(G)∗/WAP(L1E(G)) are studied. We establish general conditions for the regularity of L1E(G) and deduce from them that L1E(G) is not strongly Arens irregular if E is a small-2 set (i.e. μ∗μ∈L1(G) for every μ∈M1E(G) ), which is not a Λ(1) -set, and it is extremely non-Arens regular if E is not a small-2 set. We deduce also that L1E(G) is not Arens regular when Gˆ∖E is a Lust-Piquard set.
2023-10-27T00:00:00ZNo-go theorems for photon state transformations in quantum linear opticsV. Parellada, PabloGimeno i Garcia, VicentMoyano-Fernández, Julio JoséGarcia-Escartin, Juan Carloshttp://hdl.handle.net/10234/2058512024-02-14T04:02:36Z2023-01-01T00:00:00ZNo-go theorems for photon state transformations in quantum linear optics
V. Parellada, Pablo; Gimeno i Garcia, Vicent; Moyano-Fernández, Julio José; Garcia-Escartin, Juan Carlos
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 give 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 with an arbitrary ancilla from the Fock basis and (iii) a restriction for the conversion between different types of entanglement (converting GHZ to W states). These tools and results can help in the design of experiments for optical quantum state generation.
2023-01-01T00:00:00Z