Related papers: Locality for quantum systems on graphs depends on …
This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…
In this Letter we make progress on a longstanding open problem of Aaronson and Ambainis [Theory of Computing 1, 47 (2005)]: we show that if A is the adjacency matrix of a sufficiently sparse low-dimensional graph then the unitary operator…
Consider a graph whose vertices are populated by identical objects, together with an algorithm for the time-evolution of the number of objects placed at each of the vertices. The discrete dynamics of these objects can be observed and…
We review some recent results that express or rely on the locality properties of the dynamics of quantum spin systems. In particular, we present a slightly sharper version of the recently obtained Lieb-Robinson bound on the group velocity…
A major application of the mathematical concept of graph in quantum mechanics is to model networks of electrical wires or electromagnetic wave-guides. In this paper, we address the dynamics of a particle trapped on such a network in…
A calculational framework is proposed for phylogenetics, using nonlocal quantum field theories in hypercubic geometry. Quadratic terms in the Hamiltonian give the underlying Markov dynamics, while higher degree terms represent branching…
We consider non-local properties of quanternionic quantum mechanics, in which the complex numbers are replaced by the quaternions as the underlying algebra. Specifically, we show that it is possible to construct a non-local box. This allows…
The simulation of complex quantum systems on a quantum computer is studied, taking the kicked Harper model as an example. This well-studied system has a rich variety of dynamical behavior depending on parameters, displays interesting…
Subsystems of entangled quantum systems are not traditionally described in a local way. This paper begins to address the issue by constructing an explicit local hidden variable theory for quantum subsystems. The interpretation is based on a…
We consider the dynamics on a quantum graph as the limit of the dynamics generated by a one-particle Hamiltonian in R^2 with a potential having a deep strict minimum on the graph, when the width of the well shrinks to zero. For a generic…
Having spectral correlations that, over small enough energy scales, are described by random matrix theory is regarded as the most general defining feature of quantum chaotic systems as it applies in the many-body setting and away from any…
Although local Hamiltonians exhibit local time dynamics, this locality is not explicit in the Schr\"{o}dinger picture in the sense that the wavefunction amplitudes do not obey a local equation of motion. We show that geometric locality can…
Preparation of pure states on networks of quantum systems by controlled dissipative dynamics offers important advantages with respect to circuit-based schemes. Unlike in continuous-time scenarios, when discrete-time dynamics are considered,…
Quantum nonlocality is revisited from a novel point of view by studying the problem of an originally classical particle immersed in the stochastic zero-point radiation field (zpf). The entire system is left to evolve until it reaches a…
Electromagnetism is the paradigm case of a theory that satisfies relativistic locality. This can be proven by demonstrating that, once the theory's laws are imposed, what is happening within a region fixes what will happen in the…
Characterizing the quantum complexity of local random quantum circuits is a very deep problem with implications to the seemingly disparate fields of quantum information theory, quantum many-body physics and high energy physics. While our…
The locality issue of quantum mechanics is a key issue to a proper understanding of quantum physics and beyond. What has been commonly emphasized as quantum nonlocality has received an inspiring examination through the notion of Heisenberg…
We consider a graph with a single quantum system at each node. The entire compound system evolves in discrete time steps by iterating a global evolution $U$. We require that this global evolution $U$ be unitary, in accordance with quantum…
We define a class of quantum systems called regular quantum graphs. Although their dynamics is chaotic in the classical limit with positive topological entropy, the spectrum of regular quantum graphs is explicitly computable analytically…
Except for the universe, all quantum systems are open, and according to quantum state diffusion theory, many systems localize to wave packets in the neighborhood of phase space points. This is due to decoherence from the interaction with…