Resumen: In this paper, Wielandt's inequality for classical channels is extended to quantum channels. That is, an upper bound to the number of times a channel must be applied, so that it maps any density operator to one with full rank, is found. Using this bound, dichotomy theorems for the zero--error capacity of quantum channels and for the Matrix Product State (MPS) dimension of ground states of frustration-free Hamiltonians are
derived. The obtained inequalities also imply new bounds on the required interaction-range of Hamiltonians with unique MPS ground state.
Resumen: In this letter we show that the field of Operator Space Theory provides a general and powerful mathematical framework for arbitrary Bell inequalities, in particular regarding the scaling of their violation within quantum mechanics. We illustrate the power of this connection by showing that bipartite quantum states with local Hilbert space dimension n can violate a Bell inequality by a factor
of order $\frac{\sqrt{n}}{\log^2n}$ when observables with n possible outcomes are used. Applications to resistance to noise, Hilbert space dimension estimates and communication complexity are given.
Resumen: In this work we show that bipartite quantum states with local Hilbert space dimension n can violate a Bell inequality by a factor of order $\sqrt{n}$ (up to a logarithmic factor) when observables with n possible outcomes are used. A central tool in the analysis is a close relation between this problem and operator space theory and, in particular, the very recent noncommutative $L_p$ embedding
theory. As a consequence of this result, we obtain better Hilbert space dimension witnesses and quantum violations of Bell inequalities with better resistance to noise.
Resumen: We show that two different tensors defining the same translational invariant injective Projected Entangled Pair State (PEPS) in a square lattice must be the same up to a trivial gauge freedom. This allows us to characterize the existence of any local or spatial symmetry in the state. As an application of these results we prove that
a SU(2) invariant PEPS with half-integer spin cannot be injective, which can be seen as a Lieb-Shultz-Mattis theorem in this context. We also give the natural generalization for U(1) symmetry in the spirit of Oshikawa-Yamanaka-Affleck, and show that a PEPS with Wilson loops cannot be injective.
Palabras clave: Teoría cuántica, Física matemática, Quantum Physics, Mathematical Physics
Resumen: Using tools from classical signal processing, we show how to determine the dimensionality of a quantum system as well as the effective size of the environment's memory from observable dynamics in a model-independent way. We discuss the dependence on the number of conserved quantities, the relation to ergodicity and prove a converse showing that a Hilbert space of dimension D+2 is sufficient
to describe every bounded sequence of measurements originating from any D-dimensional linear equations of motion. This is in sharp contrast to classical stochastic processes which are subject to more severe restrictions: a simple spectral analysis shows that the gap between the required dimensionality of a quantum and a classical description of an observed evolution can be arbitrary large.
Palabras clave: Teoría cuántica, Física matemática, Sistemas dinámicos, Quantum Physics, Mathematical Physics, Dynamical Systems
Resumen: We provide a framework for Bell inequalities which is based on multilinear contractions. The
derivation of the inequalities allows for an intuitive geometric depiction and their violation within
quantum mechanics can be seen as a direct consequence of non-vanishing commutators. The approach
is motivated by generalizing recent work
on non-linear inequalities which was based on the
moduli of complex numbers, quaternions and octonions. We extend results on Peres’ conjecture
about the validity of Bell inequalities for quantum states with positive partial transposes. Moreover,
we show the possibility of obtaining unbounded quantum violations albeit we also prove that
quantum mechanics can only violate the derived inequalities if three or more parties are involved.
Palabras clave: Física matemática, Teoría cuántica, Quantum Physics, Mathematical Physics
Resumen: Given a list of n complex numbers, when can it be the spectrum of a quantum channel, i.e., a completely positive trace preserving map? We provide an explicit solution for the n=4 case and show that in general the characterization of the non-zero part of the spectrum can essentially be given in terms of its classical counterpart - the non-zero spectrum of a stochastic matrix. A detailed comparison between the classical and quantum case is given. We discuss
applications of our findings in the analysis of time-series and correlation functions and provide a general characterization of the peripheral spectrum, i.e., the set of eigenvalues of modulus one. We show that while the peripheral eigen-system has the same structure for all Schwarz maps, the constraints imposed on the rest of the spectrum change immediately if one departs from complete positivity.
Palabras clave: Física matemática, Teoría cuántica, Teoría espectral, Quantum Physics, Mathematical Physics, Spectral Theory
Resumen: Se presenta un estudio de las propiedades fisicas y quimicas del medio interestelar en la región central de la via Lactea. Hemos determinado por vez primera la cantidad de gas caliente en las nubes del centro galáctico gracias a las observaciones de lineas rotacionales puras del hidrógeno molecular (H2) llevadas a cabo con el infrared Space observatory (ISO). La columna de densidad de gas caliente es de 1-2 10 22 cm-2 y
en promedio constituye un 30% de la columna de densidad total de gas. La comparación con modelos teóricos indica que el gas podría ser calentado por choques o en regiones de foto-disociación. En dos de las nubes hemos encontrado una razón orto/para de no equilibrio que se interpreta como evidencia de un calentamiento transitorio por efecto de un choque de baja velocidad. Para determinar la estructura del gas caliente a pequeña escala, hemos realizado observaciones de NH3 en la zona sur de SgrB2. Se ha encontrado que la distribución del gas caliente está dominada por burbujas en expansion, probablemente causadas por los vientos de estrellas masivas de tipo Wolf-Rayet. La cantidad de burbujas sugiere la presencia de un cumulo de estrellas masivas. Para profundizar en el estudio de la quimica se ha realizado un estudio comparativo de la emisión de gran escala de SiO y de la linea de Fe a 6.4 Ke V. Ambas emisiones están correlacionadas lo que sugiere que la emisión de Fe 6.4 KeV se origina en las nubes que emiten SiO y que ambas tienen un otigen comun. Tambien se ha estudiado el efecto a largas distacias de los cúmulos del Quintoplete y el Arco. Se ha encontrado que estos cúmulos dominan la ionización del gas y el calentamiento del polvo en una región de mas de 30 pc x 30 pc. Solo se puede explicar el largo alcance de la radiación si el medio es muy inhomogéneo. Una burbuja de polvo caliente existente en esta región coincide con una maximo de emisión de Fe 6.4 keV y probablemente está creada por una explosión de supernova. Por último se discuten las implicaciones de los resultados anteriores en cuanto al origen de la quimica, el calentamiento y la ionización del gas
Editorial: Universidad Complutense de Madrid, Servicio de Publicaciones
Departamento: Fac. de CC. Físicas - Depto. de Astrofísica y CC. de la Atmósfera
ISBN: 978-84-669-1760-5
Notas: Tesis de la Universidad Complutense de Madrid, Facultad de Ciencias Físicas, Departamento de Astrofísica y Ciencias de la Armósfera, leída el 01-02-2002
