TY - JOUR

T1 - Symmetry from entanglement suppression

AU - Low, Ian

AU - Mehen, Thomas

N1 - Funding Information:
U.S. Department of Energy National Center for Theoretical Sciences National Taiwan University National Tsing Hua University
Funding Information:
I. L. is supported in part by the U.S. Department of Energy under Contracts No. DE-AC02-06CH11357 at Argonne and No. DE-SC0010143 at Northwestern. He also acknowledges the hospitalities at the National Center for Theoretical Sciences at National Taiwan University and National Tsing Hua University in Taiwan, where part of this work was performed. T. M. acknowledges enlightening conversations with I. Marvian and Q. Liu. T. M. is supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics under grant Contracts No. DE-FG02-05ER41368 and No. DE-FG02-05ER41367.
Publisher Copyright:
© 2021 Published by the American Physical Society

PY - 2021/10/1

Y1 - 2021/10/1

N2 - 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 , which interchanges the two states of the qubits. We further demonstrate that, when viewed as an entanglement operator in the spin-space, the -matrix in the two-body scattering of fermions in the -wave channel is uniquely determined by unitarity and rotational invariance to be a linear combination of the identity and the . Realizing a minimally entangling -matrix would give rise to global symmetries, as exemplified in Wigner’s spin-flavor symmetry and Schrödinger’s conformal invariance in low energy quantum chromodynamics. For species of qubit, the identity gate is associated with an symmetry, which is enlarged to when there is a species-universal coupling constant.

AB - 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 , which interchanges the two states of the qubits. We further demonstrate that, when viewed as an entanglement operator in the spin-space, the -matrix in the two-body scattering of fermions in the -wave channel is uniquely determined by unitarity and rotational invariance to be a linear combination of the identity and the . Realizing a minimally entangling -matrix would give rise to global symmetries, as exemplified in Wigner’s spin-flavor symmetry and Schrödinger’s conformal invariance in low energy quantum chromodynamics. For species of qubit, the identity gate is associated with an symmetry, which is enlarged to when there is a species-universal coupling constant.

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U2 - 10.1103/PhysRevD.104.074014

DO - 10.1103/PhysRevD.104.074014

M3 - Article

AN - SCOPUS:85117399285

SN - 2470-0010

VL - 104

JO - Physical Review D

JF - Physical Review D

IS - 7

M1 - 074014

ER -