Testing Bell inequalities and probing quantum entanglement at CEPC

Abstract

We study quantum entanglement and test violation of Bell-type inequality at the Circular Electron Positron Collider (CEPC), which is one of the most attractive future collides. It is a promising particle collider designed to search new physics, make Standard Model (SM) precision measurements, and serving as a Higgs factory. Our study is based on a fast simulation of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>Z</a:mi> </a:math> boson pair production from Higgs boson decay at <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msqrt> <c:mi>s</c:mi> </c:msqrt> <c:mo>=</c:mo> <c:mn>250</c:mn> <c:mtext> </c:mtext> <c:mtext> </c:mtext> <c:mi>GeV</c:mi> </c:math> . The detector effects are also included in the simulation. The spin density matrix of the joint <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>Z</e:mi> <e:mi>Z</e:mi> </e:math> system is parametrized using irreducible tensor operators and reconstructed from the spherical coordinates of the decay leptons. To test Bell inequalities, we construct observable quantities for the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>H</g:mi> <g:mo stretchy="false">→</g:mo> <g:mi>Z</g:mi> <g:mi>Z</g:mi> <g:mo>*</g:mo> </g:math> process in CEPC by using the Collins-Gisin-Linden-Massar-Popescu (CGLMP) inequality, whose value is determined from the density matrix of the Z boson pairs. The sensitivity of the Bell inequality violation is observed with more than <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:mrow> <j:mn>1</j:mn> <j:mi>σ</j:mi> </j:mrow> </j:math> and the presence of the quantum entanglement is probed with more than <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:mrow> <l:mn>2</l:mn> <l:mi>σ</l:mi> </l:mrow> </l:math> confidence level.

Topics & Concepts