Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order. Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters...

Abstract. Dual Gramian analysis is one of the fundamental tools developed in a series of papers [37, 40, 38, 39, 42] for studying frames. Using dual Gramian analysis, the frame operator can be represented as a family of matrices composed of the Fourier transforms of the generators of (generalized) shiftinvariant systems, which allows us to characterize most properties of frames and tight frames...

We explore constraints on (1+1)$d$ unitary conformal field theory with an internal $\mathbb{Z}_N$ global symmetry, by bounding the lightest symmetry-preserving scalar primary operator using modular bootstrap. Among other we have found, prove existence of a $\mathbb{Z}_N$-symmetric relevant/marginal if $N-1 \le c\le 9-N$ for $N\leq4$, endpoints saturated various WZW models that can be embedded i...

In nuclear physics and elementary particle theory concept of unitary symmetry and the related idea of the hierarchy of interactions play a fundamental role [1, 2]. So the relative smallness of the electromagnetic and weak interactions as compared to the strong interaction of the nucleons in the nucleus can be considered a model of the nucleus in the limit of exact symmetry of the strong interac...

We construct a series of one-dimensional non-unitary dynamics consisting both unitary and imaginary evolutions based on the Sachdev-Ye-Kitaev model. Starting from short-range entangled state, we analyze entanglement using path integral formalism in large $N$ limit. Among all results that obtain, two them are particularly interesting: (1) By varying strength evolution, interacting model exhibits...

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 ...

We show that the units found in torsion-free group rings by Gardam are twisted unitary elements. This justifies some choices Gardam's construction might have appeared arbitrary, and yields more examples of units. note all up to date exhibit non-trivial symmetry.

A bstract We study families of dynamical maps generated from interactions with varying degrees symmetry. For a family time-independent Hamiltonians, we demonstrate the relationship between symmetry, strong-coupling, perfect entanglers, non-Markovian features, and non-time-locality. show that by perturbing initial environment state, effective time-local descriptions can be obtained are non-singu...