2,389 research outputs found
Topological reversibility and causality in feed-forward networks
Systems whose organization displays causal asymmetry constraints, from
evolutionary trees to river basins or transport networks, can be often
described in terms of directed paths (causal flows) on a discrete state space.
Such a set of paths defines a feed-forward, acyclic network. A key problem
associated with these systems involves characterizing their intrinsic degree of
path reversibility: given an end node in the graph, what is the uncertainty of
recovering the process backwards until the origin? Here we propose a novel
concept, \textit{topological reversibility}, which rigorously weigths such
uncertainty in path dependency quantified as the minimum amount of information
required to successfully revert a causal path. Within the proposed framework we
also analytically characterize limit cases for both topologically reversible
and maximally entropic structures. The relevance of these measures within the
context of evolutionary dynamics is highlighted.Comment: 9 pages, 3 figure
Local reversibility and entanglement structure of many-body ground states
The low-temperature physics of quantum many-body systems is largely governed
by the structure of their ground states. Minimizing the energy of local
interactions, ground states often reflect strong properties of locality such as
the area law for entanglement entropy and the exponential decay of correlations
between spatially separated observables. In this letter we present a novel
characterization of locality in quantum states, which we call `local
reversibility'. It characterizes the type of operations that are needed to
reverse the action of a general disturbance on the state. We prove that unique
ground states of gapped local Hamiltonian are locally reversible. This way, we
identify new fundamental features of many-body ground states, which cannot be
derived from the aforementioned properties. We use local reversibility to
distinguish between states enjoying microscopic and macroscopic quantum
phenomena. To demonstrate the potential of our approach, we prove specific
properties of ground states, which are relevant both to critical and
non-critical theories.Comment: 12 revtex pages, 2 pdf figs; minor changes, typos corrected. To be
published in Quantum Science and Technolog
- …