Related papers: Symmetry from Entanglement Suppression

Symmetry from Entanglement Suppression

URL: http://arxiv.org/abs/2104.10835v2
Date: Wed, 29 Sep 2021 18:58:57 GMT
Title: Symmetry from Entanglement Suppression
Authors: Ian Low and Thomas Mehen
Abstract summary: We show that a minimally entangling $S$-matrix would give rise to global symmetries. For $N_q$ species of qubit, the Identity gate is associated with an $[SU(2)]N_q$ symmetry.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: Symmetry is among the most fundamental and powerful concepts in nature, whose existence is usually taken as given, without explanation. We explore whether symmetry can be derived from more fundamental principles from the perspective of quantum information. Starting with a two-qubit system, we show there are only two minimally entangling logic gates: the Identity and the SWAP, where SWAP interchanges the two states of the qubits. We further demonstrate that, when viewed as an entanglement operator in the spin-space, the $S$-matrix in the two-body scattering of fermions in the $s$-wave channel is uniquely determined by unitarity and rotational invariance to be a linear combination of the Identity and the SWAP. Realizing a minimally entangling $S$-matrix would give rise to global symmetries, as exemplified in Wigner's spin-flavor symmetry and Schr\"odinger's conformal invariance in low energy Quantum Chromodynamics. For $N_q$ species of qubit, the Identity gate is associated with an $[SU(2)]^{N_q}$ symmetry, which is enlarged to $SU(2N_q)$ when there is a species-universal coupling constant.

Related papers

Controlling Symmetries and Quantum Criticality in the Anisotropic Coupled-Top Model [32.553027955412986]
We investigate the anisotropic coupled-top model, which describes the interactions between two large spins along both $x-$ and $y-$directions. We can manipulate the system's symmetry, inducing either discrete $Z$ or continuous U(1) symmetry. The framework provides an ideal platform for experimentally controlling symmetries and investigating associated physical phenomena.
arXiv Detail & Related papers (2025-02-13T15:14:29Z)
Parity symmetry breaking of spin-$j$ coherent state superpositions in Gaussian noise channel [0.0]
Wigner function and Wigner-Yanase skew information are connected through quantum coherence. We analyze parity symmetry and asymmetry in the superposition of two spin coherent states for a spin-$1/2$, as well as for a general spin-$j$.
arXiv Detail & Related papers (2024-12-11T23:48:00Z)
Entanglement asymmetry in the critical XXZ spin chain [0.0]
We study the explicit breaking of a $SU(2)$ symmetry to a $U(1)$ subgroup employing the entanglement asymmetry. We consider as specific model the critical XXZ spin chain, which breaks the $SU(2)$ symmetry of spin rotations except at the isotropic point.
arXiv Detail & Related papers (2024-07-08T22:16:22Z)
Entanglement Suppression, Enhanced Symmetry and a Standard-Model-like Higgs Boson [0.0]
We study information-theoretic properties of scalar models containing two Higgs doublets. We analyze the entanglement power of the S-matrix at the tree-level, in the limit the gauge coupling is turned off.
arXiv Detail & Related papers (2023-07-16T17:35:32Z)
Quantum Current and Holographic Categorical Symmetry [62.07387569558919]
A quantum current is defined as symmetric operators that can transport symmetry charges over an arbitrary long distance. The condition for quantum currents to be superconducting is also specified, which corresponds to condensation of anyons in one higher dimension.
arXiv Detail & Related papers (2023-05-22T11:00:25Z)
Emergence of non-Abelian SU(2) invariance in Abelian frustrated fermionic ladders [37.69303106863453]
We consider a system of interacting spinless fermions on a two-leg triangular ladder with $pi/2$ magnetic flux per triangular plaquette. Microscopically, the system exhibits a U(1) symmetry corresponding to the conservation of total fermionic charge, and a discrete $mathbbZ$ symmetry. At the intersection of the three phases, the system features a critical point with an emergent SU(2) symmetry.
arXiv Detail & Related papers (2023-05-11T15:57:27Z)
Towards Antisymmetric Neural Ansatz Separation [48.80300074254758]
We study separations between two fundamental models of antisymmetric functions, that is, functions $f$ of the form $f(x_sigma(1), ldots, x_sigma(N)) These arise in the context of quantum chemistry, and are the basic modeling tool for wavefunctions of Fermionic systems.
arXiv Detail & Related papers (2022-08-05T16:35:24Z)
The Asymmetric Valence-Bond-Solid States in Quantum Spin Chains: The Difference Between Odd and Even Spins [0.0]
We develop an intuitive diagrammatic explanation of the difference between chains with odd $S$ and even $S$. This is at the heart of the theory of symmetry-protected topological (SPT) phases. It also extends to spin chains with general integer $S$ and provides us with an explanation of the essential difference between models with odd and even spins.
arXiv Detail & Related papers (2022-05-02T04:58:31Z)
$\PT$ Symmetry and Renormalisation in Quantum Field Theory [62.997667081978825]
Quantum systems governed by non-Hermitian Hamiltonians with $PT$ symmetry are special in having real energy eigenvalues bounded below and unitary time evolution. We show how $PT$ symmetry may allow interpretations that evade ghosts and instabilities present in an interpretation of the theory within a Hermitian framework.
arXiv Detail & Related papers (2021-03-27T09:46:36Z)
Fermion and meson mass generation in non-Hermitian Nambu--Jona-Lasinio models [77.34726150561087]
We investigate the effects of non-Hermiticity on interacting fermionic systems. We do this by including non-Hermitian bilinear terms into the 3+1 dimensional Nambu--Jona-Lasinio (NJL) model.
arXiv Detail & Related papers (2021-02-02T13:56:11Z)

This list is automatically generated from the titles and abstracts of the papers in this site.