Locality Estimates for Complex Time Evolution in 1D.

It is a generalized belief that there are no thermal phase transitions in short range 1D quantum systems. However, the only known case for which this is rigorously proven is for the particular case of finite range translationally invariant interactions. The proof was obtained by Araki in his seminal paper of 1969 as a consequence of pioneering locality estimates for the time-evolution operator that allowed him to prove its analyticity on the whole complex plane, when applied to a local observable. However, as for now there is no mathematical proof of the absence of 1D thermal phase transitions if one allows exponential tails in the interactions. In this work we extend Araki's result to include exponential (or faster) tails. Our main result is the analyticity of the time-evolution operator applied on a local observable on a suitable strip around the real line. As a consequence we obtain that thermal states in 1D exhibit exponential decay of correlations above a threshold temperature that decays to zero with the exponent of the interaction decay, recovering Araki's result as a particular case. Our result however still leaves open the possibility of 1D thermal short range phase transitions. We conclude with an application of our result to the spectral gap problem for Projected Entangled Pair States (PEPS) on 2D lattices, via the holographic duality due to Cirac et al.

Rapid Thermalization of Spin Chain Commuting Hamiltonians.

We prove that spin chains weakly coupled to a large heat bath thermalize rapidly at any temperature for finite-range, translation-invariant commuting Hamiltonians, reaching equilibrium in a time which scales logarithmically with the system size. This generalizes to the quantum regime a seminal result of Holley and Stroock from 1989 for classical spin chains and represents an exponential improvement over previous bounds based on the nonclosure of the spectral gap. We discuss the implications in the context of dissipative phase transitions and in the study of symmetry protected topological phases.

Resource Quantification for the No-Programing Theorem.

The no-programing theorem prohibits the existence of a universal programmable quantum processor. This statement has several implications in relation to quantum computation but also to other tasks of quantum information processing, making this construction a central notion in this context. Nonetheless, it is well known that, even when the strict model is not implementable, it is possible to conceive of it in an approximate sense. Unfortunately, the minimal resources necessary for this aim are still not completely understood. Here, we investigate quantitative statements of the theorem, improving exponentially previous bounds on the resources required by such a hypothetical machine. The proofs exploit a new connection between quantum channels and embeddings between Banach spaces which allows us to use classical tools from geometric Banach space theory in a clean and simple way.

Memory effects can make the transmission capability of a communication channel uncomputable.

Most communication channels are subjected to noise. One of the goals of information theory is to add redundancy in the transmission of information so that the information is transmitted reliably and the amount of information transmitted through the channel is as large as possible. The maximum rate at which reliable transmission is possible is called the capacity. If the channel does not keep memory of its past, the capacity is given by a simple optimization problem and can be efficiently computed. The situation of channels with memory is less clear. Here we show that for channels with memory the capacity cannot be computed to within precision 1/5. Our result holds even if we consider one of the simplest families of such channels-information-stable finite state machine channels-restrict the input and output of the channel to 4 and 1 bit respectively and allow 6 bits of memory.

Size-driven quantum phase transitions.

Can the properties of the thermodynamic limit of a many-body quantum system be extrapolated by analyzing a sequence of finite-size cases? We present models for which such an approach gives completely misleading results: translationally invariant, local Hamiltonians on a square lattice with open boundary conditions and constant spectral gap, which have a classical product ground state for all system sizes smaller than a particular threshold size, but a ground state with topological degeneracy for all system sizes larger than this threshold. Starting from a minimal case with spins of dimension 6 and threshold lattice size [Formula: see text], we show that the latter grows faster than any computable function with increasing local spin dimension. The resulting effect may be viewed as a unique type of quantum phase transition that is driven by the size of the system rather than by an external field or coupling strength. We prove that the construction is thermally robust, showing that these effects are in principle accessible to experimental observation.

Undecidability of the spectral gap.

The spectral gap--the energy difference between the ground state and first excited state of a system--is central to quantum many-body physics. Many challenging open problems, such as the Haldane conjecture, the question of the existence of gapped topological spin liquid phases, and the Yang-Mills gap conjecture, concern spectral gaps. These and other problems are particular cases of the general spectral gap problem: given the Hamiltonian of a quantum many-body system, is it gapped or gapless? Here we prove that this is an undecidable problem. Specifically, we construct families of quantum spin systems on a two-dimensional lattice with translationally invariant, nearest-neighbour interactions, for which the spectral gap problem is undecidable. This result extends to undecidability of other low-energy properties, such as the existence of algebraically decaying ground-state correlations. The proof combines Hamiltonian complexity techniques with aperiodic tilings, to construct a Hamiltonian whose ground state encodes the evolution of a quantum phase-estimation algorithm followed by a universal Turing machine. The spectral gap depends on the outcome of the corresponding 'halting problem'. Our result implies that there exists no algorithm to determine whether an arbitrary model is gapped or gapless, and that there exist models for which the presence or absence of a spectral gap is independent of the axioms of mathematics.

Unbounded number of channel uses may be required to detect quantum capacity.

