Let X be a connected, locally finite graph with symmetric growth. We prove that there is vertex coloring ϕ : → {0, 1} and some R ∈ ℝ such every automorphism f preserving -close to the identity map; this can seen as coarse geometric version of symmetry breaking. also infinite motion conjecture true for graphs where at least one stabilizer S x satisfies following condition: non-identity , sequenc...

We discover novel transitions characterized by distinguishability of bosons in non-unitary dynamics with parity-time ($\mathcal{PT}$) symmetry. show that $\mathcal{PT}$ symmetry breaking, a unique transition non-Hermitian open systems, enhances regions which can be regarded as distinguishable. This means classical computers sample the boson distributions efficiently these sampling distribution ...

Distinguishability theory is developed for quantum interference of the squeezed vacuum states on unitary linear interferometers. It found that entanglement photon pairs over Schmidt modes one sources distinguishability. The distinguishability quantified by symmetric part internal state $n$ photons, whose normalization $q_{2n}$ probability $2n$ photons interfere as indistinguishable. For two $q_...

Typically, quantum superpositions, and thus measurement projections of quantum states involving interference, decrease (or increase) monotonically as a function of increased distinguishability. Distinguishability, in turn, can be a consequence of decoherence, for example caused by the (simultaneous) loss of excitation or due to inadequate mode matching (either deliberate or indeliberate). It is...

The computational problem of distinguishing two quantum channels is central to quantum computing. It is a generalization of the well-known satisfiability problem from classical to quantum computation. This problem is shown to be surprisingly hard: it is complete for the class QIP of problems that have quantum interactive proof systems, which implies that it is hard for the class PSPACE of probl...

Efficient learnability using the state merging algorithm is known for a subclass of probabilistic automata termed μ-distinguishable. In this paper, we prove that state merging algorithms can be extended to efficiently learn a larger class of automata. In particular, we show learnability of a subclass which we call μ2-distinguishable. Using an analog of the Myhill-Nerode theorem for probabilisti...

Information-theoretical quantities such as statistical distinguishability typically result from optimisations over all conceivable observables. Physical theories, however, are not generally considered valid for all mathematically allowed measurements. For instance, quantum field theories are not meant to be correct or even consistent at arbitrarily small lengthscales. A general way of limiting ...