Transmitting data reliably over noisy communication channels is one of the most important applications of information theory, and is well understood for channels modelled by classical physics. However, when quantum effects are involved, we do not know how to compute channel capacities. This is because the formula for the quantum capacity involves maximizing the coherent information over an unbounded number of channel uses. In fact, entanglement across channel uses can even increase the coherent information from zero to non-zero. Here we study the number of channel uses necessary to detect positive coherent information. In all previous known examples, two channel uses already sufficed. It might be that only a finite number of channel uses is always sufficient. We show that this is not the case: for any number of uses, there are channels for which the coherent information is zero, but which nonetheless have capacity.

Topological order in the projected entangled-pair states formalism: transfer operator and boundary Hamiltonians.

We study the structure of topological phases and their boundaries in the projected entangled-pair states (PEPS) formalism. We show how topological order in a system can be identified from the structure of the PEPS transfer operator and subsequently use these findings to analyze the structure of the boundary Hamiltonian, acting on the bond variables, which reflects the entanglement properties of the system. We find that in a topological phase, the boundary Hamiltonian consists of two parts: A universal nonlocal part which encodes the nature of the topological phase and a nonuniversal part which is local and inherits the symmetries of the topological model, which helps to infer the structure of the boundary Hamiltonian and thus possibly of the physical edge modes.

Existence of an information unit as a postulate of quantum theory.

Does information play a significant role in the foundations of physics? Information is the abstraction that allows us to refer to the states of systems when we choose to ignore the systems themselves. This is only possible in very particular frameworks, like in classical or quantum theory, or more generally, whenever there exists an information unit such that the state of any system can be reversibly encoded in a sufficient number of such units. In this work, we show how the abstract formalism of quantum theory can be deduced solely from the existence of an information unit with suitable properties, together with two further natural assumptions: the continuity and reversibility of dynamics, and the possibility of characterizing the state of a composite system by local measurements. This constitutes a set of postulates for quantum theory with a simple and direct physical meaning, like the ones of special relativity or thermodynamics, and it articulates a strong connection between physics and information.

Quantum steering and spacelike separation.

In nonrelativistic quantum mechanics, measurements performed by separate observers are modeled via tensor products. In algebraic quantum field theory, though, local observables corresponding to spacelike separated parties are just required to commute. The problem of determining whether these two definitions of separation lead to the same set of bipartite correlations is known in nonlocality as Tsirelson's problem. In this article, we prove that the analog of Tsirelson's problem in steering scenarios is false. That is, there exists a steering inequality that can or cannot be violated depending on how we define spacelike separation at the operator level.

Order parameter for symmetry-protected phases in one dimension.

We introduce an order parameter for symmetry-protected phases in one dimension which allows us to directly identify those phases. The order parameter consists of stringlike operators and swaps, but differs from conventional string order operators in that it only depends on the symmetry but not on the state. We verify our framework through numerical simulations for the SO(3) invariant spin-1 bilinear-biquadratic model which exhibits a dimerized and a Haldane phase, and find that the order parameter not only works very well for the dimerized and the Haldane phase, but it also returns a distinct signature for gapless phases. Finally, we discuss possible ways to measure the order parameter in experiments with cold atoms.

Gapless Hamiltonians for the toric code using the projected entangled pair state formalism.

We study Hamiltonians which have Kitaev's toric code as a ground state, and show how to construct a Hamiltonian which shares the ground space of the toric code, but which has gapless excitations with a continuous spectrum in the thermodynamic limit. Our construction is based on the framework of projected entangled pair states, and can be applied to a large class of two-dimensional systems to obtain gapless "uncle Hamiltonians."

Assessing quantum dimensionality from observable dynamics.

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.

Measurements incompatible in quantum theory cannot be measured jointly in any other no-signaling theory.

It is well known that jointly measurable observables cannot lead to a violation of any Bell inequality--independent of the state and the measurements chosen at the other site. In this Letter we prove the converse: every pair of incompatible quantum observables enables the violation of a Bell inequality and therefore must remain incompatible within any other no-signaling theory. While in the case of von Neumann measurements it is sufficient to use the same pair of observables at both sites, general measurements can require different choices. The main result is obtained by showing that for arbitrary dimension the Clauser-Horne-Shimony-Holt inequality provides the Lagrangian dual of the characterization of joint measurability. This leads to a simple criterion for joint measurability beyond the known qubit case.

Quantum capacities of bosonic channels.

We investigate the capacity of bosonic quantum channels for the transmission of quantum information. We calculate the quantum capacity for a class of Gaussian channels, including channels describing optical fibers with photon losses, by proving that Gaussian encodings are optimal. For arbitrary channels we show that achievable rates can be determined from few measurable parameters by proving that every channel can asymptotically simulate a Gaussian channel which is characterized by second moments of the initial channel. Along the way we provide a complete characterization of degradable Gaussian channels and those arising from teleportation protocols.

PHILIPS. Reconocimiento del habla: acelerando la creación de informes médicos / PHILIPS- Speech recognizement: creating the medical informs accelerator

Las instituciones médicas pueden, con ayuda del reconocimiento del habla, aumentar eficazmente su productividad y reducir sus gastos administrativos. Integrado en los diferentes sistemas de información hospitalarios hace que el proceso de creación del informe sea más rápido, reduciendo el tiempo de espera de médicos y pacientes. Antes de elegir un sistema y para asegurar una implementación sencilla y lo más eficaz posible, hay que tener en cuenta una serie de criterios importantes que harán más fácil la instalación en instituciones con un gran volumen de dictado, diferentes sistemas de TI y distintos tipos de usuarios (AU)

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